diff --git "a/minimize_length_of_array_using_operations/haskell_tests/Main.hs" "b/minimize_length_of_array_using_operations/haskell_tests/Main.hs" new file mode 100644--- /dev/null +++ "b/minimize_length_of_array_using_operations/haskell_tests/Main.hs" @@ -0,0 +1,44 @@ + +module Main where +import Test.HUnit + +--Program start +minimumArrayLength :: [Int] -> Int +minimumArrayLength nums = undefined + +--Program end + +-- Test cases + +test1 :: Test +test1 = TestCase (assertEqual "for (minimumArrayLength [1,4,3,1])," 1 (minimumArrayLength [1,4,3,1])) + +test2 :: Test +test2 = TestCase (assertEqual "for (minimumArrayLength [5,5,5,10,5])," 2 (minimumArrayLength [5,5,5,10,5])) + +test3 :: Test +test3 = TestCase (assertEqual "for (minimumArrayLength [2,3,4])," 1 (minimumArrayLength [2,3,4])) + +test4 :: Test +test4 = TestCase (assertEqual "for (minimumArrayLength [7, 5, 3, 2, 4])," 1 (minimumArrayLength [7, 5, 3, 2, 4])) + +test5 :: Test +test5 = TestCase (assertEqual "for (minimumArrayLength [65, 7, 5, 67, 75, 39, 34, 13, 48, 65])," 1 (minimumArrayLength [65, 7, 5, 67, 75, 39, 34, 13, 48, 65])) + +test6 :: Test +test6 = TestCase (assertEqual "for (minimumArrayLength [895, 535, 66, 348, 458, 823, 698, 558, 55, 155, 340, 252, 115, 433, 59, 14, 610, 890, 533, 305, 356, 823, 380, 965, 881, 252, 489, 852, 562, 171, 990, 976, 28, 82, 820, 192, 275, 618, 79, 752, 504, 720, 519, 115, 507, 255, 298, 86, 108, 417, 437, 935, 371, 704, 962, 333, 487, 478, 640, 203, 94, 709, 269, 173, 375, 538, 488, 101, 986, 899, 58, 543, 167, 701, 212, 226, 671, 562, 728, 969, 733, 647, 825, 117, 968, 364, 434, 161, 311, 623, 615, 717, 482, 945, 313, 134, 520, 390, 499, 756, 614, 454, 987, 129, 155, 523, 544, 935, 130, 885, 89, 338, 423, 950, 933, 949, 40, 644, 769, 272, 236, 873, 337, 211, 349, 930, 253, 499, 788, 843, 632, 330, 257, 333, 47, 843, 914, 490, 939, 721, 733, 44, 898, 192, 528, 306, 260, 358, 95, 424, 804, 496, 973, 322, 391, 664, 257, 147, 684, 389, 803, 326, 15, 697, 140, 105, 929, 316, 310, 56, 726, 583, 954, 388, 452, 416, 446, 112, 200, 134, 495, 232, 361, 915, 538, 199, 853, 771, 562, 868, 342, 936, 276, 770, 120, 108, 28, 474, 903, 772, 962, 728, 340, 928, 671, 889, 13, 263, 589, 916, 476, 501, 310, 501, 879, 538, 806, 864, 769, 409, 838, 198, 81, 755, 166, 476, 824, 461, 182, 231, 171, 669, 643, 689, 513, 745, 357, 217, 784, 583, 195, 810, 42, 133, 645, 28, 334, 245, 155, 27, 352, 139, 982, 943, 211, 217, 775, 182, 924, 443, 984, 265, 96, 24, 668, 987, 77, 825, 685, 705, 209, 132, 20, 891, 50, 498, 383, 473, 917, 151, 177, 451, 692, 725, 393, 666, 771, 215, 862, 451, 11, 998, 158, 714, 467, 918, 771, 340, 359, 838, 889, 253, 534, 263, 38, 323, 717, 331, 125, 182, 656, 155, 668, 505, 91, 341, 157, 393, 234, 343, 296, 970, 608, 521, 111, 310, 606, 908, 208, 660, 477, 596, 202, 821, 250, 469, 593, 753, 320, 806, 503, 892, 471, 148, 253, 146, 634, 165, 555, 103, 268, 570, 531, 1000, 158, 846, 856, 852, 596, 710, 922, 202, 313, 24, 276, 493, 617, 337, 631, 867, 66, 131, 254, 262, 543, 676, 846, 50, 499, 504, 502, 536, 110, 500, 11, 428, 810, 237, 702, 926, 143, 5, 547, 625, 599, 681, 960, 627, 282, 273, 835, 932, 538, 691, 366, 336, 849, 505, 399, 693, 480, 652, 303, 847, 104, 662, 96, 696, 986, 977, 831, 164, 57, 236, 471, 542, 629, 519, 351, 316, 228, 380, 418, 375, 973, 707, 970, 168, 467, 262, 737, 681, 723, 514, 403, 298, 265, 155, 794, 220, 809, 737, 457, 990, 420, 917, 488, 685, 302, 222, 993, 792, 26, 800, 577, 840, 258, 213, 406, 21, 32, 101, 844, 798, 916, 400, 130, 710, 700, 302, 171, 379, 595, 118, 237, 21, 734, 27, 980, 753, 688, 191, 476, 234, 128, 718, 317, 465, 755, 751, 159, 869, 202, 489, 78, 867, 303, 775, 886, 711, 204, 716, 138, 615, 819, 478, 622, 801, 474, 632, 681, 319, 183, 212, 725, 65, 948, 563, 556, 232, 445, 993, 126, 464, 317, 450, 160, 699, 560, 280, 688, 178, 303, 166, 358, 94, 751, 891, 261, 805, 648, 552, 428, 826, 745, 387, 957, 411, 776, 40, 398, 430, 835, 195, 14, 988, 630, 204, 789, 590, 809, 978, 322, 975, 436, 983, 356, 895, 725, 911, 107, 724, 226, 943, 788, 429, 741, 240, 809, 325, 796, 251, 380, 395, 949, 277, 931, 121, 301, 633, 977, 608, 81, 46, 838, 807, 436, 202, 273, 853, 369, 735, 692, 111, 804, 43, 802, 838, 287, 51, 221, 603, 92, 361, 763, 177, 883, 827, 370, 242, 841, 317, 638, 725, 610, 357, 965, 677, 27, 607, 909, 117, 405, 246, 747, 624, 168, 159, 425, 111, 704, 473, 52, 402, 85, 914, 123, 21, 139, 47, 904, 286, 108, 713, 304, 47, 655, 474, 378, 319, 821, 62, 400, 894, 668, 823, 601, 403, 236, 474, 873, 282, 982, 807, 808, 530, 740, 268, 886, 623, 261, 673, 775, 543, 581, 989, 623, 513, 779, 352, 316, 934, 496, 764, 902, 103, 675, 67, 572, 488, 314, 194, 821, 437, 74, 989, 937, 859, 576, 114, 925, 87, 230, 778, 869, 839, 635, 106, 846, 845, 316, 857, 207, 389, 568, 432, 86, 380, 460, 800, 497, 191, 830, 401, 490, 816, 967, 595, 397, 557, 943, 858, 581])," 1 (minimumArrayLength [895, 535, 66, 348, 458, 823, 698, 558, 55, 155, 340, 252, 115, 433, 59, 14, 610, 890, 533, 305, 356, 823, 380, 965, 881, 252, 489, 852, 562, 171, 990, 976, 28, 82, 820, 192, 275, 618, 79, 752, 504, 720, 519, 115, 507, 255, 298, 86, 108, 417, 437, 935, 371, 704, 962, 333, 487, 478, 640, 203, 94, 709, 269, 173, 375, 538, 488, 101, 986, 899, 58, 543, 167, 701, 212, 226, 671, 562, 728, 969, 733, 647, 825, 117, 968, 364, 434, 161, 311, 623, 615, 717, 482, 945, 313, 134, 520, 390, 499, 756, 614, 454, 987, 129, 155, 523, 544, 935, 130, 885, 89, 338, 423, 950, 933, 949, 40, 644, 769, 272, 236, 873, 337, 211, 349, 930, 253, 499, 788, 843, 632, 330, 257, 333, 47, 843, 914, 490, 939, 721, 733, 44, 898, 192, 528, 306, 260, 358, 95, 424, 804, 496, 973, 322, 391, 664, 257, 147, 684, 389, 803, 326, 15, 697, 140, 105, 929, 316, 310, 56, 726, 583, 954, 388, 452, 416, 446, 112, 200, 134, 495, 232, 361, 915, 538, 199, 853, 771, 562, 868, 342, 936, 276, 770, 120, 108, 28, 474, 903, 772, 962, 728, 340, 928, 671, 889, 13, 263, 589, 916, 476, 501, 310, 501, 879, 538, 806, 864, 769, 409, 838, 198, 81, 755, 166, 476, 824, 461, 182, 231, 171, 669, 643, 689, 513, 745, 357, 217, 784, 583, 195, 810, 42, 133, 645, 28, 334, 245, 155, 27, 352, 139, 982, 943, 211, 217, 775, 182, 924, 443, 984, 265, 96, 24, 668, 987, 77, 825, 685, 705, 209, 132, 20, 891, 50, 498, 383, 473, 917, 151, 177, 451, 692, 725, 393, 666, 771, 215, 862, 451, 11, 998, 158, 714, 467, 918, 771, 340, 359, 838, 889, 253, 534, 263, 38, 323, 717, 331, 125, 182, 656, 155, 668, 505, 91, 341, 157, 393, 234, 343, 296, 970, 608, 521, 111, 310, 606, 908, 208, 660, 477, 596, 202, 821, 250, 469, 593, 753, 320, 806, 503, 892, 471, 148, 253, 146, 634, 165, 555, 103, 268, 570, 531, 1000, 158, 846, 856, 852, 596, 710, 922, 202, 313, 24, 276, 493, 617, 337, 631, 867, 66, 131, 254, 262, 543, 676, 846, 50, 499, 504, 502, 536, 110, 500, 11, 428, 810, 237, 702, 926, 143, 5, 547, 625, 599, 681, 960, 627, 282, 273, 835, 932, 538, 691, 366, 336, 849, 505, 399, 693, 480, 652, 303, 847, 104, 662, 96, 696, 986, 977, 831, 164, 57, 236, 471, 542, 629, 519, 351, 316, 228, 380, 418, 375, 973, 707, 970, 168, 467, 262, 737, 681, 723, 514, 403, 298, 265, 155, 794, 220, 809, 737, 457, 990, 420, 917, 488, 685, 302, 222, 993, 792, 26, 800, 577, 840, 258, 213, 406, 21, 32, 101, 844, 798, 916, 400, 130, 710, 700, 302, 171, 379, 595, 118, 237, 21, 734, 27, 980, 753, 688, 191, 476, 234, 128, 718, 317, 465, 755, 751, 159, 869, 202, 489, 78, 867, 303, 775, 886, 711, 204, 716, 138, 615, 819, 478, 622, 801, 474, 632, 681, 319, 183, 212, 725, 65, 948, 563, 556, 232, 445, 993, 126, 464, 317, 450, 160, 699, 560, 280, 688, 178, 303, 166, 358, 94, 751, 891, 261, 805, 648, 552, 428, 826, 745, 387, 957, 411, 776, 40, 398, 430, 835, 195, 14, 988, 630, 204, 789, 590, 809, 978, 322, 975, 436, 983, 356, 895, 725, 911, 107, 724, 226, 943, 788, 429, 741, 240, 809, 325, 796, 251, 380, 395, 949, 277, 931, 121, 301, 633, 977, 608, 81, 46, 838, 807, 436, 202, 273, 853, 369, 735, 692, 111, 804, 43, 802, 838, 287, 51, 221, 603, 92, 361, 763, 177, 883, 827, 370, 242, 841, 317, 638, 725, 610, 357, 965, 677, 27, 607, 909, 117, 405, 246, 747, 624, 168, 159, 425, 111, 704, 473, 52, 402, 85, 914, 123, 21, 139, 47, 904, 286, 108, 713, 304, 47, 655, 474, 378, 319, 821, 62, 400, 894, 668, 823, 601, 403, 236, 474, 873, 282, 982, 807, 808, 530, 740, 268, 886, 623, 261, 673, 775, 543, 581, 989, 623, 513, 779, 352, 316, 934, 496, 764, 902, 103, 675, 67, 572, 488, 314, 194, 821, 437, 74, 989, 937, 859, 576, 114, 925, 87, 230, 778, 869, 839, 635, 106, 846, 845, 316, 857, 207, 389, 568, 432, 86, 380, 460, 800, 497, 191, 830, 401, 490, 816, 967, 595, 397, 557, 943, 858, 581])) + +test7 :: Test +test7 = TestCase (assertEqual "for (minimumArrayLength [3721, 332, 7193, 3646, 7062, 4704, 6262, 4369, 8052, 3640, 8655, 9043, 7741, 2130, 6761, 2336, 8367, 3725, 8659, 9759, 7038, 9190, 2703, 2665, 9834, 2287, 4351, 4548, 7896, 4637, 1349, 4258, 3135, 8522, 5425, 5142, 7611, 2352, 253, 1118, 6364, 3002, 7801, 9328, 9234, 3367, 5276, 7319, 8683, 3484, 3970, 6919, 2176, 2471, 364, 1819, 4556, 3441, 4405, 5333, 9121, 9598, 7396, 3891, 3406, 6566, 3247, 1505, 6232, 6880, 51, 5129, 223, 1246, 9562, 3930, 1017, 2742, 2720, 4777, 2904, 9647, 9935, 5929, 7279, 5719, 3017, 3390, 1813, 6660, 5491, 1691, 7873, 5277, 2819, 8786, 1767, 5346, 5858, 3338, 8626, 2655, 6228, 8895, 1675, 1206, 5951, 3707, 2932, 7322, 5885, 3241, 5449, 8221, 1581, 4373, 8269, 5770, 8894, 8837, 4469, 5096, 3382, 6760, 6343, 5279, 9948, 2372, 8375, 2186, 1755, 2450, 1478, 9408, 2390, 3334, 8800, 1245, 8366, 9040, 5554, 6115, 6953, 7472, 6612, 1244, 2363, 5153, 301, 9310, 7481, 4678, 432, 115, 5752, 5208, 2822, 5789, 7237, 1747, 9259, 93, 2411, 1715, 9117, 8548, 394, 2942, 534, 2198, 7050, 1824, 4490, 8519, 8164, 464, 8455, 6350, 295, 2861, 9809, 3255, 9852, 1021, 1473, 7377, 4613, 4154, 3717, 5558, 4647, 1693, 2714, 4889, 7559, 5775, 8978, 3702, 5053, 1672, 1938, 7194, 9886, 9711, 2970, 6434, 6504, 191, 5522, 8708, 1000, 7974, 1979, 6675, 5010, 3977, 8214, 4879, 8065, 6687, 9502, 1105, 6808, 6555, 9537, 7782, 3283, 5950, 7207, 5616, 933, 514, 2252, 7454, 5292, 2966, 8707, 2708, 2088, 3167, 5780, 1747, 7271, 8556, 2156, 7239, 2373, 7927, 3431, 3570, 1150, 3465, 7850, 6456, 1145, 957, 2814, 5372, 5526, 309, 8786, 5734, 3298, 6424, 7418, 5994, 2004, 267, 7733, 5212, 4763, 1736, 1815, 8736, 932, 2902, 8421, 5918, 6992, 8636, 9402, 1567, 3372, 5128, 6580, 4384, 7039, 8428, 5260, 4923, 6958, 5491, 5420, 9382, 2853, 6080, 5015, 1897, 7617, 2234, 3158, 1411, 1924, 9699, 9016, 7707, 6567, 5850, 5186, 5709, 1951, 9878, 7080, 5069, 9383, 3971, 3457, 4332, 3645, 1801, 1836, 9526, 3869, 4335, 420, 5348, 8939, 5893, 6172, 6144, 3072, 1704, 4080, 3844, 2178, 7107, 1623, 4292, 1472, 377, 3296, 8048, 3477, 608, 8251, 1846, 4063, 7261, 2319, 6773, 9877, 5562, 5058, 1532, 5628, 9269, 5996, 1361, 8730, 8, 66, 6079, 4460, 3008, 4334, 2242, 9717, 5635, 5921, 1844, 8586, 499, 4982, 622, 3498, 7012, 365, 8242, 2363, 2586, 6650, 1514, 5177, 8146, 9185, 6838, 126, 760, 9382, 6060, 6819, 7205, 8866, 2591, 286, 6712, 1940, 8353, 807, 5656, 7107, 1872, 5451, 9888, 6050, 3907, 909, 8982, 5615, 9370, 6478, 2629, 754, 4789, 618, 6971, 7444, 2599, 3186, 1248, 8325, 5565, 9178, 1336, 3693, 8517, 2727, 1307, 8797, 6481, 5743, 5184, 630, 5311, 4660, 8900, 4322, 1930, 511, 2291, 9566, 8741, 5014, 1417, 1004, 5344, 1118, 9417, 825, 5392, 6059, 4736, 5726, 4647, 9453, 202, 105, 5259, 2146, 8072, 4694, 7243, 8684, 1649, 6915, 5043, 8233, 7728, 3118, 3439, 4844, 5415, 2809, 8213, 4424, 7937, 6095, 3637, 6873, 6479, 8539, 5845, 3051, 617, 3049, 8682, 6335, 3730, 3129, 4138, 5471, 3919, 2510, 3096, 4506, 8595, 3513, 8470, 6369, 9767, 4598, 7650, 9641, 3410, 5166, 8832, 9871, 9705, 9675, 3326, 3087, 1587, 6812, 7939, 5261, 4668, 8735, 4866, 3743, 6946, 2818, 5167, 485, 8669, 146, 9370, 5011, 4708, 7570, 4736, 1314, 6901, 3969, 6798, 9984, 6882, 1793, 5047, 8077, 7969, 7228, 2764, 9659, 667, 7663, 3722, 489, 7990, 1659, 4181, 7494, 7328, 7043, 2686, 750, 1984, 3029, 8772, 5824, 6213, 4841, 4515, 974, 1629, 468, 6518, 1133, 493, 5945, 6211, 2513, 723, 902, 766, 8731, 1987, 8304, 787, 923, 9677, 2607, 2293, 2282, 2596, 1689, 6330, 4214, 9232, 5042, 5525, 2814, 7519, 5598, 8311, 8786, 6205, 9382, 194, 460, 2080, 9092, 9637, 5700, 7583, 3341, 1437, 3303, 8197, 3853, 3693, 7972, 3146, 6784, 9291, 6781, 4443, 3731, 251, 4630, 8826, 3969, 6734, 9650, 9523, 341, 8727, 8115, 9376, 1069, 8542, 163, 5898, 4403, 4569, 5810, 7859, 5892, 8359, 1049, 728, 6797, 2899, 3453, 9771, 2675, 236, 96, 6938, 476, 1531, 9529, 8649, 1206, 5497, 1259, 1151, 6588, 2319, 124, 1680, 6883, 1954, 5494, 4528, 5748, 6323, 5008, 6390, 5290, 1510, 1717, 1253, 1232, 5236, 1213, 8187, 336, 6543, 7564, 2179, 2515, 4802, 6943, 1119, 1288, 7695, 5469, 1118, 3013, 8453, 8659, 3887, 6094, 9437, 2841, 7975, 9693, 6032, 2456, 8563, 6777, 7878, 2520, 8619, 8141, 9689, 5346, 7104, 6452, 569, 1359, 8133, 8374, 9874, 262, 3001, 7337, 2445, 3975, 6833, 6684, 3316, 4359, 2612, 5668, 2961, 3731, 9916, 273, 7389, 1187, 7273, 5754, 4770, 5738, 395, 8794, 2276, 9944, 2270, 676, 4132, 9022, 8505, 5154, 9033, 8402, 5814, 9732, 8794, 5647, 8243, 9204, 2965, 6294, 9588, 2398, 8154, 4278, 6886, 2704, 6124, 6207, 8773, 3867, 6317, 4934, 5202, 1734, 8007, 3011, 4321, 2631, 6594, 2139, 2461, 6001, 9897, 4999, 1542, 7945, 8305, 2752, 6584, 4169, 9190, 5899, 3086, 7877, 9164, 1287, 5016, 1750, 437, 1787, 1429, 1420, 2075, 3000, 3348, 4818, 6608, 4769, 5358, 3544, 6196, 1064, 5019, 9432, 1110, 9171, 6244, 4872, 2861, 2324, 4377, 9491, 8306, 4394, 7267, 1845, 8243, 6938, 4226, 2359, 8881, 1702, 9721, 7838, 5960, 9778, 9590, 5613, 8523, 8062, 9206, 3977, 8718, 6825, 3625, 7399, 5480, 5803, 763, 7941, 4721, 252, 7553, 8254, 1993, 3895, 6747, 7615, 8965, 2657, 7608, 930, 3174, 5835, 9638, 7756, 9776, 976, 2373, 8791, 8781, 8386, 6635, 6356, 6373, 4876, 5659, 7156, 1092, 109, 6155, 9983, 285, 8930, 6971, 125, 2225, 3290, 7793, 923, 150, 1973, 7022, 9586, 3811, 719, 2411, 4354, 3175, 6119, 741, 4896, 4861, 393, 5286, 1375, 5437, 4308, 6448, 3951, 2968, 1104, 9060, 4180, 1490, 9561, 8658, 3197, 6082, 2315, 6076, 9157, 8856, 2488, 9746, 4206, 6865, 9401, 6188, 9111, 9973, 9653, 2706, 3958, 2378, 7155, 260, 9037, 2918, 8491, 393, 8107, 4767, 5090, 8214, 1082, 894, 5579, 457, 1464, 1552, 5568, 6732, 7003, 5075, 482, 9829, 1350, 4768, 3028, 1171, 7996, 5826, 8876, 9053, 3168, 8400, 2056, 2477, 9011, 1540, 19, 14, 5453, 2815, 4677, 9865, 7732, 9566, 302, 5336, 3328, 1358, 4149, 9716, 3951, 7201, 4159, 9985, 6329, 2825, 9731, 3936, 8950, 524, 6386, 3385, 282, 3358, 4444, 5189, 2386, 8722, 5135, 5045, 7141, 1090, 7215, 6310, 4567, 4418, 6466, 5915, 193, 3929, 9539, 342, 4469, 3052, 6143, 6283, 505, 9588, 4842, 7092, 2004, 2152, 7113, 2640, 6931, 4863, 9392, 8803, 9973, 1468, 4850, 3503, 1658, 6624, 5108, 4022, 197, 8813, 554, 1478, 4805, 3075, 306, 2252, 8329, 5763, 3884, 8741, 8103, 5769, 2892, 9377, 4536, 9897, 6077, 7054, 8102, 2608, 4140, 1024, 7834, 1872, 5052, 1863, 1828, 5404, 6285, 9544, 9888, 3912, 6200, 9738, 2660, 901, 1819, 5303, 2996, 9001, 6512, 5677, 9543, 6710, 6412, 108, 883, 4513, 7924, 6217, 9756, 9326, 1468, 6029, 7301, 2249, 5735, 5326, 8580, 8977, 6915, 6958, 8916, 7886, 519, 8575, 9038, 6532, 7248, 2084, 6304, 3377, 1195, 8028, 5414, 7894, 6078, 5396, 1935, 5176, 6877, 5086, 6993, 2384, 1604, 8876, 8735, 6111, 520, 982, 2135, 1152, 8781, 5708, 340, 2932, 8997, 7344, 247, 7230, 6726, 1282, 944, 9779, 8296, 2891, 5099, 9886, 7444, 6524, 4252, 6554, 4921, 6166, 9553, 1152, 9222, 4524, 6269, 6464, 8865, 7901, 6576, 9052, 6389, 8946, 1593, 141, 5613, 7925, 9559, 9332, 8988, 8768, 7381, 3521, 9786, 339, 9916, 3333, 4264, 3718, 4753, 4055, 5044, 7316, 9595, 6589, 8475, 8728, 7716, 6854, 2539, 8709, 3524, 1977, 7492, 2620, 1459, 9093, 338, 762, 9741, 3949, 2358, 4190, 7149, 9571, 5277, 9835, 8973, 3676, 277, 6973, 2911, 6544, 837, 862, 7298, 5643, 381, 4033, 9329, 2996, 8166, 9608, 9058, 4693, 6674, 2448, 2650, 4745, 1501, 5370, 4655, 5971, 9290, 8580, 8563, 9010, 3892, 298, 574, 4432, 2284, 6415, 9843, 5561, 6200, 1164, 9929, 8966, 1970, 6663, 7675, 7986, 6792, 9175, 9495, 7993, 3750, 4801, 7616, 1269, 6816, 6299, 7660, 5958, 7223, 9542, 5790, 6152, 9240, 2071, 5006, 927, 7770, 9347, 4413, 7411, 5426, 8080, 7729, 2998, 75, 2917, 1780, 1763, 698, 10000, 8732, 4983, 5151, 9444, 2178, 8840, 6902, 1538, 6951, 450, 4752, 7337, 5671, 7525, 5031, 3191, 6999, 125, 7105, 872, 2519, 4698, 9439, 4570, 1271, 6723, 1525, 2480, 3910, 1331, 625, 600, 4434, 356, 7389, 870, 3889, 3350, 4182, 7067, 3409, 3081, 2210, 1603, 4144, 3760, 447, 8299, 6251, 9903, 6004, 10, 1586, 3682, 3794, 9485, 1475, 5308, 7112, 967, 2182, 8668, 8671, 810, 5701, 1731, 9667, 846, 7312, 3233, 2214, 6784, 861, 8418, 1684, 3359, 6608, 8465, 5989, 1699, 2183, 2605, 3324, 2733, 3690, 4805, 203, 4051, 1303, 9837, 4548, 7659, 8080, 9333, 853, 829, 9318, 5018, 2514, 2322, 2775, 5372, 2897, 2840, 2576, 9722, 6676, 5899, 6679, 5732, 219, 8009, 5205, 2908, 4376, 397, 5137, 7040, 9309, 3166, 908, 5192, 6125, 7310, 6928, 3898, 4442, 8332, 9566, 3915, 6232, 249, 9090, 3960, 6598, 3395, 2831, 6537, 2306, 1096, 2987, 4624, 5285, 8120, 7589, 3790, 7118, 4137, 3590, 5840, 7992, 9697, 3978, 7172, 9008, 6239, 2145, 7471, 3456, 4260, 7774, 153, 1066, 4669, 4557, 5417, 6358, 9328, 8437, 9411, 580, 4703, 2569, 7150, 4298, 3065, 1020, 6967, 3675, 7824, 477, 3183, 7893, 5729, 3296, 7217, 612, 4040, 7470, 4099, 604, 8404, 9413, 1134, 640, 4765, 536, 8798, 3067, 1802, 4394, 9446, 5233, 897, 4650, 5063, 3699, 251, 4331, 4976, 4400, 9903, 1086, 6596, 788, 6506, 4738, 6373, 9371, 3289, 929, 9111, 3092, 9186, 5638, 9107, 3174, 1823, 9341, 8930, 500, 6486, 1525, 557, 137, 4594, 8385, 4157, 3401, 754, 7404, 1599, 946, 1916, 1587, 5803, 208, 1079, 7575, 7290, 1434, 7826, 855, 7741, 304, 5227, 1018, 6616, 7747, 2689, 5008, 2422, 2496, 3470, 1565, 7100, 2811, 3668, 7890, 6808, 5787, 9289, 9815, 8587, 1645, 7115, 9435, 427, 4347, 4884, 9136, 9318, 6393, 8758, 3247, 3960, 982, 1383, 5755, 3727, 1, 3331, 3088, 5273, 4428, 627, 9132, 9563, 1078, 9478, 9902, 5764, 8683, 1085, 2758, 8396, 5663, 2154, 9123, 7296, 8583, 1959, 2127, 2004, 3921, 4319, 252, 5500, 2472, 4021, 8850, 4299, 6168, 2731, 1304, 8284, 6351, 2712, 6632, 2599, 466, 1003, 8559, 143, 3528, 386, 661, 5498, 3392, 2419, 4420, 5253, 3667, 6928, 2360, 4206, 7384, 771, 4143, 3589, 2240, 5873, 5017, 7792, 7683, 6881, 2330, 4580, 7802, 912, 8133, 7915, 8036, 3316, 323, 5553, 1529, 9855, 3980, 3597, 2469, 4639, 8585, 3713, 3770, 8918, 7185, 1646, 7889, 3324, 7526, 4476, 5879, 6928, 1243, 1478, 111, 5164, 1157, 9757, 6978, 8091, 454, 3352, 4773, 4590, 5616, 8882, 5794, 5337, 9573, 6223, 8857, 4682, 5390, 1701, 1684, 8675, 1831, 371, 7233, 9294, 6008, 6798, 6359, 6540, 5582, 2497, 8265, 5191, 6903, 8513, 5822, 3598, 2119, 5222, 6948, 9055, 394, 2766, 488, 3824, 3803, 2690, 6420, 4900, 7112, 61, 5532, 2799, 793, 9910, 5242, 5379, 120, 4262, 8476, 8583, 3391, 1481, 6846, 2132, 7145, 410, 5865, 3867, 5256, 5980, 2779, 5859, 9212, 8305, 6303, 1584, 6215, 1921, 3334, 1410, 3571, 3973, 2625, 9722, 8825, 6395, 6707, 2228, 129, 3661, 7828, 6358, 4241, 138, 7928, 6052, 5748, 3227, 8258, 9879, 129, 50, 2904, 9322, 2180, 8871, 6130, 7418, 302, 1013, 4598, 7300, 5583, 9619, 7828, 8601, 4270, 7749, 2870, 6989, 470, 1638, 4364, 1138, 4054, 6437, 5272, 1478, 1918, 8037, 9626, 7930, 3911, 5175, 4375, 956, 3377, 4799, 6499, 6618, 9463, 2053, 5148, 9576, 586, 5658, 866, 8961, 9101, 3081, 9750, 1696, 7282, 458, 1257, 1662, 8897, 6026, 6612, 3754, 4875, 8067, 8615, 9788, 1268, 340, 7023, 464, 1294, 6797, 4727, 234, 5419, 9082, 5148, 4703, 8746, 202, 7567, 7254, 2636, 2688, 3356, 6189, 9681, 6326, 1556, 6099, 5250, 2288, 8370, 6661, 5858, 2637, 6267, 8909, 9215, 8779, 7811, 4877, 1707, 2448, 1807, 5253, 3154, 112, 7732, 5260, 682, 5468, 2701, 2057, 3990, 2736, 8600, 2051, 4385, 7381, 322, 458, 7543, 2874, 9258, 9714, 3521, 5630, 2772, 8391, 9408, 1442, 8118, 9687, 7660, 9034, 341, 5762, 2999, 2304, 9307, 6002, 2522, 7315, 7180, 9665, 1884, 958, 6800, 7069, 1319, 9129, 5381, 9697, 6921, 2582, 1676, 7914, 8195, 566, 521, 2116, 6170, 7809, 490, 6706, 1188, 7364, 3247, 6804, 1916, 1953, 8733, 4514, 1881, 9707, 9646, 4352, 1155, 3517, 8850, 185, 4711, 7695, 4149, 5301, 5534, 8126, 6360, 8742, 5470, 1825, 9918, 9474, 6000, 8089, 1355, 703, 5103, 1990, 8645, 2550, 189, 3176, 2399, 9063, 3169, 5427, 2384, 6262, 8250, 5836, 9967, 7995, 1649, 4535, 7935, 1177, 5286, 7953, 9724, 9825, 3551, 4508, 4809, 7929, 6303, 5140, 5799, 629, 5555, 4695, 2755, 8995, 7564, 3552, 15, 4328, 9622, 4632, 5724, 7013, 2531, 1923, 8124, 6599, 8368, 6911, 4337, 4139, 8649, 7713, 5759, 5388, 1180, 3176, 8501, 8967, 9976, 7837, 9493, 4086, 3320, 6476, 4387, 3405, 7894, 4042, 1554, 4113, 65, 9729, 8176, 8375, 1995, 7424, 3501, 6725, 8342, 6895, 4961, 927, 8701, 191, 5831, 6931, 7083, 7096, 2145, 3570, 5577, 871, 1528, 244, 6471, 176, 8435, 7059, 4403, 8856, 2764, 579, 1388, 914, 8917, 1393, 9529, 9926, 8043, 7298, 9687, 5436, 4667, 8135, 4862, 8875, 6046, 8435, 571, 2963, 565, 3812, 6529, 1703, 5003, 534, 7944, 9259, 496, 4969, 5249, 5595, 5359, 2977, 3516, 207, 5627, 4143, 5392, 8882, 1777, 8348, 6142, 1523, 1120, 5819, 69, 3032, 2422, 3979, 1842, 9344, 778, 4268, 7845, 4280, 2946, 8941, 6754, 6557, 8961, 922, 8467, 2235, 1304, 5556, 4379, 6895, 8320, 5217, 990, 6016, 7337, 5286, 4935, 5542, 7254, 6464, 7681, 6999, 2537, 1451, 4282, 3035, 5273, 3967, 8408, 5139, 8346, 8043, 2983, 7484, 8533, 4805, 7525, 8488, 9417, 1167, 3798, 4939, 7410, 1541, 2966, 7258, 129, 5014, 7043, 7840, 8139, 6036, 6365, 8424, 829, 4841, 4714, 5319, 788, 8301, 1113, 103, 6596, 4419, 4052, 8545, 6839, 7020, 6766, 9980, 5979, 830, 8428, 1619, 7968, 3483, 3103, 9190, 4978, 9351, 579, 1652, 6434, 7781, 1177, 7105, 3978, 9763, 670, 6458, 3381, 8100, 2996, 2577, 9350, 4396, 3027, 1392, 5534, 3420, 9200, 4341, 9051, 4456, 3648, 9639, 6415, 7202, 494, 5079, 1198, 5491, 9625, 6680, 1052, 1665, 5750, 4694, 388, 6822, 5751, 1757, 9133, 3684, 4055, 2295, 5464, 1654, 2219, 2433, 3800, 3259, 7862, 5401, 2201, 9681, 2742, 4274, 3933, 352, 5944, 6303, 4062, 6558, 6860, 4525, 9947, 937, 1635, 768, 8909, 446, 4457, 8170, 7048, 5402, 990, 2303, 6793, 1832, 3814, 8663, 5681, 7377, 9541, 7831, 2247, 9580, 6190, 9703, 3107, 5020, 6437, 6421, 4330, 6449, 1272, 9807, 8809, 6494, 2395, 825, 4164, 3680, 1488, 1275, 3286, 6288, 4435, 2347, 8339, 9795, 3288, 7776, 4535, 5434, 2242, 4022, 6199, 8953, 5618, 6640, 3376, 7643, 3696, 1829, 198, 9387, 3508, 6657, 8477, 5807, 6870, 3692, 1436, 8683, 3584, 9458, 8559, 5876, 5250, 2700, 6841, 6676, 3022, 1650, 9241, 880, 1835, 1147, 7019, 9467, 9186, 3857, 3693, 5005, 8845, 4840, 4095, 2781, 4294, 2420, 8609, 9249, 1770, 7628, 2156, 7620, 399, 7706, 5142, 1997, 4931, 5170, 1686, 2166, 7092, 6707, 3381, 4836, 197, 736, 9779, 2337, 9762, 3246, 2383, 4502, 1762, 6046, 4712, 5863, 9649, 6446, 9436, 3484, 5052, 1770, 3855, 3351, 3324, 9434, 8037, 3149, 6489, 8412, 3283, 7276, 4497, 2984, 579, 2266, 285, 1041, 1767, 8507, 1304, 1140, 5624, 1034, 2632, 137, 2808, 2223, 7278, 8231, 4516, 8899, 5347, 8502, 7940, 62, 1751, 2745, 4204, 9208, 9451, 2602, 2645, 3479, 2828, 6855, 6549, 8956, 5040, 3966, 4320, 4280, 1789, 2496, 5032, 1961, 4373, 2740, 3735, 3737, 5246, 1990, 3055, 6526, 751, 5607, 4828, 1174, 3659, 7803, 3441, 8630, 4815, 4143, 8314, 9910, 7735, 3860, 8387, 9284, 6411, 9329, 8245, 2369, 337, 201, 9963, 1035, 6652, 7391, 2407, 5219, 8955, 4128, 4582, 1884, 6168, 1039, 1607, 8190, 7034, 157, 2478, 8209, 9833, 2564, 2350, 6623, 8298, 7611, 3268, 1133, 4626, 3695, 7513, 8088, 7253, 8831, 7840, 2531, 8919, 7648, 4743, 6222, 7618, 244, 3170, 415, 4288, 1589, 4612, 3091, 6536, 7837, 5485, 1263, 3652, 6098, 1633, 9762, 9080, 5131, 9370, 2568, 3010, 9957, 6586, 6432, 6599, 6640, 588, 4034, 2843, 9051, 8990, 5005, 1919, 2414, 8429, 6282, 3406, 7982, 2353, 3113, 2439, 9382, 6599, 1437, 772, 1786, 4115, 5820, 1557, 6816, 1818, 109, 349, 8609, 6571, 3438, 5873, 5681, 5019, 4990, 6488, 456, 7038, 9514, 3862, 5254, 1892, 4896, 9928, 7569, 5624, 2657, 2387, 3389, 2034, 2929, 5136, 9569, 3090, 8396, 5507, 627, 8907, 6984, 2050, 9364, 6902, 4374, 7223, 535, 4810, 2075, 7979, 6943, 4144, 6648, 4776, 2763, 1486, 3139, 4336, 7303, 3611, 9852, 8055, 929, 9651, 8500, 1995, 4107, 5020, 5622, 2588, 7835, 1635, 7503, 6212, 9025, 8034, 8055, 8223, 1098, 6249, 7734, 1384, 1132, 2072, 6766, 7017, 5351, 7809, 6386, 8441, 2807, 758, 1456, 6100, 9417, 322, 2171, 2654, 4131, 4332, 3843, 172, 4271, 4013, 3909, 9953, 3129, 6288, 7751, 5970, 7508, 9357, 5412, 6220, 6113, 4587, 2236, 6270, 3846, 8480, 7592, 8319, 9776, 8546, 7861, 9790, 571, 327, 8572, 1028, 9217, 2119, 4933, 1991, 1980, 9802, 8485, 1673, 4833, 1320, 2180, 2781, 7392, 100, 4912, 2428, 2737, 5983, 906, 5087, 5147, 4529, 5800, 3426, 6369, 4157, 3513, 8904, 7040, 2687, 7817, 2672, 7959, 9784, 8776, 9746, 1630, 24, 4481, 8562, 4745, 525, 1109, 7836, 2619, 6287, 7914, 4193, 6548, 2223, 1612, 1183, 7118, 8595, 1988, 8204, 2577, 4726, 5712, 4530, 5917, 655, 2427, 4476, 5460, 4665, 3857, 2002, 372, 1739, 3925, 7494, 176, 3234, 7109, 5158, 5649, 2918, 7284, 3372, 612, 9741, 2367, 6174, 6520, 7307, 1821, 207, 6380, 8813, 4521, 6650, 2995, 2398, 879, 5537, 2414, 5397, 1925, 5960, 6391, 1266, 4690, 2038, 413, 2211, 7855, 4060, 3610, 552, 1327, 745, 4142, 9294, 5453, 9609, 4687, 842, 8310, 4599, 9887, 9463, 9486, 2336, 3847, 5232, 7161, 8686, 8878, 4278, 9348, 5786, 7057, 6710, 7471, 2509, 7711, 3855, 9349, 9522, 8437, 9483, 4068, 6706, 9617, 4491, 7980, 7116, 2867, 9850, 3250, 5263, 2864, 6716, 1987, 6095, 6550, 7356, 7423, 6080, 216, 9092, 1505, 8720, 8107, 4915, 5002, 9762, 5880, 4282, 8384, 7616, 8293, 3797, 8371, 154, 6200, 797, 3624, 4590, 809, 9953, 8272, 7207, 2293, 8174, 6864, 9202, 2218, 7927, 8106, 1312, 1212, 8267, 6505, 8845, 8232, 8025, 1357, 6916, 8704, 4185, 8231, 1033, 5574, 5455, 5413, 4478, 5345, 3764, 9926, 1897, 7538, 9552, 8462, 778, 9155, 4176, 4591, 9396, 642, 8745, 5196, 6274, 2441, 1335, 3947, 7922, 3841, 7357, 4595, 2518, 9767, 3546, 4930, 3271, 2107, 4021, 8704, 8177, 9012, 6659, 4368, 8220, 258, 1094, 559, 9629, 1970, 3747, 7346, 5391, 4376, 2910, 1560, 3889, 3682, 9436, 1413, 144, 8093, 1885, 3344, 6323, 6062, 5994, 4471, 6804, 9313, 8055, 8246, 8062, 8558, 7795, 6568, 9820, 5332, 8323, 8337, 8582, 2053, 8854, 3039, 3273, 4614, 4007, 1114, 1259, 403, 8952, 5017, 6732, 5382, 2652, 9343, 2909, 1052, 6363, 9798, 9578, 193, 6638, 1988, 553, 5423, 9862, 7495, 5720, 6680, 6332, 3321, 8321, 4070, 8532, 8210, 3194, 8061, 1482, 4473, 8872, 3380, 105, 6863, 2670, 3191, 4569, 2287, 5968, 2848, 7951, 6454, 7639, 6486, 381, 1060, 4671, 664, 435, 913, 7175, 3050, 4593, 2903, 1315, 1512, 4585, 228, 1273, 6161, 5015, 5759, 2058, 6749])," 1 (minimumArrayLength [3721, 332, 7193, 3646, 7062, 4704, 6262, 4369, 8052, 3640, 8655, 9043, 7741, 2130, 6761, 2336, 8367, 3725, 8659, 9759, 7038, 9190, 2703, 2665, 9834, 2287, 4351, 4548, 7896, 4637, 1349, 4258, 3135, 8522, 5425, 5142, 7611, 2352, 253, 1118, 6364, 3002, 7801, 9328, 9234, 3367, 5276, 7319, 8683, 3484, 3970, 6919, 2176, 2471, 364, 1819, 4556, 3441, 4405, 5333, 9121, 9598, 7396, 3891, 3406, 6566, 3247, 1505, 6232, 6880, 51, 5129, 223, 1246, 9562, 3930, 1017, 2742, 2720, 4777, 2904, 9647, 9935, 5929, 7279, 5719, 3017, 3390, 1813, 6660, 5491, 1691, 7873, 5277, 2819, 8786, 1767, 5346, 5858, 3338, 8626, 2655, 6228, 8895, 1675, 1206, 5951, 3707, 2932, 7322, 5885, 3241, 5449, 8221, 1581, 4373, 8269, 5770, 8894, 8837, 4469, 5096, 3382, 6760, 6343, 5279, 9948, 2372, 8375, 2186, 1755, 2450, 1478, 9408, 2390, 3334, 8800, 1245, 8366, 9040, 5554, 6115, 6953, 7472, 6612, 1244, 2363, 5153, 301, 9310, 7481, 4678, 432, 115, 5752, 5208, 2822, 5789, 7237, 1747, 9259, 93, 2411, 1715, 9117, 8548, 394, 2942, 534, 2198, 7050, 1824, 4490, 8519, 8164, 464, 8455, 6350, 295, 2861, 9809, 3255, 9852, 1021, 1473, 7377, 4613, 4154, 3717, 5558, 4647, 1693, 2714, 4889, 7559, 5775, 8978, 3702, 5053, 1672, 1938, 7194, 9886, 9711, 2970, 6434, 6504, 191, 5522, 8708, 1000, 7974, 1979, 6675, 5010, 3977, 8214, 4879, 8065, 6687, 9502, 1105, 6808, 6555, 9537, 7782, 3283, 5950, 7207, 5616, 933, 514, 2252, 7454, 5292, 2966, 8707, 2708, 2088, 3167, 5780, 1747, 7271, 8556, 2156, 7239, 2373, 7927, 3431, 3570, 1150, 3465, 7850, 6456, 1145, 957, 2814, 5372, 5526, 309, 8786, 5734, 3298, 6424, 7418, 5994, 2004, 267, 7733, 5212, 4763, 1736, 1815, 8736, 932, 2902, 8421, 5918, 6992, 8636, 9402, 1567, 3372, 5128, 6580, 4384, 7039, 8428, 5260, 4923, 6958, 5491, 5420, 9382, 2853, 6080, 5015, 1897, 7617, 2234, 3158, 1411, 1924, 9699, 9016, 7707, 6567, 5850, 5186, 5709, 1951, 9878, 7080, 5069, 9383, 3971, 3457, 4332, 3645, 1801, 1836, 9526, 3869, 4335, 420, 5348, 8939, 5893, 6172, 6144, 3072, 1704, 4080, 3844, 2178, 7107, 1623, 4292, 1472, 377, 3296, 8048, 3477, 608, 8251, 1846, 4063, 7261, 2319, 6773, 9877, 5562, 5058, 1532, 5628, 9269, 5996, 1361, 8730, 8, 66, 6079, 4460, 3008, 4334, 2242, 9717, 5635, 5921, 1844, 8586, 499, 4982, 622, 3498, 7012, 365, 8242, 2363, 2586, 6650, 1514, 5177, 8146, 9185, 6838, 126, 760, 9382, 6060, 6819, 7205, 8866, 2591, 286, 6712, 1940, 8353, 807, 5656, 7107, 1872, 5451, 9888, 6050, 3907, 909, 8982, 5615, 9370, 6478, 2629, 754, 4789, 618, 6971, 7444, 2599, 3186, 1248, 8325, 5565, 9178, 1336, 3693, 8517, 2727, 1307, 8797, 6481, 5743, 5184, 630, 5311, 4660, 8900, 4322, 1930, 511, 2291, 9566, 8741, 5014, 1417, 1004, 5344, 1118, 9417, 825, 5392, 6059, 4736, 5726, 4647, 9453, 202, 105, 5259, 2146, 8072, 4694, 7243, 8684, 1649, 6915, 5043, 8233, 7728, 3118, 3439, 4844, 5415, 2809, 8213, 4424, 7937, 6095, 3637, 6873, 6479, 8539, 5845, 3051, 617, 3049, 8682, 6335, 3730, 3129, 4138, 5471, 3919, 2510, 3096, 4506, 8595, 3513, 8470, 6369, 9767, 4598, 7650, 9641, 3410, 5166, 8832, 9871, 9705, 9675, 3326, 3087, 1587, 6812, 7939, 5261, 4668, 8735, 4866, 3743, 6946, 2818, 5167, 485, 8669, 146, 9370, 5011, 4708, 7570, 4736, 1314, 6901, 3969, 6798, 9984, 6882, 1793, 5047, 8077, 7969, 7228, 2764, 9659, 667, 7663, 3722, 489, 7990, 1659, 4181, 7494, 7328, 7043, 2686, 750, 1984, 3029, 8772, 5824, 6213, 4841, 4515, 974, 1629, 468, 6518, 1133, 493, 5945, 6211, 2513, 723, 902, 766, 8731, 1987, 8304, 787, 923, 9677, 2607, 2293, 2282, 2596, 1689, 6330, 4214, 9232, 5042, 5525, 2814, 7519, 5598, 8311, 8786, 6205, 9382, 194, 460, 2080, 9092, 9637, 5700, 7583, 3341, 1437, 3303, 8197, 3853, 3693, 7972, 3146, 6784, 9291, 6781, 4443, 3731, 251, 4630, 8826, 3969, 6734, 9650, 9523, 341, 8727, 8115, 9376, 1069, 8542, 163, 5898, 4403, 4569, 5810, 7859, 5892, 8359, 1049, 728, 6797, 2899, 3453, 9771, 2675, 236, 96, 6938, 476, 1531, 9529, 8649, 1206, 5497, 1259, 1151, 6588, 2319, 124, 1680, 6883, 1954, 5494, 4528, 5748, 6323, 5008, 6390, 5290, 1510, 1717, 1253, 1232, 5236, 1213, 8187, 336, 6543, 7564, 2179, 2515, 4802, 6943, 1119, 1288, 7695, 5469, 1118, 3013, 8453, 8659, 3887, 6094, 9437, 2841, 7975, 9693, 6032, 2456, 8563, 6777, 7878, 2520, 8619, 8141, 9689, 5346, 7104, 6452, 569, 1359, 8133, 8374, 9874, 262, 3001, 7337, 2445, 3975, 6833, 6684, 3316, 4359, 2612, 5668, 2961, 3731, 9916, 273, 7389, 1187, 7273, 5754, 4770, 5738, 395, 8794, 2276, 9944, 2270, 676, 4132, 9022, 8505, 5154, 9033, 8402, 5814, 9732, 8794, 5647, 8243, 9204, 2965, 6294, 9588, 2398, 8154, 4278, 6886, 2704, 6124, 6207, 8773, 3867, 6317, 4934, 5202, 1734, 8007, 3011, 4321, 2631, 6594, 2139, 2461, 6001, 9897, 4999, 1542, 7945, 8305, 2752, 6584, 4169, 9190, 5899, 3086, 7877, 9164, 1287, 5016, 1750, 437, 1787, 1429, 1420, 2075, 3000, 3348, 4818, 6608, 4769, 5358, 3544, 6196, 1064, 5019, 9432, 1110, 9171, 6244, 4872, 2861, 2324, 4377, 9491, 8306, 4394, 7267, 1845, 8243, 6938, 4226, 2359, 8881, 1702, 9721, 7838, 5960, 9778, 9590, 5613, 8523, 8062, 9206, 3977, 8718, 6825, 3625, 7399, 5480, 5803, 763, 7941, 4721, 252, 7553, 8254, 1993, 3895, 6747, 7615, 8965, 2657, 7608, 930, 3174, 5835, 9638, 7756, 9776, 976, 2373, 8791, 8781, 8386, 6635, 6356, 6373, 4876, 5659, 7156, 1092, 109, 6155, 9983, 285, 8930, 6971, 125, 2225, 3290, 7793, 923, 150, 1973, 7022, 9586, 3811, 719, 2411, 4354, 3175, 6119, 741, 4896, 4861, 393, 5286, 1375, 5437, 4308, 6448, 3951, 2968, 1104, 9060, 4180, 1490, 9561, 8658, 3197, 6082, 2315, 6076, 9157, 8856, 2488, 9746, 4206, 6865, 9401, 6188, 9111, 9973, 9653, 2706, 3958, 2378, 7155, 260, 9037, 2918, 8491, 393, 8107, 4767, 5090, 8214, 1082, 894, 5579, 457, 1464, 1552, 5568, 6732, 7003, 5075, 482, 9829, 1350, 4768, 3028, 1171, 7996, 5826, 8876, 9053, 3168, 8400, 2056, 2477, 9011, 1540, 19, 14, 5453, 2815, 4677, 9865, 7732, 9566, 302, 5336, 3328, 1358, 4149, 9716, 3951, 7201, 4159, 9985, 6329, 2825, 9731, 3936, 8950, 524, 6386, 3385, 282, 3358, 4444, 5189, 2386, 8722, 5135, 5045, 7141, 1090, 7215, 6310, 4567, 4418, 6466, 5915, 193, 3929, 9539, 342, 4469, 3052, 6143, 6283, 505, 9588, 4842, 7092, 2004, 2152, 7113, 2640, 6931, 4863, 9392, 8803, 9973, 1468, 4850, 3503, 1658, 6624, 5108, 4022, 197, 8813, 554, 1478, 4805, 3075, 306, 2252, 8329, 5763, 3884, 8741, 8103, 5769, 2892, 9377, 4536, 9897, 6077, 7054, 8102, 2608, 4140, 1024, 7834, 1872, 5052, 1863, 1828, 5404, 6285, 9544, 9888, 3912, 6200, 9738, 2660, 901, 1819, 5303, 2996, 9001, 6512, 5677, 9543, 6710, 6412, 108, 883, 4513, 7924, 6217, 9756, 9326, 1468, 6029, 7301, 2249, 5735, 5326, 8580, 8977, 6915, 6958, 8916, 7886, 519, 8575, 9038, 6532, 7248, 2084, 6304, 3377, 1195, 8028, 5414, 7894, 6078, 5396, 1935, 5176, 6877, 5086, 6993, 2384, 1604, 8876, 8735, 6111, 520, 982, 2135, 1152, 8781, 5708, 340, 2932, 8997, 7344, 247, 7230, 6726, 1282, 944, 9779, 8296, 2891, 5099, 9886, 7444, 6524, 4252, 6554, 4921, 6166, 9553, 1152, 9222, 4524, 6269, 6464, 8865, 7901, 6576, 9052, 6389, 8946, 1593, 141, 5613, 7925, 9559, 9332, 8988, 8768, 7381, 3521, 9786, 339, 9916, 3333, 4264, 3718, 4753, 4055, 5044, 7316, 9595, 6589, 8475, 8728, 7716, 6854, 2539, 8709, 3524, 1977, 7492, 2620, 1459, 9093, 338, 762, 9741, 3949, 2358, 4190, 7149, 9571, 5277, 9835, 8973, 3676, 277, 6973, 2911, 6544, 837, 862, 7298, 5643, 381, 4033, 9329, 2996, 8166, 9608, 9058, 4693, 6674, 2448, 2650, 4745, 1501, 5370, 4655, 5971, 9290, 8580, 8563, 9010, 3892, 298, 574, 4432, 2284, 6415, 9843, 5561, 6200, 1164, 9929, 8966, 1970, 6663, 7675, 7986, 6792, 9175, 9495, 7993, 3750, 4801, 7616, 1269, 6816, 6299, 7660, 5958, 7223, 9542, 5790, 6152, 9240, 2071, 5006, 927, 7770, 9347, 4413, 7411, 5426, 8080, 7729, 2998, 75, 2917, 1780, 1763, 698, 10000, 8732, 4983, 5151, 9444, 2178, 8840, 6902, 1538, 6951, 450, 4752, 7337, 5671, 7525, 5031, 3191, 6999, 125, 7105, 872, 2519, 4698, 9439, 4570, 1271, 6723, 1525, 2480, 3910, 1331, 625, 600, 4434, 356, 7389, 870, 3889, 3350, 4182, 7067, 3409, 3081, 2210, 1603, 4144, 3760, 447, 8299, 6251, 9903, 6004, 10, 1586, 3682, 3794, 9485, 1475, 5308, 7112, 967, 2182, 8668, 8671, 810, 5701, 1731, 9667, 846, 7312, 3233, 2214, 6784, 861, 8418, 1684, 3359, 6608, 8465, 5989, 1699, 2183, 2605, 3324, 2733, 3690, 4805, 203, 4051, 1303, 9837, 4548, 7659, 8080, 9333, 853, 829, 9318, 5018, 2514, 2322, 2775, 5372, 2897, 2840, 2576, 9722, 6676, 5899, 6679, 5732, 219, 8009, 5205, 2908, 4376, 397, 5137, 7040, 9309, 3166, 908, 5192, 6125, 7310, 6928, 3898, 4442, 8332, 9566, 3915, 6232, 249, 9090, 3960, 6598, 3395, 2831, 6537, 2306, 1096, 2987, 4624, 5285, 8120, 7589, 3790, 7118, 4137, 3590, 5840, 7992, 9697, 3978, 7172, 9008, 6239, 2145, 7471, 3456, 4260, 7774, 153, 1066, 4669, 4557, 5417, 6358, 9328, 8437, 9411, 580, 4703, 2569, 7150, 4298, 3065, 1020, 6967, 3675, 7824, 477, 3183, 7893, 5729, 3296, 7217, 612, 4040, 7470, 4099, 604, 8404, 9413, 1134, 640, 4765, 536, 8798, 3067, 1802, 4394, 9446, 5233, 897, 4650, 5063, 3699, 251, 4331, 4976, 4400, 9903, 1086, 6596, 788, 6506, 4738, 6373, 9371, 3289, 929, 9111, 3092, 9186, 5638, 9107, 3174, 1823, 9341, 8930, 500, 6486, 1525, 557, 137, 4594, 8385, 4157, 3401, 754, 7404, 1599, 946, 1916, 1587, 5803, 208, 1079, 7575, 7290, 1434, 7826, 855, 7741, 304, 5227, 1018, 6616, 7747, 2689, 5008, 2422, 2496, 3470, 1565, 7100, 2811, 3668, 7890, 6808, 5787, 9289, 9815, 8587, 1645, 7115, 9435, 427, 4347, 4884, 9136, 9318, 6393, 8758, 3247, 3960, 982, 1383, 5755, 3727, 1, 3331, 3088, 5273, 4428, 627, 9132, 9563, 1078, 9478, 9902, 5764, 8683, 1085, 2758, 8396, 5663, 2154, 9123, 7296, 8583, 1959, 2127, 2004, 3921, 4319, 252, 5500, 2472, 4021, 8850, 4299, 6168, 2731, 1304, 8284, 6351, 2712, 6632, 2599, 466, 1003, 8559, 143, 3528, 386, 661, 5498, 3392, 2419, 4420, 5253, 3667, 6928, 2360, 4206, 7384, 771, 4143, 3589, 2240, 5873, 5017, 7792, 7683, 6881, 2330, 4580, 7802, 912, 8133, 7915, 8036, 3316, 323, 5553, 1529, 9855, 3980, 3597, 2469, 4639, 8585, 3713, 3770, 8918, 7185, 1646, 7889, 3324, 7526, 4476, 5879, 6928, 1243, 1478, 111, 5164, 1157, 9757, 6978, 8091, 454, 3352, 4773, 4590, 5616, 8882, 5794, 5337, 9573, 6223, 8857, 4682, 5390, 1701, 1684, 8675, 1831, 371, 7233, 9294, 6008, 6798, 6359, 6540, 5582, 2497, 8265, 5191, 6903, 8513, 5822, 3598, 2119, 5222, 6948, 9055, 394, 2766, 488, 3824, 3803, 2690, 6420, 4900, 7112, 61, 5532, 2799, 793, 9910, 5242, 5379, 120, 4262, 8476, 8583, 3391, 1481, 6846, 2132, 7145, 410, 5865, 3867, 5256, 5980, 2779, 5859, 9212, 8305, 6303, 1584, 6215, 1921, 3334, 1410, 3571, 3973, 2625, 9722, 8825, 6395, 6707, 2228, 129, 3661, 7828, 6358, 4241, 138, 7928, 6052, 5748, 3227, 8258, 9879, 129, 50, 2904, 9322, 2180, 8871, 6130, 7418, 302, 1013, 4598, 7300, 5583, 9619, 7828, 8601, 4270, 7749, 2870, 6989, 470, 1638, 4364, 1138, 4054, 6437, 5272, 1478, 1918, 8037, 9626, 7930, 3911, 5175, 4375, 956, 3377, 4799, 6499, 6618, 9463, 2053, 5148, 9576, 586, 5658, 866, 8961, 9101, 3081, 9750, 1696, 7282, 458, 1257, 1662, 8897, 6026, 6612, 3754, 4875, 8067, 8615, 9788, 1268, 340, 7023, 464, 1294, 6797, 4727, 234, 5419, 9082, 5148, 4703, 8746, 202, 7567, 7254, 2636, 2688, 3356, 6189, 9681, 6326, 1556, 6099, 5250, 2288, 8370, 6661, 5858, 2637, 6267, 8909, 9215, 8779, 7811, 4877, 1707, 2448, 1807, 5253, 3154, 112, 7732, 5260, 682, 5468, 2701, 2057, 3990, 2736, 8600, 2051, 4385, 7381, 322, 458, 7543, 2874, 9258, 9714, 3521, 5630, 2772, 8391, 9408, 1442, 8118, 9687, 7660, 9034, 341, 5762, 2999, 2304, 9307, 6002, 2522, 7315, 7180, 9665, 1884, 958, 6800, 7069, 1319, 9129, 5381, 9697, 6921, 2582, 1676, 7914, 8195, 566, 521, 2116, 6170, 7809, 490, 6706, 1188, 7364, 3247, 6804, 1916, 1953, 8733, 4514, 1881, 9707, 9646, 4352, 1155, 3517, 8850, 185, 4711, 7695, 4149, 5301, 5534, 8126, 6360, 8742, 5470, 1825, 9918, 9474, 6000, 8089, 1355, 703, 5103, 1990, 8645, 2550, 189, 3176, 2399, 9063, 3169, 5427, 2384, 6262, 8250, 5836, 9967, 7995, 1649, 4535, 7935, 1177, 5286, 7953, 9724, 9825, 3551, 4508, 4809, 7929, 6303, 5140, 5799, 629, 5555, 4695, 2755, 8995, 7564, 3552, 15, 4328, 9622, 4632, 5724, 7013, 2531, 1923, 8124, 6599, 8368, 6911, 4337, 4139, 8649, 7713, 5759, 5388, 1180, 3176, 8501, 8967, 9976, 7837, 9493, 4086, 3320, 6476, 4387, 3405, 7894, 4042, 1554, 4113, 65, 9729, 8176, 8375, 1995, 7424, 3501, 6725, 8342, 6895, 4961, 927, 8701, 191, 5831, 6931, 7083, 7096, 2145, 3570, 5577, 871, 1528, 244, 6471, 176, 8435, 7059, 4403, 8856, 2764, 579, 1388, 914, 8917, 1393, 9529, 9926, 8043, 7298, 9687, 5436, 4667, 8135, 4862, 8875, 6046, 8435, 571, 2963, 565, 3812, 6529, 1703, 5003, 534, 7944, 9259, 496, 4969, 5249, 5595, 5359, 2977, 3516, 207, 5627, 4143, 5392, 8882, 1777, 8348, 6142, 1523, 1120, 5819, 69, 3032, 2422, 3979, 1842, 9344, 778, 4268, 7845, 4280, 2946, 8941, 6754, 6557, 8961, 922, 8467, 2235, 1304, 5556, 4379, 6895, 8320, 5217, 990, 6016, 7337, 5286, 4935, 5542, 7254, 6464, 7681, 6999, 2537, 1451, 4282, 3035, 5273, 3967, 8408, 5139, 8346, 8043, 2983, 7484, 8533, 4805, 7525, 8488, 9417, 1167, 3798, 4939, 7410, 1541, 2966, 7258, 129, 5014, 7043, 7840, 8139, 6036, 6365, 8424, 829, 4841, 4714, 5319, 788, 8301, 1113, 103, 6596, 4419, 4052, 8545, 6839, 7020, 6766, 9980, 5979, 830, 8428, 1619, 7968, 3483, 3103, 9190, 4978, 9351, 579, 1652, 6434, 7781, 1177, 7105, 3978, 9763, 670, 6458, 3381, 8100, 2996, 2577, 9350, 4396, 3027, 1392, 5534, 3420, 9200, 4341, 9051, 4456, 3648, 9639, 6415, 7202, 494, 5079, 1198, 5491, 9625, 6680, 1052, 1665, 5750, 4694, 388, 6822, 5751, 1757, 9133, 3684, 4055, 2295, 5464, 1654, 2219, 2433, 3800, 3259, 7862, 5401, 2201, 9681, 2742, 4274, 3933, 352, 5944, 6303, 4062, 6558, 6860, 4525, 9947, 937, 1635, 768, 8909, 446, 4457, 8170, 7048, 5402, 990, 2303, 6793, 1832, 3814, 8663, 5681, 7377, 9541, 7831, 2247, 9580, 6190, 9703, 3107, 5020, 6437, 6421, 4330, 6449, 1272, 9807, 8809, 6494, 2395, 825, 4164, 3680, 1488, 1275, 3286, 6288, 4435, 2347, 8339, 9795, 3288, 7776, 4535, 5434, 2242, 4022, 6199, 8953, 5618, 6640, 3376, 7643, 3696, 1829, 198, 9387, 3508, 6657, 8477, 5807, 6870, 3692, 1436, 8683, 3584, 9458, 8559, 5876, 5250, 2700, 6841, 6676, 3022, 1650, 9241, 880, 1835, 1147, 7019, 9467, 9186, 3857, 3693, 5005, 8845, 4840, 4095, 2781, 4294, 2420, 8609, 9249, 1770, 7628, 2156, 7620, 399, 7706, 5142, 1997, 4931, 5170, 1686, 2166, 7092, 6707, 3381, 4836, 197, 736, 9779, 2337, 9762, 3246, 2383, 4502, 1762, 6046, 4712, 5863, 9649, 6446, 9436, 3484, 5052, 1770, 3855, 3351, 3324, 9434, 8037, 3149, 6489, 8412, 3283, 7276, 4497, 2984, 579, 2266, 285, 1041, 1767, 8507, 1304, 1140, 5624, 1034, 2632, 137, 2808, 2223, 7278, 8231, 4516, 8899, 5347, 8502, 7940, 62, 1751, 2745, 4204, 9208, 9451, 2602, 2645, 3479, 2828, 6855, 6549, 8956, 5040, 3966, 4320, 4280, 1789, 2496, 5032, 1961, 4373, 2740, 3735, 3737, 5246, 1990, 3055, 6526, 751, 5607, 4828, 1174, 3659, 7803, 3441, 8630, 4815, 4143, 8314, 9910, 7735, 3860, 8387, 9284, 6411, 9329, 8245, 2369, 337, 201, 9963, 1035, 6652, 7391, 2407, 5219, 8955, 4128, 4582, 1884, 6168, 1039, 1607, 8190, 7034, 157, 2478, 8209, 9833, 2564, 2350, 6623, 8298, 7611, 3268, 1133, 4626, 3695, 7513, 8088, 7253, 8831, 7840, 2531, 8919, 7648, 4743, 6222, 7618, 244, 3170, 415, 4288, 1589, 4612, 3091, 6536, 7837, 5485, 1263, 3652, 6098, 1633, 9762, 9080, 5131, 9370, 2568, 3010, 9957, 6586, 6432, 6599, 6640, 588, 4034, 2843, 9051, 8990, 5005, 1919, 2414, 8429, 6282, 3406, 7982, 2353, 3113, 2439, 9382, 6599, 1437, 772, 1786, 4115, 5820, 1557, 6816, 1818, 109, 349, 8609, 6571, 3438, 5873, 5681, 5019, 4990, 6488, 456, 7038, 9514, 3862, 5254, 1892, 4896, 9928, 7569, 5624, 2657, 2387, 3389, 2034, 2929, 5136, 9569, 3090, 8396, 5507, 627, 8907, 6984, 2050, 9364, 6902, 4374, 7223, 535, 4810, 2075, 7979, 6943, 4144, 6648, 4776, 2763, 1486, 3139, 4336, 7303, 3611, 9852, 8055, 929, 9651, 8500, 1995, 4107, 5020, 5622, 2588, 7835, 1635, 7503, 6212, 9025, 8034, 8055, 8223, 1098, 6249, 7734, 1384, 1132, 2072, 6766, 7017, 5351, 7809, 6386, 8441, 2807, 758, 1456, 6100, 9417, 322, 2171, 2654, 4131, 4332, 3843, 172, 4271, 4013, 3909, 9953, 3129, 6288, 7751, 5970, 7508, 9357, 5412, 6220, 6113, 4587, 2236, 6270, 3846, 8480, 7592, 8319, 9776, 8546, 7861, 9790, 571, 327, 8572, 1028, 9217, 2119, 4933, 1991, 1980, 9802, 8485, 1673, 4833, 1320, 2180, 2781, 7392, 100, 4912, 2428, 2737, 5983, 906, 5087, 5147, 4529, 5800, 3426, 6369, 4157, 3513, 8904, 7040, 2687, 7817, 2672, 7959, 9784, 8776, 9746, 1630, 24, 4481, 8562, 4745, 525, 1109, 7836, 2619, 6287, 7914, 4193, 6548, 2223, 1612, 1183, 7118, 8595, 1988, 8204, 2577, 4726, 5712, 4530, 5917, 655, 2427, 4476, 5460, 4665, 3857, 2002, 372, 1739, 3925, 7494, 176, 3234, 7109, 5158, 5649, 2918, 7284, 3372, 612, 9741, 2367, 6174, 6520, 7307, 1821, 207, 6380, 8813, 4521, 6650, 2995, 2398, 879, 5537, 2414, 5397, 1925, 5960, 6391, 1266, 4690, 2038, 413, 2211, 7855, 4060, 3610, 552, 1327, 745, 4142, 9294, 5453, 9609, 4687, 842, 8310, 4599, 9887, 9463, 9486, 2336, 3847, 5232, 7161, 8686, 8878, 4278, 9348, 5786, 7057, 6710, 7471, 2509, 7711, 3855, 9349, 9522, 8437, 9483, 4068, 6706, 9617, 4491, 7980, 7116, 2867, 9850, 3250, 5263, 2864, 6716, 1987, 6095, 6550, 7356, 7423, 6080, 216, 9092, 1505, 8720, 8107, 4915, 5002, 9762, 5880, 4282, 8384, 7616, 8293, 3797, 8371, 154, 6200, 797, 3624, 4590, 809, 9953, 8272, 7207, 2293, 8174, 6864, 9202, 2218, 7927, 8106, 1312, 1212, 8267, 6505, 8845, 8232, 8025, 1357, 6916, 8704, 4185, 8231, 1033, 5574, 5455, 5413, 4478, 5345, 3764, 9926, 1897, 7538, 9552, 8462, 778, 9155, 4176, 4591, 9396, 642, 8745, 5196, 6274, 2441, 1335, 3947, 7922, 3841, 7357, 4595, 2518, 9767, 3546, 4930, 3271, 2107, 4021, 8704, 8177, 9012, 6659, 4368, 8220, 258, 1094, 559, 9629, 1970, 3747, 7346, 5391, 4376, 2910, 1560, 3889, 3682, 9436, 1413, 144, 8093, 1885, 3344, 6323, 6062, 5994, 4471, 6804, 9313, 8055, 8246, 8062, 8558, 7795, 6568, 9820, 5332, 8323, 8337, 8582, 2053, 8854, 3039, 3273, 4614, 4007, 1114, 1259, 403, 8952, 5017, 6732, 5382, 2652, 9343, 2909, 1052, 6363, 9798, 9578, 193, 6638, 1988, 553, 5423, 9862, 7495, 5720, 6680, 6332, 3321, 8321, 4070, 8532, 8210, 3194, 8061, 1482, 4473, 8872, 3380, 105, 6863, 2670, 3191, 4569, 2287, 5968, 2848, 7951, 6454, 7639, 6486, 381, 1060, 4671, 664, 435, 913, 7175, 3050, 4593, 2903, 1315, 1512, 4585, 228, 1273, 6161, 5015, 5759, 2058, 6749])) + +test8 :: Test +test8 = TestCase (assertEqual "for (minimumArrayLength [880134581, 772576344, 399895356, 285967908, 867328643, 442745784, 424034268, 345772360, 916019994, 542598802, 933956188, 790793630, 683928860, 739568265, 956222957, 333512601, 626919162, 553949110, 627736799, 918401986, 613953728, 387419984, 458262981, 817382805, 248018453, 688854223, 838755468, 470061499, 869401840, 303790130, 838894964, 165822129, 594444959, 243189521, 669050758, 737400510, 231655911, 30326960, 235299222, 649728743, 671186820, 286886018, 436529751, 185275958, 547596220, 600755891, 209994949, 961919305, 375781259, 759825101, 626503060, 25211291, 934281965, 321043477, 542621448, 689843640, 219739535, 411035537, 449771194, 226860314, 896492991, 996264811, 215102042, 756270916, 178304891, 261744798, 558714022, 706782684, 956959014, 490566913, 542120187, 719256649, 416303989, 61347588, 153604934, 762771462, 603882321, 427415285, 765590810, 150127576, 154080204, 615974251, 14547133, 593013610, 676690296, 667964848, 886562719, 918748935, 986729577, 62084349, 924807360, 626914636, 218372326, 166342871, 420648285, 955220235, 891435030, 565138979, 521600366, 338037871, 754271599, 107000763, 888415279, 351965887, 701171583, 473187119, 448322308, 683063263, 621336856, 441295215, 451921142, 675330910, 627256387, 818825062, 44897016, 582385043, 393380812, 340108689, 233337944, 392598383, 130523171, 482971695, 852799954, 106048655, 369166645, 522158820, 499886164, 611754363, 216567126, 415808131, 14652524, 258245719, 924670087, 192796564, 317461463, 753866154, 890410282, 980006795, 352341946, 490438905, 169688110, 37675331, 394193105, 631912887, 669203877, 65544428, 970631344, 706011143, 8176764, 501677981, 339117111, 176773217, 791368146, 587962126, 627740643, 733236899, 611860782, 562305253, 766521040, 312178013, 47761851, 98432974, 588162107, 444674798, 571338681, 114611482, 583158315, 926899872, 897431605, 836739450, 768186063, 310965058, 139757743, 778356561, 367377726, 710071529, 865143542, 116307916, 867012046, 356666333, 921026908, 54450768, 134760156, 285246220, 388482510, 630448736, 528156768, 176528757, 931414016, 307551907, 99316255, 266686125, 313456830, 793419672, 266440651, 533941226, 886515287, 72275303, 306917683, 124564538, 377120763, 430900101, 485708981, 979664933, 657691604, 90500814, 207190418, 967831406, 179496476, 431639293, 461749564, 612003348, 491543465, 143042116, 966639695, 794974882, 867504308, 535412914, 997445736, 485066855, 255377770, 400095408, 774358859, 603140676, 468099733, 255363971, 473944888, 197176342, 973530146, 172853722, 199954001, 978998390, 830249155, 171041494, 120249799, 579789336, 107296359, 438775113, 865549448, 562505285, 231622051, 714284255, 416414838, 269725703, 813564951, 944196270, 35646766, 968437086, 546502886, 546422956, 875177829, 326017648, 683369044, 63654388, 914744887, 494446264, 832996181, 566016927, 233133088, 444528299, 204444062, 250989857, 118983280, 119662544, 320619678, 613517678, 646513731, 519700369, 622410353, 711144761, 266942622, 520873743, 104955789, 129013154, 554852411, 725295921, 899119983, 32574354, 205539784, 900472700, 608023236, 102802351, 811913593, 867657831, 425237762, 489011961, 34960631, 778647993, 48441060, 113001319, 880043047, 404956576, 873335266, 931093557, 354633711, 908299247, 424017231, 702019415, 682808317, 448773159, 272677484, 998023769, 275324422, 181769605, 135097231, 374001181, 550506573, 281125676, 574620620, 289257907, 733000269, 726248148, 900258599, 216092838, 240121451, 708935526, 506559984, 963363142, 253694543, 777066885, 419847752, 2652071, 627294638, 171007737, 907616306, 519545295, 661559856, 565333487, 898602413, 13958534, 711190046, 173167041, 758537373, 237579306, 670774187, 819935884, 433063890, 915907577, 920122143, 261554375, 289850613, 806720049, 90279520, 669013334, 722036381, 729756124, 575351689, 192568727, 859312670, 128539214, 762993428, 241916328, 486223592, 481582130, 615943868, 351001380, 594050060, 94773984, 693430750, 533892524, 449685957, 334808432, 987874779, 888479582, 370668495, 811783463, 93478705, 69267479, 872783381, 190302820, 667739790, 145636316, 63906558, 548643453, 985463619, 387166978, 330385720, 125101087, 213821867, 651438543, 834569065, 730846149, 932085945, 929269685, 661825104, 861763088, 296522335, 150480786, 559100677, 710561705, 773008032, 669361091, 40518632, 676061939, 843546521, 565118836, 825528783, 398193933, 984187516, 589127548, 813097488, 95508608, 153585091, 548697798, 132398524, 269756492, 932618409, 736498963, 626086192, 780365242, 486370081, 871224782, 677702319, 732835810, 715527718, 496235293, 156585614, 612477670, 811854968, 608070165, 127260843, 993953090, 884552894, 13981110, 658916984, 395298925, 418582978, 749389445, 208198562, 484086863, 842428799, 475951277, 104882693, 385918757, 73796067, 166532765, 132510202, 537121325, 673264417, 165438708, 913594804, 326855874, 784445863, 896610721, 667820898, 882894177, 909420690, 49880421, 16788138, 566527517, 404188221, 407323260, 732317301, 743768712, 614759288, 816320839, 315273597, 835026277, 293575911, 206271346, 90936162, 668736539, 302389864, 459844314, 162515010, 862326889, 177225784, 528516817, 823703198, 229755259, 957042756, 517440603, 45020469, 309685972, 571201613, 888817946, 339605797, 268092512, 350297303, 286439307, 892585975, 563766413, 513505346, 872215479, 854012212, 218379954, 157282502, 470437082, 761379652, 276970771, 493873962, 58666708, 781357424, 151773969, 153870990, 348396378, 697076565, 343494124, 39075594, 37153310, 747327376, 122061654, 230235985, 221466327, 883883323, 732694798, 817210114, 325957917, 18766305, 517066355, 959470517, 421080533, 435913042, 705598828, 5348100, 285893444, 78046703, 488054923, 572627920, 432743852, 948900250, 736573135, 738344964, 988861227, 398334267, 277995509, 498754434, 510417446, 475048505, 481959671, 151876203, 700786392, 417931322, 508328046, 218383798, 81050850, 4313417, 473279813, 673133917, 651855879, 381360874, 160050498, 170551997, 476899325, 738621887, 351042132, 543581701, 861974785, 355566841, 826549942, 237117440, 543117197, 483543531, 745213607, 452335783, 621175847, 111318154, 935765313, 909331452, 951966961, 512011656, 833880599, 597741088, 872274903, 560446748, 744208922, 218081788, 142263085, 573883519, 508791472, 362161935, 279607720, 384278637, 965625191, 297709186, 462405913, 592725170, 413244218, 582331867, 664571626, 985169835, 916123874, 524935945, 484435373, 137106007, 649542576, 326401842, 244266171, 489351182, 297897611, 889704034, 155945450, 174442632, 26784993, 744683236, 986668727, 90041339, 495527940, 689047218, 762033464, 155512913, 60674792, 742149376, 596709359, 163780172, 646548398, 366898016, 320965012, 995240516, 723505963, 210166510, 798029805, 478153548, 56881214, 888721357, 542004888, 775626756, 809451122, 272418222, 173639111, 286098594, 611114581, 641980247, 701500272, 611823172, 939271211, 71699397, 910264860, 262532802, 64658012, 177893373, 662385997, 132751936, 98329502, 579500005, 740419958, 794639957, 142057103, 665985676, 914527982, 861261245, 428488057, 56775855, 910959663, 68015485, 360503160, 874976061, 190543094, 987695376, 558939973, 414401767, 247235645, 304530811, 493345265, 606075312, 479464367, 997036831, 737833138, 77451196, 869699626, 324606997, 813256583, 744407651, 955824666, 754177258, 740449609, 534833485, 379245616, 573202702, 380701824, 827132959, 377627300, 189601742, 558175455, 401128069, 463201588, 560587369, 731579902, 767139271, 579312239, 81695574, 801099849, 538042779, 407492156, 636329167, 25890949, 292048859, 151982005, 634079655, 754850072, 260757988, 468748736, 561942506, 697499773, 786723516, 371086704, 876426870, 717046791, 175042717, 882575342, 645212179, 546168724, 470672062, 166754854, 274065461, 569537741, 934786224, 865097934, 847170782, 800668609, 242817177, 489067315, 466647660, 664841831, 616484459, 423313670, 217250759, 767812248, 797333026, 749631803, 570555538, 379426258, 392460932, 954688478, 999734125, 495397031, 759678331, 649160808, 563505130, 898832468, 15339902, 283184511, 544660738, 85248101, 222703515, 160211141, 878631619, 648286438, 352828235, 838019019, 512509076, 600878809, 938338531, 41425638, 211520661, 599034085, 718208994, 828142874, 458943629, 759078031, 260160591, 134766086, 527382561, 781315434, 467586385, 435971510, 805718715, 283227731, 73074346, 472269190, 596254440, 694634299, 438716978, 777087297, 483236731, 156053414, 766189998, 532906092, 185416814, 84218400, 575273728, 529965932, 809119906, 85322015, 526122603, 401655498, 780076639, 442660256, 630077768, 36342618, 542794984, 199822166, 936772901, 77180605, 818811635, 201206097, 645087205, 979075212, 529223113, 42853898, 257526141, 853670132, 1720867, 236863356, 694651676, 512028949, 187912206, 385718107, 900644686, 50834120, 690257769, 601236484, 732283314, 110237559, 77011139, 289987174, 17427166, 324629539, 192776784, 544978481, 306967470, 920161449, 908974656, 916583129, 2248877, 805749663, 237375731, 669110904, 8963267, 342045943, 111357842, 470333536, 917153092, 659765236, 532679838, 398986864, 685861428, 96358107, 180004551, 590781972, 955957460, 771681539, 543948536, 392746777, 401956067, 710398302, 106514925, 347856221, 599578170, 116437387, 154764380, 715615838, 579277010, 845671657, 494033278, 780901733, 139390024, 277952692, 179821844, 998953360, 563279363, 688607075, 789711207, 671569314, 819485210, 981261276, 461562095, 427689991, 602816934, 692361233, 93224972, 143566458, 587418818, 892790495, 467671907, 241249859, 673915634, 453065593, 958982220, 581218739, 909532277, 826566853, 32422828, 479989188, 616245339, 367747558, 865774050, 80895272, 854099804, 940735465, 713823710, 357997900, 908651039, 431558662, 511202840, 912915540, 348524445, 211561092, 662037418, 416614013, 583743789, 759661735, 191792744, 835703055, 94302797, 565989672, 407178331, 93793489, 797953111, 669445167, 517768701, 984130624, 922044946, 809419816, 240115778, 278337927, 532041230, 661214810, 535945003, 898362132, 302496266, 921440348, 927427908, 594629097, 215105436, 496506064, 538979114, 475379294, 502812442, 235637363, 432616979, 603336447, 76950014, 686533318, 70537644, 734543399, 424946745, 175372282, 844018573, 761543055, 35205055, 628687645, 950267177, 549983511, 198485422, 187359376, 176747298, 859964012, 376627453, 657128300, 183569546, 886172616, 256221030, 300621767, 31234219, 751394526, 593680602, 553840813, 22071677, 97957834, 261117661, 184885080, 831609621, 263373030, 325013264, 743131724, 363682873, 328548105, 537817330, 125466955, 975776780, 24702259, 65316095, 216264569, 158011448, 882818224, 349215164, 420639521, 452781685, 191103336, 622343398, 878372588, 907975301, 758066951, 975328122, 62985578, 61909456, 386874032, 713724838, 890473535, 185195713, 11065797, 314089135, 795360450, 706327741, 527825810, 920672612, 174968481, 981349202, 534311286, 37732071, 631176666, 841586215, 927795421, 120036032, 320628049, 782545674, 749094841, 740887370, 270207196, 67485636, 902423647, 51879070, 66981155, 523366167, 419607420, 672979049, 791043663, 530046309, 416682213, 812732392, 59711099, 120523508, 545936022, 611587157, 535590655, 285963266, 8145664, 599957583, 428105620, 174340714, 310558245, 70447271, 940842957, 570508289, 925456263, 98443414, 643220660, 277755316, 850283835, 540825140, 788939941, 998154476, 325098342, 380250563, 850094965, 859131515, 998188075, 418435195, 834469150, 387752591, 365563465, 451960681, 134334846, 891956447, 353489891, 337029105, 267027321, 89371550, 169408345, 778259043, 779660290, 42067294, 903738791, 977290722, 327805349, 153628554, 67370584, 223050152, 216192237, 422626883, 723733818, 701794979, 766535550, 736867524, 850994919, 858194214, 837536082, 112330226, 940167120, 945766578, 166409496, 812378888, 555885426, 929659699, 421668388, 601088615, 621827512, 14859556, 366179882, 280106429, 869154158, 183493139, 692369111, 171396178, 897359245, 941617762, 363206494, 78936329, 862799901, 892769282, 61190226, 795640030, 425614094, 904416199, 299516809, 116911811, 275966376, 459508017, 900447237, 941954168, 996501730, 588394149, 436021075, 645997381, 756179844, 503848726, 566747041, 209474506, 979152914, 68140211, 470617450, 617381764, 176938785, 847368396, 141207456, 305173944, 737893686, 222174823, 161525396, 504857329, 401814031, 212645175, 528881497, 651687005, 108938678, 555698488, 596216009, 58281356, 875618559, 293658280, 184101557, 259458365, 991563909, 589089716, 666700585, 599546523, 856012064, 444852982, 54340573, 218873795, 263926502, 892015658, 133745280, 699845646, 96771102, 523544304, 570136135, 51721450, 172387488, 479090931, 786819469, 171460363, 591513922, 862728817, 752485090, 526487159, 696592596, 24678964, 962421987, 769000589, 48852146, 661017008, 302618527, 680947335, 740857756, 563600952, 183924161, 452180034, 693831759, 101967127, 31054786, 91737730, 651514973, 64883071, 609927629, 357201698, 939343995, 509341846, 651440103, 57979123, 945232207, 686351205, 711889560, 875313201, 677832830, 898234859, 510122457, 265197318, 773297210, 648845235, 709706177, 657632913, 148241707, 571881428, 839670173, 988238577, 646014857, 615165986, 541727120, 73485003, 443930949, 449762269, 979604289, 383926461, 227276678, 162037204, 495227167, 433029221, 424448698, 964862201, 829425930, 102024962, 562401930, 329558494, 7311074, 419358016, 494307195, 797314957, 424710001, 602063242, 173556290, 125967227, 188150945, 756824129, 713111706, 814169505, 197166219, 712966411, 879461144, 406442641, 510256168, 347928793, 368754833, 890191749, 682372365, 138240790, 747721640, 219309338, 524181514, 370760113, 436301661, 860516073, 691836876, 692611666, 394307541, 291055171, 742487977, 670666604, 752328679, 367522778, 426769960, 567519212, 873066011, 219728513, 121789517, 81472970, 709711604, 525944912, 876902987, 42521265, 114998371, 270989922, 50771903, 779680368, 57052960, 903587836, 943165240, 152928669, 321759514, 325023225, 343090394, 879846901, 153627120, 112113062, 281766978, 214000481, 221281563, 393210444, 333557984, 769202502, 44183180, 123977758, 607898661, 163389256, 625546306, 665003068, 695035568, 270652424, 945461310, 864562928, 461380245, 481649749, 852837953, 476267006, 206786506, 209312089, 185441970, 373448724, 929552897, 200210500, 103459553, 144584992, 491412477, 184851199, 479789037, 91741401, 488779870, 964247927, 552844256, 468009547, 239812109, 609852086, 818950291, 102327732, 863709170, 813045574, 678415650, 986123934, 710239254, 210831962, 505162691, 420461693, 545438476, 7797730, 568810553, 931345382, 906217549, 430456515, 173628963, 292494095, 107219426, 549508067, 963564693, 849151182, 534795215, 480840604, 646518941, 604736001, 959477896, 467692514, 421180748, 421787878, 721141457, 581020237, 740191213, 288716393, 85717855, 619401017, 811949627, 656967405, 592961859, 9411446, 29759375, 559454848, 551489736, 502164197, 770093946, 669643578, 344958550, 541577042, 779195339, 684602386, 913457927, 200132908, 450227575, 733159299, 828704931, 393186364, 799931151, 989534405, 218836627, 160081407, 47949021, 985620554, 439767022, 600714, 495495185, 60199641, 268790512, 196435175, 113966723, 302799307, 60534034, 606501938, 457288995, 167775528, 964982527, 689021281, 226628045, 780137520, 264998706, 437816417, 728808339, 867920937, 880621703, 601897238, 609684610, 763433141, 587260378, 60814402, 827278057, 237049497, 690916996, 482725843, 654099597, 18528212, 430960501, 473937225, 482783971, 208103646, 770778613, 512019572, 880733956, 490928234, 618524844, 803238729, 665597934, 616789008, 600587092, 643721641, 158496757, 134282568, 319200580, 28258385, 743498717, 396052512, 103573165, 36531067, 223986369, 254329795, 947187062, 940789394, 164377888, 776672798, 464676212, 301994891, 75651122, 903905978, 986104978, 106547723, 268020873, 219739741, 487257993, 735791232, 989211030, 378452656, 134419170, 455535464, 705992556, 780465696, 441150358, 447708575, 728959143, 515254405, 841302849, 699058320, 334771242, 635985965, 800545078, 316446845, 526451793, 655597577, 962426078, 993821776, 416489243, 516026856, 868204626, 217210986, 859142864, 936553674, 515610154, 886003773, 698797796, 992996010, 743396685, 380582672, 528882456, 976415193, 557079670, 586004974, 16205129, 149273514, 205225407, 984103384, 482325608, 46915971, 112526002, 698204581, 985735014, 769870509, 23587066, 331246758, 816497241, 417735063, 755506684, 384056946, 287854193, 651352498, 316285895, 734301170, 438300577, 813685254, 466187095, 744997108, 132352140, 336389235, 604950873, 517850562, 449840557, 923138843, 247753537, 304262871, 936434074, 150583455, 172885342, 73138219, 514111262, 154051255, 447694590, 189667118, 836505073, 493201418, 741756469, 203092472, 31690956, 981778826, 73767046, 568051413, 429089611, 977403653, 952200436, 14455362, 573251540, 191730834, 276579102, 70853738, 171808054, 208442406, 851465524, 532989525, 653667313, 752657273, 58946045, 272740085, 886739804, 112852903, 499398597, 864446296, 730620154, 81106425, 299526731, 900727649, 100505327, 299352481, 991008226, 723257126, 563137055, 878157515, 158782475, 588053481, 502838215, 408446454, 781625212, 21127776, 896622836, 918759002, 935425080, 61888471, 612182673, 177366247, 690155543, 115011574, 748249537, 655721797, 659690898, 228417059, 537151795, 842722133, 993917243, 730423320, 449628813, 6364244, 100039232, 117368215, 259066785, 645933208, 609097517, 405748786, 551432159, 600907654, 468230450, 950926704, 387420380, 688027441, 64837348, 983246898, 721375778, 330290051, 358806879, 934728758, 469044479, 493285999, 197978023, 615097485, 651161792, 504194903, 69153659, 648684407, 349740669, 131591369, 278256733, 453913684, 662163947, 617552739, 261153686, 723600336, 396672550, 995128794, 254881104, 437279852, 48798391, 213660407, 617865204, 147315456, 585408779, 56923662, 728651466, 584396128, 919784043, 680357374, 305368272, 11529393, 167379580, 116812010, 814682781, 329090073, 941329056, 66669214, 420872178, 811550443, 837222041, 567492099, 783575592, 710768922, 137575014, 710342549, 82981288, 987943564, 258456475, 468771019, 255983643, 362200413, 47502277, 289159318, 399635479, 442212665, 111649090, 872160154, 367896929, 913241122, 104593010, 742256538, 99382518, 721327260, 730778209, 11111220, 693491268, 77197842, 986255623, 817697531, 82676340, 170633033, 724107908, 139906038, 578055297, 379030386, 365378502, 681448528, 238487398, 970659682, 178645656, 219647130, 640016793, 193327590, 842854339, 469888791, 602792684, 896367446, 895790618, 736489903, 993802620, 431518449, 771225963, 424566083, 665618103, 393455369, 297188008, 902745447, 795308555, 122243562, 302527475, 401265707, 124186401, 655007361, 452165170, 996297717, 249240501, 327468149, 704503438, 885391687, 68148599, 786724826, 545753051, 853072026, 426870106, 89241862, 520261417, 83933253, 259308983, 164457204, 763768506, 441763015, 264510823, 838686598, 67631513, 916142290, 483325405, 579048898, 498085083, 476232898, 150605306, 867076467, 972788442, 85301124, 120540672, 617160931, 149817747, 632261526, 848427828, 688408611, 978732678, 849819215, 768518709, 611630648, 638240344, 135657907, 92299879, 332481787, 511810191, 28021996, 141540783, 65787126, 586562957, 269445371, 59233012, 599170217, 39434403, 623399301, 173620216, 917426988, 611925862, 269604200, 135145280, 478531362, 373128932, 364449381, 727537493, 578711396, 378809101, 78883507, 735615072, 751887574, 225407373, 92672921, 153629933, 181387715, 379259787, 758209495, 178626801, 251235767, 533765874, 855945630, 403543512, 561320502, 905203378, 851629389, 951733071, 404594014, 751693488, 139595787, 922915032, 789803680, 151577066, 719385155, 535058971, 375930054, 414477870, 687269879, 456160510, 580337833, 24528308, 90762728, 246767754, 621541402, 794846439, 141426772, 447790020, 164921437, 731591452, 578469376, 395298172, 569038719, 864626212, 339785938, 69146035, 771499393, 70689027, 59291569, 741811434, 961303996, 508605250, 548333580, 755747157, 633038155, 148848049, 668313240, 104373766, 350354552, 162936130, 296087603, 760609343, 862695741, 951721561, 995208806, 300108028, 392859482, 984989099, 750297115, 297797683, 631804731, 981318307, 574610714, 549598639, 140394307, 503830565, 259101642, 705520360, 820390021, 859915830, 846788934, 229133577, 767976744, 331844732, 69798730, 641436386, 247177850, 596697633, 697053935, 580017933, 214227730, 953002617, 618032872, 812231634, 402774115, 177987237, 636706626, 666118197, 24460186, 792776090, 563113284, 190520849, 622985094, 728732889, 583369663, 329377401, 871472336, 641861133, 293626715, 373799186, 35695867, 479155415, 254490628, 300750322, 692446168, 694321056, 846338356, 212582822, 157416787, 919545078, 842930596, 120076839, 313133540, 904954772, 609252495, 770173639, 859608129, 969925755, 16360958, 955212592, 44157707, 190278628, 426555992, 460422723, 452244153, 419159704, 387954827, 706823702, 78285174, 438956589, 63328254, 463394999, 296821640, 769584373, 498213425, 68803662, 986819385, 80218182, 167618716, 865524752, 72735552, 316623758, 974033857, 105271371, 758583434, 9717387, 70773112, 993343705, 347679241, 481037028, 185612719, 872345821, 431825976, 812570634, 395056075, 802189373, 290366213, 875480868, 633330130, 369201188, 405095154, 572545798, 833505626, 947939598, 359122225, 433202667, 80286651, 658519099, 952492304, 714907217, 32973500, 568352327, 279790242, 19065587, 962868116, 217880562, 837383273, 621240372, 759916378, 442049269, 253180365, 90834231, 307579845, 88943641, 747922868, 438782671, 258850955, 194207089, 281747763, 774629962, 433039410, 611661669, 481490435, 333595310, 900179970, 655185148, 135789128, 980194675, 960851715, 239709283, 246534646, 960461130, 421521249, 796831313, 111278653, 674136070, 749467478, 698566870, 695240956, 157281280, 619420093, 543026019, 578052070, 577949874, 534745180, 238719521, 704613616, 100786738, 422622127, 227634021, 891045564, 22568487, 134377904, 707191161, 134738821, 260834729, 106127363, 425578281, 276730987, 114500982, 708262188, 849744077, 8695985, 952519759, 426410880, 263097653, 748578107, 985301557, 227742037, 378878077, 659929914, 795359723, 526922511, 559456295, 552487088, 111622971, 39837625, 338800241, 129607375, 111359509, 247604166, 752502743, 620086098, 863923357, 493961085, 156780742, 467995463, 700596055, 365893473, 805388765, 414743121, 462166346, 755138510, 352275527, 863297149, 897246513, 533560236, 611620748, 344047092, 511548960, 538166882, 326774152, 790792184, 969759827, 14228468, 790569648, 656749223, 901574409, 121474565, 465703526, 299275550, 204709903, 418016999, 940698960, 991006749, 859119046, 443194910, 137070530, 222897214, 54183866, 312380392, 780630321, 369682894, 2480034, 532864381, 32284294, 353630520, 585544937, 143995076, 876190582, 725301183, 418823086, 254447506, 929511656, 10249536, 965878678, 333852087, 859476766, 847392027, 548091454, 494615494, 951679252, 21496311, 91776224, 657743618, 303969631, 588258572, 746531310, 720042308, 456893573, 201306991, 857560630, 897488572, 657456847, 312885102, 604607510, 176237782, 760909188, 917764102, 538901744, 709228448, 163580968, 347078808, 280789372, 561588265, 949745639, 321879801, 481349233, 129357682, 287456062, 790099015, 503389519, 798310544, 647352229, 309257212, 234797849, 39635800, 474306494, 154174829, 521924648, 918597576, 464102856, 769510331, 724065379, 322714373, 360702606, 327708720, 272620202, 492824845, 291686464, 35709477, 521848201, 12818220, 665496599, 415225050, 734114117, 992139588, 547331410, 316797623, 703351064, 929752390, 787824152, 757360642, 256458546, 681361391, 450699039, 319461551, 44352269, 474536512, 46868709, 152686036, 386573958, 204094073, 825579934, 197151252, 560877903, 528503712, 364689940, 70620046, 659869127, 724771240, 832810343, 754116596, 49426883, 267241002, 747138124, 273144391, 478277993, 453790794, 890766060, 847152275, 262720034, 458974246, 679028981, 520702921, 483367399, 981746812, 14028504, 176728008, 658791441, 875735224, 467407109, 468214839, 269472309, 268261275, 73363443, 297967191, 54907598, 974938344, 17806392, 292662532, 895947619, 840555959, 884385441, 841708894, 257746916, 489857544, 232996929, 190619201, 423022793, 743083091, 438058220, 554408149, 111880559, 965219302, 668017885, 823259574, 472428536, 813910760, 986702605, 556845780, 433579323, 927368928, 473608965, 166680194, 283332311, 355720431, 128215598, 173709844, 163856707, 779657383, 780228060, 553135678, 694035129, 492397970, 350727737, 517127464, 878483215, 219748709, 207253745, 514304549, 431027779, 387991334, 461610399, 818427897, 847103398, 978515377, 652539219, 982444559, 993615212, 850571612, 960687715, 48944000, 742202851, 455882946, 21496059, 875233018, 596427840, 888015296, 846792885, 745388990, 118447504, 191973880, 64382136, 703577285, 103252524, 690054196, 308189091, 897929584, 872710586, 112274640, 767463251, 767290138, 952724760, 291311206, 352014967, 632984407, 501905941, 255121980, 593074290, 550734819, 553622678, 319300726, 682151721, 491122144, 795700186, 36869078, 303956606, 325317411, 327520520, 183506678, 964994271, 441377748, 932875058, 382431616, 511306776, 991732249, 967211389, 335690295, 395306130, 379167293, 481793903, 90409646, 114086824, 621442278, 241472451, 90190810, 968244321, 659585256, 296379969, 209416969, 384473440, 844575369, 468856345, 101260546, 811652275, 462950044, 93861448, 901433789, 223030023, 628211323, 881718298, 379607418, 331955406, 243841695, 124533777, 49155087, 296264050, 710571806, 58593104, 463893355, 730268310, 457565437, 16552135, 651497092, 93997826, 95881278, 959670066, 513667873, 966289241, 336946518, 863090289, 316675647, 369905251, 240966169, 562203917, 254819235, 954523195, 406261168, 989704716, 811617148, 805942349, 669298573, 922333436, 495766959, 768022814, 346283329, 80665061, 527444685, 515437651, 56817497, 174867389, 510709873, 983555850, 768574475, 506938762, 915760168, 715766339, 480193700, 207145374, 691764815, 892287236, 396738393, 150987107, 814119155, 736722811, 113129493, 135182635, 546307251, 127435873, 830569372, 291188992, 736971886, 960467793, 791057203, 911460590, 69528754, 433324528, 907867001, 780090987, 139382960, 801165571, 651259270, 521507548, 436751795, 153808064, 509878617, 567196036, 537556510, 776338834, 849023999, 340222502, 415929831, 736333387, 241422204, 219298991, 986199650, 289741199, 648777652, 516108253, 444615167, 783980859, 793363357, 676120389, 570184159, 819033135, 75535488, 300066219, 773278827, 451014167, 185068744, 164200345, 805605623, 77006993, 937996921, 843320920, 367229113, 42840142, 610608164, 10972894, 964124946, 558898715, 226164289, 348070882, 561992089, 610678903, 363948351, 294505764, 111587811, 80006759, 229403605, 909993966, 929850367, 732102768, 17040263, 728766037, 321227193, 767600099, 207661541, 464910357, 232668355, 450946302, 966684884, 782808877, 897993721, 465118310, 124561280, 527900867, 725610669, 194090322, 179788987, 707062152, 160728261, 973048993, 921184038, 423853397, 870466952, 742677869, 864580595, 201523670, 235766777, 704388351, 45917948, 193774480, 905296432, 176894635, 236912686, 614488260, 962052167, 674555229, 922119958, 701485511, 904012554, 355469519, 142567181, 102625984, 83532121, 317432383, 535893663, 713108608, 255708417, 826352987, 617926694, 652586716, 801788709, 268511627, 381245261, 478063929, 726875318, 850366219, 54454013, 835225928, 6166094, 55866645, 551548516, 698483712, 770704894, 870096613, 308675252, 553047494, 922311472, 944040560, 180288397, 646407218, 188125223, 72463609, 415461677, 803015332, 993367544, 827036484, 793395299, 327229055, 911109358, 440305471, 30153036, 650239477, 441164598, 205119301, 244069022, 972503849, 762679101, 909836228, 463363925, 596615288, 393459699, 973990140, 661772404, 983770394, 222644062, 260850523, 699712164, 834288108, 896053421, 804953673, 361108198, 764260449, 387786231, 876055102, 733912460, 496327412, 28906063, 742522280, 835899426, 167001884, 721601621, 93917791, 17744687, 704978276, 630176563, 138389261, 673890514, 956990842, 657980310, 632674839, 658423364, 346887378, 96958369, 792655726, 354000256, 434244671, 612020773, 792019673, 145949764, 350556720, 88502093, 816843348, 235552278, 754323284, 497443103, 55318948, 867055699, 773683539, 788552042, 351513256, 605329669, 985896236, 796044510, 18318804, 361584718, 568236444, 993887814, 629974510, 14056167, 216664654, 986971943, 781163539, 534481592, 418460557, 570205087, 742816843, 836692632, 666841808, 933401201, 622046792, 971313156, 796600480, 13794002, 419957322, 158449101, 997450624, 414974852, 919851708, 672868381, 174892855, 280972602, 272482210, 927609504, 573587730, 676339321, 332036593, 153071535, 511270624, 432031659, 569789161, 621456789, 737839181, 336933984, 330416480, 455615059, 133752696, 931141544, 477683891, 924840141, 274965781, 870826416, 561586854, 409846459, 756537093, 267311638, 90623554, 26533151, 330369024, 587476827, 460760665, 977740816, 343299788, 295053106, 791378913, 720355053, 280472762, 806856571, 211491855, 884357770, 902008889, 557880149, 124419528, 680573207, 199985189, 599242259, 459787465, 893252389, 775922515, 889571665, 815978086, 999775890, 546735512, 693730544, 884889311, 504429606, 570431720, 301654576, 109074769, 620793591, 106852855, 950285865, 636998811, 948330806, 434854123, 76336199, 87037364, 126875410, 257404116, 415957109, 450901735, 982811168, 652813311, 96789243, 479394058, 402027280, 804418577, 256750393, 310122095, 550095414, 213343238, 436112674, 970157153, 347627411, 924751075, 263324922, 405989909, 953672635, 395130854, 220216423, 598098972, 390486101, 570305912, 147127222, 135162789, 910814514, 392825345, 199228979, 904056378, 706822341, 796348124, 195651094, 55090466, 51404839, 831242045, 71053383, 706793573, 365404648, 910864736, 615848151, 14040903, 533191573, 256059452, 272224994, 650044067, 955263900, 463962933, 288567186, 1059290, 362518991, 238664170, 215464522, 578581578, 410088224, 331716891, 598103799, 797007738, 542060965, 890139565, 409733946, 489382288, 888577990, 932370496, 827881207, 914382843, 858649374, 591942253, 333184193, 200447622, 785482464, 293449843, 873016338, 817529732, 876038335, 642151293, 553193932, 733840042, 137977518, 918846105, 521015156, 49644976, 93574011, 561348823, 141279894, 194024133, 584145723, 710897726, 857903368, 870621594, 747637295, 203142752, 306547309, 479038854, 73282208, 524282220, 580600766, 722359618, 204874237, 570956293, 533566142, 142645675, 519885631, 197606526, 814260815, 318093659, 800481754, 440490494, 192718433, 179352440, 344864854, 506132428, 304563239, 438505945, 489082912, 107544023, 478909596, 562705626, 736609117, 216374588, 995382803, 255321652, 132167848, 298973257, 866391899, 540479898, 227036188, 630809582, 817532550, 332810716, 146894316, 507054191, 444362786, 667965827, 923634961, 877880578, 249989192, 14898486, 539826443, 547889572, 806756175, 532262933, 813127498, 720254853, 205195315, 862492372, 810737066, 584878575, 384203520, 119141621, 683663171, 195928392, 453003032, 304067196, 476836096, 848749725, 835881380, 585873030, 727565936, 285477434, 757326406, 568507555, 682082937, 527848281, 213205650, 221152408, 911706457, 70694944, 815684282, 303822894, 198651827, 609528639, 757159847, 119402432, 332766224, 70520799, 183107082, 6015025, 269223199, 975666668, 671034337, 608343774, 7733205, 842929343, 399400795, 347397681, 924393384, 387948451, 343177287, 511796746, 635489005, 478992215, 914824459, 720655351, 463371696, 442116776, 563952720, 349628288, 238306824, 145787247, 397392068, 736871573, 609284354, 261778891, 837621769, 972229118, 316662297, 446242402, 620364484, 285759421, 102391441, 49821084, 529376411, 301346556, 792725271, 752847219, 19606588, 68322406, 926562896, 875313624, 940141258, 805233937, 866335231, 464119828, 774249769, 542626114, 260300869, 160131392, 297259556, 682626302, 380514599, 368496145, 767287077, 51033754, 808085364, 720254435, 585838696, 164936849, 86668194, 539292703, 296739006, 382410329, 666651647, 164146624, 727629670, 371562736, 791755799, 219879086, 944776441, 65733122, 879686581, 783187187, 535438748, 266398843, 346960927, 958854889, 887821383, 48848797, 375664882, 6601841, 264275589, 729837000, 25363950, 3498445, 770362583, 644998548, 375989318, 606002411, 835883550, 201580326, 317441248, 794211481, 7210717, 398879694, 716682770, 368251954, 695270297, 333999755, 141600013, 737554884, 293484900, 837672634, 129245889, 867573931, 580119374, 913999056, 764820265, 336516332, 859998647, 943239384, 96192992, 63360356, 381230045, 588792549, 132859371, 270814525, 512659945, 188237960, 889468382, 655075210, 207168250, 887929270, 609854032, 957974249, 674655543, 87508141, 143729067, 843607804, 174479291, 941145656, 495220403, 329140743, 240060384, 551948939, 61941507, 339744783, 98641702, 588902916, 214292932, 757280471, 556616858, 72817925, 518624794, 775535762, 101996668, 176516478, 971544746, 547494665, 463165568, 321972433, 701479274, 874886829, 555966677, 544814220, 813284662, 588066396, 370057978, 736083696, 667295787, 809087215, 965708412, 730246651, 281855061, 139316966, 299372089, 395904154, 683438244, 694566403, 105505448, 348098169, 397986618, 924094929, 642083120, 73421702, 297964295, 841897137, 478519716, 911628904, 967770471, 28973035, 395502229, 724202687, 905462666, 651720743, 628622317, 122192207, 203924878, 793303119, 810760931, 172610033, 359557007, 617360680, 869123641, 284859831, 144335523, 776337900, 910500686, 401805191, 636162023, 352156631, 855188794, 223033767, 567501411, 229791377, 19511173, 277302825, 233289092, 37791261, 225142993, 874685244, 187126225, 285846969, 885664904, 902428605, 266335161, 838086798, 262776164, 238701940, 288447789, 458647171, 481152043, 961482773, 928311384, 580161094, 869304570, 300777512, 556127642, 473857967, 930483027, 970645309, 707434368, 170131100, 549346706, 272578009, 509565345, 613173892, 751359362, 725817754, 659510236, 864752856, 746221644, 421993953, 190999588, 188287770, 142430024, 351920374, 863812543, 400969501, 246038929, 962933934, 53744872, 121665871, 79737161, 136023059, 626507177, 90281498, 688596628, 58943141, 755285157, 293290127, 292342583, 883364655, 850394396, 491632557, 899684436, 395748263, 790468351, 414579929, 856719364, 882938687, 794211192, 206940108, 776736, 436575138, 484895259, 773283766, 8809984, 216748895, 295492106, 14140123, 373993964, 561753250, 171520731, 755408422, 203087322, 79068990, 779361578, 701978894, 555537656, 54771459, 757119820, 88715750, 770162915, 810108319, 342135890, 255582108, 184074599, 496315337, 104908941, 261996669, 385084151, 23601665, 323424138, 523690595, 108513093, 916676162, 564261066, 538450577, 451984897, 642241231, 504349044, 496645380, 716090839, 588371860, 647878070, 563635501, 807122538, 981303916, 398496651, 126180417, 275298989, 266693423, 56712929, 789285936, 376628847, 350133807, 942731597, 497500127, 99103108, 727154939, 170009926, 788945464, 60662061, 820865279, 464411818, 341126122, 483255514, 766219160, 180027434, 438228633, 10098450, 942084823, 175765207, 844732696, 632544411, 903236096, 353992117, 528050515, 579129079, 370208810, 753424167, 39569493, 555857383, 259808505, 715905470, 298445642, 909354154, 266350409, 520368776, 915685683, 458575255, 800979378, 75292975, 641367096, 834155316, 816108094, 654351668, 235559309, 635033025, 312306814, 175956998, 796688802, 630046553, 798923836, 433801005, 464146382, 160117272, 182340545, 566891216, 308334382, 26295098, 581610815, 942746090, 342711479, 572575106, 653104220, 359339345, 845599134, 342903346, 865015279, 436986773, 686093031, 618478741, 191845648, 650935906, 268928361, 594754478, 360666637, 706535463, 813415878, 156192596, 565892602, 848411844, 783422241, 105077991, 156041502, 636858751, 636331427, 700346479, 248281495, 385890794, 33781830, 588304430, 925195974, 815650634, 506272131, 92660242, 380973580, 790562096, 920622579, 849722836, 132468869, 92935171, 163324983, 701790704, 689308168, 605351924, 193882497, 367335732, 864985638, 233641662, 524703629, 246369392, 457228461, 881721385, 444014121, 925581040, 457923535, 995187887, 737543077, 843686909, 216597861, 138643448, 565917668, 969636024, 842805996, 840971129, 828288937, 761149897, 348271281, 695879940, 667216424, 903078258, 397525531, 934141886, 993730584, 4735899, 494938308, 800083351, 765941201, 637401606, 900966734, 259622531, 509520865, 266745640, 372963788, 82126517, 952387819, 500370389, 268041591, 547069513, 104089501, 616935628, 403831475, 629897579, 884044426, 746762132, 556187222, 107407339, 294866649, 896349578, 710370968, 760426145, 58412972, 251911809, 76989223, 756885335, 685195342, 477546730, 50980413, 686045585, 840529210, 46135819, 332345562, 377098078, 745226509, 5322720, 50705096, 690854733, 570300016, 151279462, 732648774, 580042267, 695880737, 686789789, 586312017, 955153493, 627818876, 531479331, 226568966, 759247414, 133215932, 66225957, 334332781, 531015000, 807190510, 950382481, 757014042, 553926409, 218062721, 644950002, 336314663, 577558395, 883442078, 889175168, 807044813, 506442050, 464418522, 327653887, 213474144, 326829266, 836547073, 295916132, 853832486, 315986389, 218437138, 542721607, 476637614, 506837195, 502480932, 576360738, 912684430, 574035845, 187837674, 18796986, 521066136, 626115837, 267716830, 365875508, 946134001, 327778673, 42723681, 610404364, 589200680, 13113228, 248531608, 904965550, 926571901, 157924153, 852625222, 253068432, 942970458, 770971644, 841600990, 913283778, 431835096, 127701545, 478115772, 774894189, 43908397, 617756480, 274266143, 777205639, 48436117, 307443798, 306538936, 510728881, 317678196, 795395664, 621593057, 688247337, 976029814, 327993277, 948440397, 480378356, 966690718, 665809615, 100432262, 976857390, 886332098, 873476823, 564751098, 922164883, 89557981, 714268503, 579357314, 719971399, 623545657, 201893267, 133982505, 958366251, 188136455, 111128181, 331798975, 691408490, 28831126, 6775001, 389199668, 146065215, 388435881, 170763116, 942650367, 784902834, 859018783, 40091388, 408170389, 537755027, 91705508, 897836136, 804538818, 751857422, 150722947, 252292879, 906764829, 876861903, 572827041, 774231497, 966883782, 600669538, 60727346, 594849838, 137369791, 60151235, 279548987, 740482972, 365022610, 437421257, 472472776, 325693648, 462659347, 901939347, 329549203, 690609580, 432205164, 9157621, 742222914, 867716465, 391176607, 142824827, 919797755, 29422219, 858212791, 113243081, 515206347, 123352417, 124310355, 581902871, 692955514, 193179223, 120947612, 780667084, 195845686, 282668929, 773399011, 902370267, 72743490, 447927540, 539970413, 202279126, 618179301, 757727971, 805236810, 587926366, 913086970, 719864351, 253084109, 21846546, 148016384, 177864964, 813811611, 177037415, 778026288, 905864225, 879014793, 319163686, 685948883, 816665283, 339084004, 899249783, 819146688, 527436856, 513870628, 788931159, 568653060, 34991929, 996765027, 920518752, 806700487, 959821437, 267997479, 181919380, 139427519, 322837696, 971247558, 898793783, 141034000, 47064671, 651861915, 35086504, 166109558, 528392704, 149618522, 262414755, 614472139, 486647147, 494254189, 245691628, 225397917, 771234796, 493281498, 429754018, 369102842, 284504182, 14066854, 922998025, 387087423, 401124734, 813784588, 523552982, 888063375, 2780235, 60383251, 184399857, 908693674, 629022306, 809614407, 909270088, 251625985, 430745056, 720630766, 246860881, 198878428, 757951061, 733440638, 736131215, 699313932, 337243294, 570704448, 364204858, 456525009, 954981464, 404334987, 705495032, 686919890, 216412449, 390528199, 383451243, 132400905, 261934898, 341733037, 985840218, 974034486, 114271227, 857894643, 534596624, 931659514, 595085799, 32830291, 39647797, 654163924, 528855273, 4163342, 290230882, 408652105, 536093775, 667250961, 389917672, 629092315, 999450648, 971476784, 480046574, 862846223, 520726960, 711900, 551892082, 927149816, 445714364, 920633995, 916583065, 768716360, 496190617, 891421291, 76197819, 714388753, 638722831, 933063722, 695983506, 213229474, 343888563, 302442438, 544403001, 131198613, 745325242, 100701469, 591768667, 400415060, 507407809, 865193032, 116359748, 899145702, 944023234, 207155618, 799655861, 345263167, 418005088, 411897764, 672510429, 22600415, 118787049, 998737128, 234312040, 781997429, 769722754, 831316579, 712871081, 733698423, 598778664, 220907032, 271960907, 957611509, 208440159, 861577264, 967238881, 411625980, 586601042, 31719116, 272335531, 600581978, 470750673, 987950526, 261726094, 467273992, 901983038, 538611613, 225652353, 793254257, 204180096, 378716572, 664448740, 693881871, 839899577, 764475526, 266600222, 929501041, 507376520, 250116696, 224669799, 457017903, 133196122, 924703312, 26239488, 405843737, 661202830, 220200731, 299764280, 639979754, 679137159, 485513356, 63525400, 660861265, 723051326, 194234073, 6189175, 4940641, 904873142, 493982596, 411368875, 745562888, 331404346, 509906787, 954521422, 32640292, 404850513, 701854898, 291710210, 690721043, 760483851, 637314822, 525861163, 593861334, 731510714, 111100769, 148725503, 951950588, 268641578, 655813636, 286432518, 728031645, 653033289, 154437464, 678105744, 990468424, 978122233, 925627685, 720559438, 802092890, 776725803, 973222759, 179535230, 433444836, 621585749, 683431896, 891600330, 153075488, 716239588, 363697568, 549660085, 734964305, 669861153, 337284999, 93266559, 279733320, 980731461, 809775392, 683093364, 113578100, 364170401, 826625648, 616117392, 601229389, 844131111, 996589078, 72602323, 871903812, 682176966, 571741668, 777999223, 244639293, 999577531, 704164217, 850885214, 561120263, 150580631, 110025599, 474258865, 479464651, 665203750, 983236011, 466079958, 460144500, 389127370, 746427865, 81175346, 141635259, 772278259, 522949561, 999375162, 440820155, 716541506, 693346353, 640408470, 630615834, 163022026, 393668813, 616828456, 229131703, 2412587, 12294336, 513863155, 140876111, 431352122, 34883960, 448972095, 140755480, 939015544, 734235693, 551521290, 396033048, 4149768, 727955208, 414964435, 947438184, 876884060, 326702095, 626269364, 527686663, 405861532, 657023516, 728828355, 258733585, 876808207, 243000351, 866023334, 412330504, 530377894, 785068463, 355837179, 653576374, 222767463, 570908155, 640734930, 949208833, 38831890, 731920276, 848804754, 695126396, 455630591, 498936699, 519308347, 82109727, 238067085, 218182478, 139574790, 180429266, 522210421, 77527403, 613613492, 590838697, 11926175, 502335492, 308404094, 616437276, 761371914, 184977032, 782059846, 280001309, 11927892, 524208726, 686121466, 858651710, 547028887, 624696561, 774823572, 472480839, 124316134, 326106526, 210819929, 644884489, 1343671, 245403188, 334936991, 262543185, 321538591, 716393651, 917848660, 764160243, 169767408, 609768419, 900707996, 998511126, 983039154, 450174782, 55504538, 547114589, 537939590, 103579505, 89764400, 499060390, 637576283, 922462861, 623051201, 270377986, 890402635, 262701236, 467001171, 159044112, 709162711, 815222942, 151003562, 818775764, 488131936, 848624275, 71450854, 745112634, 262682477, 37924678, 534928391, 665564801, 102683437, 846203906, 291332406, 68849837, 415595672, 553769204, 845982950, 21588256, 813561246, 240195245, 989724376, 535437375, 600102086, 451751172, 674976834, 313770734, 822853548, 600821898, 650905106, 641246955, 218427387, 224391087, 754727151, 681521127, 667766811, 244880664, 362950515, 733244051, 343444408, 967469830, 149423327, 719201383, 182089659, 986203540, 29011796, 870498989, 171732664, 514743605, 375666054, 333608574, 138562039, 862404750, 719025887, 56009660, 682539953, 746036723, 785011749, 665312701, 102991323, 109988203, 433332181, 449569210, 543381559, 78360608, 229422931, 316273687, 653128913, 291118305, 367033528, 354710556, 500897961, 219233984, 226576592, 838930779, 417459117, 292845441, 84602220, 675175188, 945473021, 517845033, 648078998, 160207906, 648649914, 375160597, 606199996, 471183966, 954393555, 689794053, 431031433, 150102334, 916610517, 905777587, 360890199, 850899138, 240630736, 443669701, 48433269, 824372388, 425664823, 285703100, 305334223, 361709041, 717817130, 179000360, 22945206, 346908812, 649624837, 20170505, 712450518, 363814046, 923670183, 638830024, 61696735, 535131671, 642997116, 149404229, 404135851, 825685775, 941723964, 489770264, 491059513, 225953857, 560213359, 37381747, 478195287, 62289684, 43088982, 511633201, 13573168, 590983808, 861413758, 212187091, 28766105, 88573500, 542767436, 814761843, 106149206, 109265322, 168139134, 39588156, 888956027, 963977908, 876801940, 808538325, 796205940, 98901023, 553111699, 251371369, 925993364, 275332774, 353717302, 929306911, 149942386, 458059983, 958895709, 296560809, 978477384, 300483889, 37755941, 752542151, 217790131, 498041350, 937603851, 145536104, 418403807, 523162280, 79565821, 185879672, 278844397, 285640054, 804754853, 112479171, 2861596, 462200381, 636694272, 513904413, 157177342, 836280404, 184367370, 39289255, 403856351, 610344408, 833280427, 181347066, 335687503, 462679806, 676084168, 62480982, 318662902, 201889070, 116884043, 680246875, 553070118, 671074635, 267975454, 957648018, 421946304, 857712873, 273649091, 529741171, 415926534, 528974234, 802612655, 399987876, 846844985, 309698160, 775507669, 903684035, 165577354, 839728227, 23314109, 580507739, 518326716, 339349883, 322917474, 403780146, 101248936, 183351208, 485183992, 899287009, 230216388, 476153534, 476180881, 126872321, 461482354, 209826151, 202199348, 861283539, 443326814, 140107613, 865756176, 766226341, 424330470, 717028809, 498299923, 608087393, 780066013, 998012147, 277589888, 636892530, 915263301, 960275975, 742789189, 869125153, 828401347, 67305991, 401508942, 266211210, 391178858, 999604450, 99821455, 669502030, 671713539, 43271555, 258296097, 246353842, 430770486, 60303, 223469743, 159450586, 27998647, 338201520, 795043157, 247235419, 268633373, 612391187, 181564339, 52570901, 236386178, 863242103, 7678825, 473458473, 318010217, 906646618, 879691340, 966178235, 75780991, 370824841, 116624861, 576549259, 944040769, 986195432, 824554420, 679196196, 799126052, 587662237, 561795735, 42355331, 108984884, 407828316, 465197912, 966481559, 893227525, 6795154, 746807368, 956601637, 842362556, 788793565, 825282315, 294503251, 66141413, 501306726, 554349921, 378508021, 67255273, 409932925, 132510741, 839067377, 544698248, 425052546, 454631494, 253882207, 282033677, 473613276, 409123796, 212259467, 219507552, 432051513, 134552237, 782589502, 104587457, 805099852, 621686092, 307677090, 149127423, 738555759, 37091998, 326275650, 383234334, 806427721, 751437504, 438843618, 520928746, 911631242, 202301160, 861926799, 326322946, 499263980, 828409281, 599841411, 867420740, 925785656, 28711916, 906146755, 649130256, 874456776, 617574247, 516321250, 971095261, 103859731, 197436243, 690601790, 777983924, 831308642, 499837113, 342843208, 866153407, 32770461, 215641641, 71436856, 581312876, 146890445, 383187688, 273693177, 724837601, 551716450, 494345814, 39520618, 680201151, 762771021, 956022376, 929320618, 509370460, 498283605, 160713860, 191768148, 586313956, 654163874, 79916786, 772788632, 422138495, 907028585, 733815728, 920722380, 914763921, 868362416, 148485132, 903114571, 798150975, 67457889, 646387851, 99708242, 632239330, 278591696, 179592392, 184729438, 287806359, 407219041, 784718253, 69721491, 930354925, 895201432, 687908854, 836338718, 589228052, 300509746, 494516678, 206697133, 378463131, 490352449, 693472309, 409918506, 220644021, 828277036, 173914740, 204896122, 606243202, 40301597, 153552096, 974330964, 660023490, 716079297, 815684250, 103558465, 982664142, 258809696, 152641969, 202591601, 163899103, 994906817, 585093459, 683591612, 201003775, 497576039, 262522396, 37828791, 277369834, 900994408, 506017878, 844237799, 723699604, 233804001, 899089482, 466561118, 528040275, 288406710, 836203606, 785980489, 628655494, 43261734, 207115046, 696365649, 705056529, 683643403, 641462721, 371512969, 834555095, 201393204, 879007237, 618142198, 549712120, 458219540, 717288811, 34860271, 822273050, 227705657, 525039836, 859952718, 254644020, 947105971, 142810503, 446633396, 780695772, 731581263, 623257091, 312551899, 233721043, 93523055, 437469135, 378941459, 160391489, 196704840, 77006501, 709463535, 419702806, 437283271, 295170512, 614120860, 936408982, 347034594, 93382315, 695423766, 270139380, 252725, 803344799, 85225899, 427296361, 555323618, 233133837, 918619780, 797357979, 352315640, 403758121, 699335142, 233637578, 344511428, 950881430, 758192197, 789669696, 205468194, 285105309, 197163772, 312368791, 621913299, 697228543, 875245373, 433117553, 284384640, 470179353, 8444376, 208744058, 372707189, 156194697, 406743001, 434400566, 364687364, 594968395, 695397211, 55948840, 683344559, 979069432, 534293505, 309084727, 187051626, 816628362, 978579426, 265658374, 600880858, 296245550, 542424593, 110739241, 10276331, 91621325, 388370316, 492914032, 276802354, 604366877, 623452743, 806858505, 449146410, 313894710, 886503824, 573383623, 855827797, 193668767, 386068605, 876146368, 675023967, 15696195, 24256176, 660023795, 30181978, 17584916, 691445663, 874281186, 767821870, 569342509, 935431676, 150373153, 563667042, 638663738, 902389347, 952013547, 898338050, 764972961, 260241056, 258424481, 174044528, 454714853, 142911426, 189317039, 486892826, 451274134, 967532401, 469461175, 226186167, 873568232, 24899818, 965102317, 642284849, 515462306, 508830842, 560504650, 758749914, 526600173, 413889574, 679064381, 219209453, 796923916, 111804355, 282087985, 236881997, 800834230, 525042374, 228058331, 893366181, 371136683, 909719192, 641056845, 97410286, 302853331, 810993527, 763514029, 306961333, 699679877, 257896013, 806565650, 537709563, 876754489, 748334113, 81995219, 157881863, 140842264, 670282077, 547985458, 64513214, 405928609, 994525577, 376947787, 304233154, 915511490, 863968649, 873667084, 122461715, 797712349, 375774139, 897830234, 971416937, 186664125, 107717316, 887630980, 378935547, 552317867, 823875799, 271799030, 549100442, 750932927, 181122136, 683205237, 953835599, 799411681, 161647711, 518973034, 458722690, 29111485, 726813390, 711840987, 758857822, 573611555, 90038192, 345107778, 299452619, 194944513, 4666924, 782941744, 54925165, 305996020, 469147598, 887746949, 348483533, 985127971, 508548865, 151477073, 868536934, 80821492, 933206658, 179469716, 425829410, 893897979, 34667461, 720672741, 160143784, 319860638, 198799829, 785290106, 145639426, 764012831, 540715677, 410956625, 391885080, 466611052, 874019715, 484318287, 50294484, 997290875, 399313346, 852020155, 105152784, 204170844, 219260526, 158512409, 707395269, 153696777, 287569801, 620145605, 482753765, 266302509, 215680523, 199117104, 743997999, 899779784, 950991754, 622097178, 420341233, 463516342, 501647306, 745975833, 113018382, 960022410, 291602574, 263962459, 188116449, 954094284, 382849089, 46590717, 348069866, 485389647, 508458554, 89525595, 233652481, 696516926, 24321184, 163872200, 735951302, 300226949, 248741928, 632317909, 136282234, 143719374, 975195597, 55208784, 564752192, 981124424, 223828321, 538830707, 711313649, 66974071, 437098027, 336175281, 590238409, 167356767, 526276073, 514768947, 868519304, 221412521, 816670724, 18801863, 379524911, 883331803, 242017101, 893190695, 82237653, 934864756, 852672273, 416459172, 246374481, 741868360, 280981989, 43715295, 405549333, 415067929, 820035538, 544928107, 866603690, 503156359, 547226788, 97248285, 22159204, 959837922, 403646071, 488036984, 345874502, 653887929, 189576369, 233490135, 478231519, 508179005, 25340513, 26478687, 810417562, 730620894, 607298558, 560947072, 235915960, 398674805, 565106168, 662628926, 312399783, 754856819, 585232429, 597194457, 305675515, 74459999, 377900109, 522643437, 228637621, 861375469, 336670545, 448349245, 829531542, 13531289, 358909926, 11563703, 538337238, 929960995, 192173963, 939460069, 8389419, 890620625, 531532432, 258499297, 694712933, 264653999, 386159160, 448095995, 67838328, 981277457, 348170804, 515999819, 262238375, 381082040, 572959823, 294562831, 87770856, 271361957, 591427066, 563210504, 70251544, 318825048, 530836914, 574371096, 396777387, 320126943, 497018950, 598846491, 438541602, 756191772, 853387698, 411348887, 908007414, 671603185, 269756636, 697390505, 369766151, 756858016, 956197792, 561950482, 404392790, 716221604, 43246742, 624350133, 526883941, 818821270, 365755519, 258826429, 898101016, 664534882, 259303149, 368628354, 37404244, 848104107, 745110804, 381716125, 339951589, 586708010, 454065748, 71316035, 515206090, 237836906, 968014943, 565825718, 890667493, 31226507, 508594272, 50955851, 503890031, 564294466, 197712730, 274175372, 593339530, 305436426, 51776934, 417045366, 690567719, 722347073, 121887735, 636846, 512102589, 718907937, 160650633, 414966735, 574292294, 260747385, 191997848, 470374250, 946488980, 641494831, 56205254, 932319973, 887660777, 958753808, 442171022, 589483473, 725592812, 244616412, 117573291, 647070249, 565860621, 858831203, 553639809, 56040835, 118411056, 164407534, 322194030, 419610972, 666942108, 25802237, 221901613, 39840244, 786745379, 676336474, 939300035, 334930840, 121542381, 690663717, 191409310, 283016110, 795501849, 282921733, 362047173, 377572928, 378480347, 316194427, 633424204, 249498490, 249628144, 895488240, 141289038, 272388798, 39463673, 45049505, 376528305, 210179894, 4017612, 765645235, 204981814, 135735651, 571614673, 113738763, 990547483, 157829164, 118386828, 341141042, 354510356, 394922004, 449842189, 871555953, 699194617, 670042312, 447279936, 582317882, 1940768, 98273502, 776115414, 78997919, 190916599, 802764879, 553454346, 103954446, 835339133, 878234966, 854172638, 310481275, 566555306, 4827650, 254452092, 829095682, 858395929, 998156182, 414121733, 576247307, 981597730, 865373827, 490714776, 496762144, 491743134, 177607724, 630245385, 893315060, 732826454, 488915486, 533315707, 135071200, 136067571, 919534489, 542487929, 706386933, 590939102, 237893857, 132938132, 107694361, 328898991, 121484995, 277681880, 107860831, 336585002, 586712386, 273320974, 162940780, 159093931, 210861603, 390443515, 174031772, 947755415, 528380380, 600438489, 470851073, 22642529, 584317181, 77828744, 992573789, 501604831, 626911249, 794697508, 525999330, 422097790, 7017574, 449625986, 100410684, 416624579, 545678797, 1265032, 903335123, 249187808, 68331025, 385538065, 831521089, 93135389, 687373064, 806324465, 890752633, 63069127, 999375199, 222994774, 703575047, 866218339, 511820586, 183420397, 158491556, 272519360, 224179399, 537460989, 159633697, 747610142, 392291181, 499851857, 800942699, 94209326, 538402059, 86791634, 199726542, 496071039, 952316915, 911925699, 180388437, 561989133, 389876895, 754982287, 554988352, 561502683, 404442959, 185498990, 902861475, 235682024, 875047597, 353320622, 276889634, 753322412, 686129529, 817945105, 428840147, 469791041, 71218325, 329787101, 875838129, 824133780, 831832514, 379067057, 526981431, 226292434, 809213613, 222768309, 431381502, 400524577, 202870433, 845394727, 259955145, 187763726, 465121830, 346314649, 320618507, 665618727, 599905082, 754461801, 405389186, 857018504, 889477477, 651978919, 209143232, 569193395, 98921660, 361997820, 616528367, 855802305, 153283187, 237567371, 751406283, 593844100, 345130588, 599285003, 129063650, 113855211, 72587103, 590815347, 640765707, 421089207, 164922934, 385109240, 287810894, 168528536, 404808336, 486590084, 696469943, 608464094, 74467210, 838232319, 539089408, 396068999, 915599626, 362636577, 841602591, 580097173, 280703823, 278101088, 404871083, 914361822, 137309648, 268742932, 884288832, 43911715, 789872596, 892665295, 250479643, 577329952, 576315413, 506158942, 108852218, 504392083, 405531695, 534883148, 392198980, 882945432, 509397114, 471617656, 790704890, 411370532, 114382991, 372416505, 368471305, 226578505, 27875610, 53774096, 494946819, 50415946, 75099234, 269109491, 846265466, 861701084, 116827553, 346374561, 361055818, 895645402, 934792876, 850250270, 694812370, 787423986, 433399809, 245666961, 766188603, 23049881, 955543901, 905728306, 462235474, 82672144, 480670745, 741215897, 199563051, 385482569, 298635756, 851373061, 829327678, 189727707, 128912617, 963425809, 110802210, 990682153, 474363121, 871990026, 340329925, 482431799, 399925325, 255205448, 342079157, 715711859, 39847254, 904088100, 982786021, 478186541, 587438430, 330764922, 505339093, 860935445, 135183198, 769135979, 290394826, 389008135, 43429799, 982628510, 318762927, 500314578, 937054149, 487902775, 121372993, 13709225, 392449771, 162464475, 566184074, 531267749, 301477215, 624785468, 389341419, 385435134, 227322135, 801781926, 188104232, 283196615, 160365113, 581056190, 317857363, 865785190, 937913028, 126940639, 560715083, 826826858, 696527655, 228660818, 341330262, 490264674, 99035217, 956769417, 43415017, 626974220, 484739338, 398044696, 629066880, 511035683, 917652682, 816666236, 738289452, 562023190, 763721953, 811347185, 872413421, 298962947, 683302008, 806492002, 311288274, 758878112, 781642740, 546929653, 86838099, 347954160, 410800277, 708019071, 428796195, 240381087, 111249697, 470521723, 878004287, 749893101, 926115153, 766918872, 313384902, 282514125, 693559512, 410619175, 550574002, 407264197, 842111779, 659304626, 408802622, 365498663, 789707351, 889638136, 334285344, 494976651, 968668286, 954846953, 368720128, 760936126, 831181971, 552170313, 412087386, 572626412, 143030824, 786996318, 749700913, 762341634, 114337125, 628008929, 929185922, 934028724, 491686710, 771401120, 325826225, 202348777, 615107456, 273284693, 600543652, 50752360, 126805969, 614737460, 636765451, 647109158, 94437640, 788397681, 284207207, 382573419, 929742652, 175298806, 716723880, 108141843, 166305017, 616313653, 74722255, 555618663, 518007720, 586481551, 651507213, 488005339, 620294443, 717100095, 9717322, 357740149, 671767197, 910916252, 424069911, 599048828, 869717096, 529228725, 469225815, 515460374, 594338267, 520333183, 541090644, 912264580, 904337760, 231987686, 862786820, 802363828, 537763354, 858161862, 792479596, 852123267, 859618453, 578460562, 215256569, 985573552, 967853472, 646617428, 91309097, 862662274, 110458276, 662116844, 693710585, 168520340, 432655071, 932398443, 976468558, 68592319, 721838937, 730171891, 248385497, 708534510, 163710167, 292095449, 650717376, 384781381, 743704575, 967799158, 323357458, 682193918, 274946255, 995632778, 269137745, 690331831, 359002061, 938163282, 700167185, 441672117, 106606811, 599862772, 634798515, 994372954, 663848195, 594144281, 927632734, 551702665, 329759823, 490147282, 859850790, 760227946, 453739783, 543959965, 579362595, 823994490, 722053778, 677036864, 449909459, 495166545, 730780537, 155549731, 335369447, 570066131, 704098367, 285469967, 987132026, 559732429, 540410959, 159228312, 565909814, 895746125, 770040567, 197382773, 78676379, 953438936, 603004260, 500936672, 218021666, 108803126, 962280751, 493199984, 275799633, 655325422, 117544957, 67882297, 832840614, 895904863, 161439503, 193914677, 999811802, 271184450, 223965536, 321557566, 604804816, 464713825, 416286916, 717398357, 708059032, 592207029, 140214521, 941799187, 319151700, 15291444, 847182472, 417155278, 863201543, 587064960, 238506183, 836526635, 249795870, 81061827, 272359471, 545600756, 371697085, 763755565, 232618784, 426640390, 402728803, 226944363, 70831802, 82494286, 47171629, 763751272, 877549282, 305117867, 138828288, 755795023, 289702146, 678986457, 871810178, 67193163, 120052191, 954786038, 747466406, 370056051, 316177627, 678620700, 479497118, 251778792, 151857509, 7077282, 804770544, 12116986, 303816762, 783125253, 350517603, 46967405, 724105147, 547380804, 666863832, 807569095, 40346021, 800106796, 661559140, 665173898, 280463093, 31074576, 322138290, 599321817, 725887140, 243145555, 760727039, 915643557, 747028016, 361042556, 894809813, 577086541, 989451413, 84956926, 38888761, 665232001, 904241394, 931570960, 258546120, 53961456, 635979889, 345007332, 797931551, 918889723, 728512363, 27100800, 303917354, 62805133, 654051042, 655533258, 645278238, 724238932, 589514164, 805328818, 158784661, 125486099, 219091020, 304643090, 420468971, 757453148, 560259634, 727239974, 903087849, 699986947, 675949719, 935997518, 582924635, 336469611, 614097112, 942252990, 199221366, 831072648, 587643128, 385735445, 168142593, 556922810, 417405662, 329065738, 163026156, 840396234, 607539188, 374843690, 669697568, 316305352, 605653073, 472444499, 799289649, 5532541, 650266281, 908555849, 933138546, 860990846, 623466296, 109796920, 584498060, 350025516, 838413983, 56579103, 434796545, 696928870, 174463777, 102883399, 641519407, 344379012, 227243608, 885650530, 984889845, 872409764, 122494110, 181658728, 589283123, 35057101, 47380874, 721999086, 457605499, 124243585, 41419963, 59663770, 874399262, 367747447, 928452355, 842944276, 508718153, 121126902, 46827602, 515091845, 221428344, 481888470, 567414921, 473194436, 209389437, 228873364, 321061797, 841760778, 985486962, 405734041, 315771199, 451485835, 314407439, 379378607, 389414735, 287736463, 449313374, 140468628, 388856224, 956381493, 718303417, 58484561, 602398830, 664838024, 686643003, 613603750, 416297718, 281437202, 283723289, 993700708, 446290658, 177070294, 465380303, 20893500, 263180947, 586100343, 641350356, 568064335, 430067240, 814200544, 3567442, 678205760, 963812405, 5454662, 882118012, 989033018, 232020473, 802258265, 616794291, 75840527, 446564186, 60370171, 377084395, 45837857, 254027712, 863258937, 633787774, 843307359, 901566376, 458479242, 908727799, 111114474, 79109951, 937722111, 489669138, 457376752, 355603028, 739521490, 458955330, 810060311, 257754372, 283208811, 932651230, 969919994, 659432050, 227733030, 374222468, 460275823, 969601145, 462016313, 503905488, 206081523, 783051750, 972220761, 384399402, 709208064, 882127022, 539417312, 660275008, 843606073, 753053480, 613537001, 635216179, 160997453, 131114301, 471532844, 20051654, 632054216, 119474483, 739361674, 387434727, 388506446, 720667059, 542357321, 30562057, 254434164, 507337002, 293416315, 113940441, 333855272, 838517635, 236620935, 986007058, 438968291, 537442288, 639470852, 871837629, 316479540, 46933564, 35774178, 129419506, 201279556, 821381798, 778839415, 886105382, 344307782, 873550367, 588711921, 776177207, 573848830, 282660687, 580938295, 581281942, 667751962, 690934143, 346412941, 101867075, 372732157, 699646389, 323269763, 314915448, 466933915, 284770712, 671865971, 955139052, 760113685, 884388647, 100895882, 915695156, 468675065, 540590271, 290183982, 815685406, 160613378, 355143423, 313432517, 857543316, 462823962, 734821719, 497243277, 29162460, 825376784, 782906448, 406882721, 908727777, 407875032, 60288004, 232623240, 734861264, 663842988, 470879842, 507767374, 775478191, 75193663, 155859958, 915445869, 707415831, 261309633, 622736095, 893809054, 576939527, 351804799, 648225574, 501509789, 815979444, 766622992, 153700874, 395358500, 713865332, 581210797, 481445631, 549835015, 301304300, 291888950, 747924108, 410371589, 985582887, 571929626, 551675702, 956029061, 82402804, 104893878, 66460170, 145996633, 653756537, 76854097, 522675148, 857601709, 315350935, 609872790, 743056100, 10290668, 850978662, 646002570, 942132543, 457137174, 953034925, 626565588, 956796768, 168671130, 618518818, 482762276, 756169102, 773830852, 564770931, 156236886, 913541838, 198264906, 261270788, 700151910, 982850738, 807514705, 642484888, 268814421, 973890390, 332393578, 256226335, 548032193, 746276232, 14965220, 449203065, 475591467, 450927734, 402836993, 966379948, 487886229, 565109301, 109377857, 330244610, 483285356, 675611747, 149415529, 587796778, 558422809, 460546550, 482836461, 692763117, 368508689, 388202470, 60954542, 808758825, 562888743, 572765398, 733029857, 861904455, 239842326, 667100302, 193139094, 842664278, 496588707, 442737485, 865708308, 240037998, 339091539, 644030248, 217276417, 547790371, 777551319, 871591325, 699568382, 256522539, 363115456, 578090236, 20691150, 54493771, 509875932, 832788116, 83775256, 95923646, 581934307, 137616677, 231504737, 957746752, 29436027, 59584405, 451413067, 54874763, 816668805, 671229567, 930790237, 159583389, 251518215, 25264721, 196288042, 852221960, 119796398, 784199117, 157766725, 376689328, 63975925, 653565846, 275071181, 320602829, 724419619, 242348220, 942058090, 234941555, 699563922, 722092216, 389102861, 996276086, 651949173, 939328987, 266073259, 929687564, 337930201, 321325573, 559323711, 686055839, 768403546, 743141393, 453550650, 394859039, 379778228, 738944807, 748783687, 980799175, 652027468, 659289120, 137657, 216327066, 64573497, 480953810, 24610623, 75075422, 423231718, 429223716, 102480287, 623920276, 50111737, 188594822, 60370349, 278101133, 263020853, 305671423, 470437590, 862999123, 208103445, 810865801, 708568586, 191082083, 391324720, 478227104, 723267228, 684975202, 125713971, 904206207, 192777025, 966349701, 72157773, 660603727, 777805510, 408625874, 663706244, 817508868, 34901011, 398931444, 218679528, 658381318, 366280942, 858991986, 936707950, 558481535, 985562464, 549532782, 385267796, 293846877, 457953406, 938874690, 437185270, 797469272, 887022183, 252894543, 88926513, 170406627, 735104856, 512459895, 208178933, 871797316, 473165858, 301399145, 209816870, 598145315, 309718012, 796305091, 498066683, 17825754, 550528081, 621451166, 649476299, 355783481, 741641622, 759341721, 433099985, 501565184, 88932769, 649961467, 974813613, 675047827, 116031492, 32019323, 767376963, 86999109, 19121768, 474828967, 358541041, 943322613, 982108093, 708909189, 835302523, 726689511, 999142504, 534362710, 316045480, 34619127, 575619520, 76263275, 969949501, 114708174, 540281884, 622786878, 957492434, 350849804, 179298647, 313241771, 162586442, 142158064, 514242080, 868230450, 820659724, 857540468, 785191701, 362891153, 486150784, 777170000, 492026078, 798039520, 185769037, 753102021, 853606422, 427625100, 639257235, 535604816, 995321504, 262393481, 815388674, 422697295, 48147555, 676761599, 154286519, 48577932, 815833710, 884125321, 632970074, 894235738, 362576464, 159328838, 35430185, 729499639, 436266769, 776649271, 120118498, 570513597, 701421691, 115980820, 71416763, 579528587, 987804530, 484822013, 243444711, 880587221, 922859164, 884909783, 851959317, 29399536, 369343603, 505732731, 916593763, 510131119, 540801054, 653184030, 187753011, 928711041, 709847553, 506088485, 782679315, 522839078, 418168965, 709002609, 90270500, 248660466, 560190737, 32571711, 230044390, 932438923, 976817630, 939838531, 544197230, 775711724, 333606106, 671129638, 597233748, 883892508, 669845183, 261336736, 922978719, 795998337, 50608423, 246799393, 624467322, 59178255, 24046132, 703440979, 712409682, 85546089, 852088556, 42170354, 948651642, 984162856, 237823862, 421154555, 199897334, 558134773, 607149313, 638523761, 833666516, 991948550, 249494963, 757449586, 442347429, 76119307, 390260552, 884504379, 392681516, 166416488, 649194582, 218541808, 271187088, 383291635, 796279794, 274196696, 684405333, 548472713, 906051184, 751054300, 485586257, 144386271, 888344929, 74748512, 447809936, 583446762, 19581893, 894152515, 390460861, 488528169, 652798618, 14444536, 175632075, 987455175, 295097537, 973540034, 460323872, 105249470, 649043995, 776676652, 282150216, 714310662, 718779979, 398223952, 299198175, 328991635, 36393279, 340221541, 827920729, 457381378, 684680628, 929119244, 22354383, 789137600, 650408687, 444549636, 553665248, 582612189, 555590739, 212253201, 965989973, 594239168, 253608745, 995768864, 457435154, 543035078, 2248885, 654759280, 834849662, 309274846, 530083128, 366691311, 660961255, 58619697, 728295044, 587707606, 102357175, 310094318, 288080786, 321338701, 1182051, 220156242, 328295173, 592034956, 901287287, 747865792, 188106321, 589912844, 852171067, 740059286, 357949380, 384644691, 588978300, 523094135, 217788490, 89494962, 180234948, 736656731, 318943299, 160499898, 291398476, 922693216, 777437558, 624086432, 148456182, 830642854, 251624795, 423970932, 202949644, 491732252, 565132469, 456316311, 27294474, 10035858, 53525883, 451859416, 643412752, 733328874, 969411146, 822300500, 762025683, 207013906, 770417506, 488161061, 463677463, 322997933, 315725620, 319380490, 85540312, 434546554, 387080446, 197991575, 300705099, 419718760, 40408396, 478262670, 871427645, 310941319, 648344704, 891769098, 237210541, 144998535, 650827289, 24862955, 856412834, 484581405, 770849262, 607348091, 844430826, 115986906, 425338034, 674728775, 778769777, 991953447, 783732657, 982255925, 836946564, 681235788, 798397769, 363445362, 925820880, 894609452, 131751947, 918886485, 167128016, 776091654, 902179214, 670994100, 889968414, 970130491, 862844392, 934921294, 290641727, 263990486, 2864898, 149750784, 876099263, 128683527, 886820246, 239679034, 949634624, 621345277, 818023832, 990247814, 435235006, 48977319, 453399809, 750024669, 285359138, 114144531, 807555322, 809491321, 162756319, 52291363, 934341339, 207246222, 118035422, 171790607, 857212698, 24839663, 499620264, 578997501, 345718438, 205937020, 82673247, 453471154, 231577118, 303131208, 39853326, 518260968, 569328908, 63496602, 488358763, 910109771, 21360296, 558002536, 704131473, 697249226, 711301632, 129597963, 388615960, 943869557, 143350160, 988547273, 676227895, 845462245, 886626767, 528137195, 513788313, 668898292, 269084948, 551154063, 807788613, 26103586, 310426727, 311339013, 834380238, 154493386, 483695126, 289318437, 586280190, 26548261, 7283416, 89245440, 360280220, 952577866, 816747470, 557028923, 802131872, 508060257, 620521231, 474537912, 744825374, 69604801, 308525730, 84695174, 591867610, 120212845, 175611464, 231751606, 446624590, 845826964, 430374047, 527783653, 969359864, 64822786, 841062228, 316631041, 826138528, 852049229, 412712052, 561206530, 121570441, 444847715, 840493482, 709945745, 848677410, 245960863, 479574179, 472697818, 715320524, 697320624, 720393157, 747239366, 729294919, 924468096, 295101091, 652083784, 885843515, 13371458, 148593491, 205359243, 734589082, 59728493, 884680624, 18457062, 822863653, 507946405, 973450327, 773557980, 496486605, 255558398, 706776931, 145377721, 406410711, 79570497, 939529110, 306324733, 486148326, 86785080, 476541897, 653840476, 757250851, 67489028, 126182943, 69140492, 29574647, 949491848, 252625109, 73599928, 672348729, 149095247, 571889151, 489380583, 826090102, 851865426, 848630840, 831143770, 927940860, 619503143, 129907681, 772739462, 794501576, 31304554, 311155653, 332351895, 333654826, 116503577, 73710831, 417918694, 368975389, 133068778, 354758169, 248430663, 15843119, 336985152, 295584574, 600987564, 636887706, 838429041, 188235390, 324880755, 388380709, 336657773, 879941224, 848384691, 36146591, 600276757, 728053496, 707376712, 111507621, 650811524, 575452974, 152463533, 490815455, 416086578, 168615573, 481769626, 952616323, 471489029, 735902093, 470005652, 652087958, 579245266, 616320015, 704325889, 969504370, 914774334, 503395228, 718377621, 800321314, 662138244, 6305005, 530296332, 981461091, 549347225, 599600263, 388860091, 186879757, 438495100, 617857424, 385653770, 90478742, 671507059, 254842250, 135901418, 733491512, 150922238, 379157592, 799451221, 233502622, 625804484, 466305954, 377490104, 688288485, 273241383, 309478424, 835594738, 720842300, 982357554, 115656373, 834676933, 430478248, 503143171, 173238472, 427571859, 921830248, 137338547, 821487827, 201615458, 886867187, 793265870, 367463903, 984268128, 298311787, 933911332, 565413266, 268896445, 839990026, 666091212, 881359265, 580118873, 678283023, 842096409, 170481283, 140151982, 488301253, 79449612, 456525577, 600833054, 468411945, 736193161, 204745685, 37032092, 370242281, 13723900, 706597542, 366170135, 553449206, 569296242, 123730591, 374694847, 699909675, 288651045, 603067735, 738244691, 508276561, 174868985, 490936549, 633658369, 463863416, 557658950, 170838087, 682390346, 808653635, 943357045, 550973281, 216486041, 225356018, 509775253, 289879348, 301573230, 959442725, 97256980, 142519622, 182283062, 9566189, 200082690, 866306861, 752394944, 759729168, 980275533, 420244172, 238861132, 906712901, 295687898, 404613276, 427586780, 381750141, 862864683, 1297251, 692368336, 331106344, 850796084, 299866963, 523052043, 429288334, 25186276, 356164021, 728677867, 170361583, 672968286, 575731929, 651875664, 309149936, 925208609, 262290293, 932961282, 982315072, 360354091, 299742556, 329332864, 999362836, 28981786, 194400579, 772952052, 470546122, 537154999, 169370061, 229859370, 965311921, 193023775, 742834672, 530940332, 421685641, 381773403, 232062151, 335332054, 892876981, 760258017, 85394643, 4113555, 464698385, 596152962, 71958802, 788346187, 454850605, 120047356, 516416623, 999972, 895426000, 728187299, 406064332, 782153642, 893692752, 594531964, 563093747, 998362760, 2470949, 745610253, 371912117, 864002068, 336961344, 667200436, 887467851, 596158984, 710380000, 705716631, 400482622, 88539067, 316535414, 348370305, 688635391, 589424065, 608234029, 859934335, 388684826, 102248102, 578087852, 493001442, 828276357, 687740139, 222207346, 508622193, 881707278, 728572102, 175115485, 815903101, 979166259, 882084880, 181803828, 848406949, 754930462, 284981828, 637872412, 927494091, 810928174, 488106964, 842874688, 950530136, 663699859, 136630003, 512462453, 57083877, 794411550, 128563213, 232761918, 342805214, 266664459, 944621031, 144624113, 616825274, 819704090, 110505496, 327014583, 188440279, 952664801, 400320523, 964563963, 873409756, 146866028, 828094442, 768323002, 857632658, 161127238, 315726244, 876211356, 22685653, 996418457, 326989922, 640691378, 217881742, 799952346, 969841960, 13203400, 396902194, 173428387, 214927456, 368687246, 933091033, 162047364, 888555110, 268534779, 628182257, 275119034, 712025845, 924630465, 680414136, 50237978, 82220767, 680036585, 344010712, 809251897, 708560156, 638102011, 197079394, 911366089, 253657728, 986003455, 796774641, 246833453, 948657485, 301873356, 945127344, 13951295, 513744554, 798339102, 741189932, 535287569, 613469297, 253605547, 1800560, 520562570, 277329926, 589477608, 455945981, 710430285, 582489850, 281384298, 503497045, 511891915, 327161488, 815717416, 152401285, 286784010, 905234567, 203714002, 196367122, 711385025, 381521303, 212867426, 808606469, 201490735, 571210428, 411262499, 487552031, 472149612, 303203536, 941803373, 782042650, 730217815, 873280843, 704363366, 274999822, 741983096, 81083702, 612976873, 662209987, 755129588, 747170078, 958476579, 573875679, 158311987, 923340080, 591023194, 125553023, 669213501, 675141580, 358827979, 810069312, 398593225, 214054304, 97179496, 402183501, 704891888, 408470632, 62893040, 850751525, 699273128, 638930668, 777603883, 178499229, 548549432, 863950270, 113794654, 54988280, 904685702, 553679790, 187502790, 168858834, 458023718, 268917259, 187500090, 449289589, 662285318, 596185633, 838091909, 913938334, 254746751, 693613635, 216642677, 822697343, 845363251, 495885321, 601677789, 839062432, 529507783, 64434825, 124296920, 987029009, 680068745, 127374444, 118834555, 2863136, 661605656, 303973869, 290671081, 268081302, 191082244, 105040655, 221594662, 852198801, 990747204, 350369744, 865784729, 92617364, 189209287, 877466513, 464106106, 837478816, 314890040, 99640989, 599094142, 532323373, 141007793, 494106325, 314313824, 494957658, 610530720, 445565194, 977675134, 4162831, 690435067, 304133372, 310901006, 295135660, 509659227, 76544957, 292505392, 268905771, 94637348, 2141479, 591349, 999751743, 50435268, 438766902, 319327131, 943603117, 945932314, 851492293, 353266066, 921916622, 34607418, 535111543, 779045629, 939234255, 704958178, 152340085, 803905944, 851486590, 764036824, 335530310, 141690159, 57300842, 978841652, 654983930, 577948888, 902078083, 11946615, 645331410, 673198746, 1335135, 929713321, 124805759, 781712942, 801702334, 60398301, 295550045, 808315346, 712263022, 893729223, 156088814, 896992956, 445648173, 281250759, 68744316, 111605468, 2694717, 811568672, 308290290, 667784634, 790379514, 893833336, 304567376, 546724975, 930197338, 188093331, 865622934, 437728777, 738051237, 949881258, 582849525, 421634580, 358930384, 433522582, 997444807, 835962371, 80001165, 703265196, 313693843, 883368708, 687318883, 350812536, 59419419, 319853683, 883314210, 730431335, 431816450, 654909009, 180773041, 817249814, 591226173, 817098197, 642037801, 164700715, 903855940, 110382893, 764489475, 786116710, 904138969, 684286306, 70076604, 688581605, 726297464, 875997579, 607050254, 988457175, 346361738, 94055062, 301162263, 468770888, 619303949, 924804096, 795592534, 472202399, 90961313, 862543137, 950915502, 702164228, 31069988, 501982936, 576484821, 123640743, 57857243, 760091545, 365487923, 131861923, 945679602, 968529643, 515842042, 143240508, 66563648, 468839898, 614832714, 379845205, 91238117, 20445027, 762640657, 214381176, 793464743, 326816402, 517970761, 86736295, 495731745, 256670885, 214985148, 644645537, 900415129, 833914612, 367176694, 990901929, 617592137, 373887206, 73800046, 787723641, 530025531, 303535023, 500286414, 183716150, 575715844, 216829638, 579272370, 772185652, 465263202, 183765672, 635682593, 637777438, 992250701, 365940458, 924368015, 368262148, 528051475, 235237149, 81920684, 359616699, 158143666, 716277680, 646724350, 976010441, 999016025, 758331349, 873601511, 616385299, 576177104, 716411532, 404772990, 123753160, 206365718, 556683294, 38244380, 228998209, 361418778, 918986179, 619334480, 618354149, 53220092, 687276283, 665548534, 409701167, 460966019, 728043238, 544502818, 235621922, 974329286, 20768706, 182976962, 427180766, 533108884, 104547960, 159552897, 416392405, 887195713, 782476209, 815802159, 128584236, 120446613, 656565750, 308140529, 80421937, 538256581, 400067688, 586391470, 709818641, 175442272, 776423691, 160106332, 52141345, 187462193, 465280658, 240836361, 953256800, 115517311, 650268836, 211828638, 581591878, 448597769, 653030367, 113127542, 136099181, 935743748, 785003456, 671853642, 314127157, 347543101, 485539181, 337266127, 137005206, 262483544, 89957397, 956274660, 489851308, 509217124, 699870532, 722504877, 687288149, 80958156, 923593965, 218068021, 779683339, 40191735, 904853798, 64763288, 406745783, 149493121, 640487989, 560485689, 776971579, 260949072, 312976058, 797959177, 926147519, 552226611, 840171430, 269432475, 803629266, 424979420, 626903683, 28257564, 449393180, 944641834, 559936177, 678731006, 184083533, 878856587, 269480454, 200299500, 667373228, 924250489, 665721615, 960238012, 6727635, 379260533, 572573842, 385211721, 475175265, 497021086, 358215404, 817942701, 929188049, 503698688, 146232100, 576432156, 410889648, 112733364, 356303678, 842731274, 814370712, 160788762, 126499371, 939376998, 659977549, 402128272, 607092080, 434298277, 967084681, 352728549, 758358634, 776552580, 755540341, 567726687, 530108302, 146170195, 874700841, 121065119, 68045983, 421747073, 583020202, 917379575, 97835452, 181505544, 499338528, 243817826, 948719477, 555265455, 553672009, 200744656, 51474650, 328683421, 629523782, 785899411, 168351678, 668699603, 831769140, 17817315, 425505758, 193139191, 598521512, 848386535, 199706918, 304962698, 941580207, 735919415, 972257645, 100240947, 508565612, 278143450, 705328572, 665316131, 276050948, 588010910, 469642376, 341002875, 484688645, 962061392, 583830187, 309310593, 926272169, 428866272, 354652023, 3942377, 836012099, 842534737, 579243385, 101811970, 675727877, 194676691, 713007107, 633957873, 528418921, 11853540, 74639221, 762966141, 952860996, 948616442, 235546288, 21619697, 417013153, 214490225, 799646544, 574538880, 64608604, 620334747, 313074201, 827563971, 285238441, 967787908, 834579147, 483507992, 548511006, 365595377, 897113666, 681185187, 419441343, 481039056, 701515035, 47359321, 711188860, 771636380, 19611126, 171606143, 964319888, 502443315, 85594931, 666389196, 930019124, 288342833, 280348017, 364967058, 1114430, 975099259, 157220170, 679655924, 242877600, 575757289, 919657510, 744878398, 355892191, 18217738, 903011018, 792775856, 881706992, 423320604, 794069670, 22744826, 317460690, 88979808, 510574340, 283456524, 708836627, 377388551, 823555837, 404458093, 670189368, 217893605, 517860330, 644814471, 193938569, 861430452, 7541238, 352149717, 460773988, 970420740, 126404776, 274799131, 597160490, 469110459, 191452113, 41674181, 665876165, 468257306, 367842477, 77877011, 766812461, 597496308, 227052279, 791398668, 941197176, 166215242, 943538232, 150425716, 794878484, 83852550, 76248764, 820932037, 822283190, 720308108, 963179387, 379901064, 204021943, 955364626, 708629417, 601716868, 945633726, 839883133, 519892166, 86541654, 903686202, 849233582, 671085109, 772010318, 674261714, 832231313, 352999885, 364959731, 467354166, 502094587, 969322994, 25040656, 81269788, 421601736, 536289868, 403165159, 633125706, 66191573, 436375500, 384762019, 8921969, 672114493, 309651440, 264117317, 196012653, 229300836, 419090827, 928629685, 620488182, 154509852, 212913607, 282020715, 816040296, 23919458, 332585290, 39807784, 421912483, 919148346, 114382555, 760429159, 608556106, 272592431, 9053834, 525518991, 810500871, 793745584, 167857753, 57890245, 271774821, 586873049, 348538384, 501250451, 800425893, 673200903, 908156854, 15077525, 577253498, 912815107, 38719967, 689821603, 840208776, 83744557, 12746769, 854356059, 12181646, 858503027, 203999927, 668765690, 878500513, 514946667, 876769137, 462915843, 920628539, 490646110, 617220827, 353842501, 797121190, 616024083, 317078773, 243343900, 433201206, 465311347, 71422699, 621646320, 620977751, 256953687, 768171628, 647404300, 536760161, 590991802, 121997223, 991614184, 923935749, 403638127, 355119757, 252331200, 434433516, 212430714, 322897592, 611649303, 798782990, 701933181, 155253372, 804778446, 486095096, 508308132, 185516057, 82078922, 531829953, 922361573, 561752341, 53546122, 882329757, 229680135, 100915974, 180043077, 734747946, 4649066, 837110082, 151157004, 160569416, 77680700, 191945275, 636200935, 746366588, 984738294, 959655455, 767135935, 128813184, 721623948, 371194415, 917347567, 525631953, 52106338, 765163843, 192607547, 913379742, 962891345, 187127876, 893368590, 735274037, 445718245, 623538902, 824274989, 458367351, 831845406, 239866828, 61216781, 740792994, 552661556, 251975811, 977836669, 198953679, 657600918, 351028560, 725906670, 330646327, 965458296, 246360167, 430574159, 791465144, 56784092, 102906328, 912843226, 733180937, 753327985, 772302032, 95114603, 450698020, 144309864, 614947917, 384920064, 781898902, 468321491, 746076617, 109265572, 773188399, 788684627, 268094882, 200107432, 460856640, 441692513, 891622547, 259011624, 509212290, 197603734, 174132604, 345871572, 981277905, 296265665, 668984997, 369997733, 490771800, 859426004, 954629915, 70508933, 392742724, 669046615, 575801843, 943982442, 351252792, 125208151, 199434927, 649343486, 354794837, 630252174, 213508909, 414154929, 228136371, 747422508, 777271407, 231117820, 138080547, 241423211, 24660981, 382456876, 369990211, 257661449, 125358109, 67859854, 795970385, 550974713, 188650784, 763747994, 120651132, 752872598, 137262124, 347455152, 934836254, 734641298, 723195800, 874312962, 40452319, 750784029, 40417494, 133686508, 255699889, 166405532, 152678625, 303370737, 621360569, 262871481, 954522004, 958894350, 453734831, 858477364, 163704476, 276040863, 708844007, 261808036, 757747159, 865376469, 571839548, 786741102, 138216288, 488206849, 836952556, 331226441, 597548259, 727195858, 224799813, 933379038, 222311115, 198059580, 763091639, 315258616, 762807618, 156958323, 766430167, 390052946, 801085747, 317258593, 817771064, 313221220, 481923357, 216483786, 195244521, 301970597, 878019175, 347649364, 227143920, 485764253, 671382009, 715911573, 176275146, 861348167, 85153845, 182100314, 347827171, 356951269, 417391666, 414547360, 546214212, 403662778, 603668638, 502834124, 853075596, 621937179, 316443278, 244946576, 518623090, 384688490, 840289246, 307052973, 969461252, 433218338, 233614531, 328397228, 356937106, 744713093, 311071671, 265062676, 354362246, 804349512, 621818942, 954035180, 638364979, 900466667, 567918230, 136369507, 725174468, 940771380, 628182590, 525502392, 127828451, 680802163, 107320586, 722847079, 879352904, 67804011, 427032431, 752692420, 702695838, 243993679, 977219270, 89722660, 185364942, 248944230, 830842961, 521142323, 33320390, 84717306, 789923144, 800297145, 927886118, 187890744, 634774578, 189544765, 129015342, 153737705, 628957385, 365099991, 174167704, 828007103, 121378649, 503935726, 384270805, 621804634, 225190181, 468631587, 517802716, 567113793, 826443952, 71195003, 163162644, 484066064, 673227034, 647206986, 854992382, 692629741, 51113320, 362804389, 709591499, 186042154, 599346491, 240168884, 978926693, 682674797, 210488673, 912868543, 115661545, 754348883, 12501460, 706703069, 226475791, 552120482, 845514533, 357882665, 982554282, 411457457, 593984292, 7495405, 227890338, 821503315, 673524178, 423928623, 451996834, 456163685, 548300219, 514954106, 925905043, 212748475, 255699471, 729916721, 112632435, 127778159, 223477947, 466095464, 184224332, 572791053, 270608009, 741375617, 753993159, 664793086, 579474172, 231951067, 658023479, 431332106, 754365140, 388638432, 164011880, 280519771, 501629435, 801615536, 185871542, 455314293, 406509295, 616482973, 961961178, 533425923, 701294183, 515940007, 546133033, 261226834, 50645875, 72226894, 942554354, 618813181, 170313925, 609993303, 865042731, 446998825, 656273234, 965285769, 93372471, 330430010, 235389234, 853140923, 262276171, 576711497, 370941423, 893709138, 295750035, 158846524, 885857280, 770312840, 574914795, 167358944, 377805141, 699519489, 937368857, 756570208, 495067860, 781471765, 18258168, 775618568, 288409504, 138380625, 401571496, 424479609, 632741739, 760874012, 973499911, 412606301, 294615803, 185458985, 534337307, 481048518, 422283636, 489875247, 332874892, 685069586, 863233151, 776952014, 182302781, 511798179, 627927289, 581795093, 857247500, 355819022, 684638353, 599793718, 553254780, 801946269, 231197388, 209437007, 408585612, 124231183, 729927899, 441864381, 485685119, 90268775, 715544370, 247200326, 678901835, 415422119, 853164222, 165836622, 862690615, 229412853, 90676573, 894615566, 566093630, 27103899, 830920047, 891975149, 278489498, 364770977, 548852133, 602105921, 699850000, 794738747, 364949085, 607735083, 508464425, 262147291, 200797204, 781768270, 840329073, 17084157, 452473519, 521346987, 176065291, 356764634, 990214226, 416219162, 136911897, 296393774, 200811956, 317948221, 566102589, 62059832, 667568085, 544619539, 37259088, 761920369, 935370720, 317441846, 772588905, 127039326, 913389303, 650564845, 124756034, 319784165, 920925622, 298540510, 925542641, 610229503, 466803539, 739233061, 879675865, 684556377, 247349489, 666448556, 820967198, 547051237, 878748982, 487998796, 340961324, 938236037, 467390262, 630834080, 599213990, 802071175, 652486501, 86011465, 930311830, 65625327, 929080173, 240323694, 283181862, 27315929, 369839716, 959883729, 466978872, 415118073, 194785891, 443556270, 885326618, 100201939, 311032592, 183147826, 993551520, 402165744, 779956175, 739531034, 931614863, 290056024, 387469522, 386737316, 469126581, 698099004, 647375485, 700321345, 10038863, 406472585, 827217933, 622633663, 505720368, 988041145, 670112062, 500978805, 962738921, 642513765, 4621962, 301835372, 380393792, 155569208, 854365325, 615468577, 449306177, 81064894, 320440343, 975797476, 891832603, 227744831, 592639657, 227362568, 182432457, 344480080, 527249201, 310883716, 498458614, 477381485, 556383432, 996882481, 576267725, 799009273, 919257266, 852216064, 693860348, 275960216, 545670326, 368303977, 787399212, 237314144, 740120178, 544910277, 470769903, 879081535, 435063642, 192268681, 637572398, 164013629, 86077978, 94052914, 640301224, 245846347, 725172430, 770741952, 646324465, 872055719, 356735052, 334377377, 265436215, 809136749, 336446787, 318389058, 747357288, 271695953, 914300429, 216268272, 114685468, 859013212, 721196002, 380128039, 878718673, 311611536, 585506156, 457271396, 758677730, 389262679, 835862255, 48224013, 295105234, 460945779, 436259030, 173327372, 59885531, 306165110, 878444256, 903284231, 115560765, 677599439, 661973445, 746701163, 889803963, 890623234, 302162456, 447920254, 898197764, 574863291, 783583678, 591908792, 910470572, 826406487, 711469212, 40725902, 115483710, 55568779, 59053864, 676038743, 390929481, 18042476, 541362473, 69910719, 411146835, 103686822, 728758379, 510873321, 236263533, 124605221, 12929519, 596542311, 498732104, 35393780, 301902724, 478915245, 703280672, 533420085, 136447718, 45285853, 231770302, 837485122, 607094990, 361189843, 851657971, 404964952, 754432585, 576148363, 618819799, 405174915, 87298255, 772213436, 901863523, 753202946, 255843261, 963562272, 848366989, 786502775, 878178068, 177705958, 322807567, 894557192, 398734605, 346053307, 960916765, 565637429, 315445994, 587177009, 682416824, 746417694, 376278453, 612503217, 726115593, 830106423, 958102776, 953368189, 388951068, 747270736, 453447764, 860586903, 9991163, 121583837, 210906045, 990615624, 46162323, 210510833, 526996144, 980303915, 13817129, 759962434, 687202276, 25931626, 400304508, 58366042, 603759553, 671696775, 956157741, 898319879, 785978393, 756273788, 203468197, 790454803, 148480688, 47330838, 118209117, 100645001, 563092961, 918063661, 446356274, 156823576, 850528315, 520921802, 961200664, 826117357, 167140244, 615734701, 437169593, 443097258, 418614500, 715380517, 866945532, 511793950, 997258022, 531659221, 481453467, 305976533, 368416260, 145302375, 217754477, 424956265, 785141777, 538135517, 133916451, 193914643, 135884502, 538586411, 628619979, 988463000, 357909847, 634809572, 952847346, 631390208, 538408178, 85541566, 302244234, 905687573, 109257416, 111954432, 409346984, 48885269, 486631813, 820601187, 857481590, 252943304, 190513841, 359962455, 555918245, 222738361, 566021234, 660980946, 598103995, 348438305, 330688431, 847094478, 728324818, 299028611, 690265077, 999757978, 278999317, 586646403, 671335545, 992907265, 773375886, 789203887, 187321288, 950513819, 254082918, 85873463, 443881849, 568576368, 423455640, 313600472, 640232875, 744618830, 526949673, 684715101, 627722425, 956786619, 886408251, 390848192, 351828560, 125117381, 736593769, 327244043, 157746985, 877370998, 674587392, 386601990, 465175192, 468879152, 197494104, 999540253, 507855139, 811892856, 183717337, 756130956, 746121641, 549781844, 619118225, 650915194, 588089709, 348947314, 798202983, 394895921, 40420098, 164561410, 182035336, 435959536, 654791410, 917615623, 217038833, 28448867, 527223582, 730885934, 714436004, 968330152, 815433291, 961152238, 162978789, 717332277, 514342618, 754816274, 112802993, 840477176, 353423833, 696223149, 880989637, 508379926, 311958768, 148617510, 953316785, 939671874, 635573014, 698041793, 2090401, 148543071, 435933186, 627107629, 176803857, 637473307, 802738224, 291544471, 730239969, 31550680, 554833965, 437939187, 150697339, 156942867, 544033797, 864347471, 645061705, 519656175, 65126648, 810361137, 939596723, 742977122, 624391739, 702678995, 273056605, 607371221, 585731355, 880776136, 25593310, 560506959, 514394014, 642672857, 457301282, 726080388, 199707958, 677244936, 150285771, 129983140, 396153090, 141327050, 913923963, 435648851, 365001380, 493110758, 70166917, 465374480, 318394835, 631669322, 659695493, 242529544, 440066723, 285904618, 366893681, 209236263, 148092110, 387467015, 921266147, 467694369, 896311577, 571938345, 647807418, 812010802, 327058955, 996536064, 480866620, 38495645, 460752683, 389765416, 58411395, 940751096, 585024614, 113674812, 691736925, 572345219, 809757567, 169404638, 906886551, 159738863, 779482409, 247722451, 460342514, 114319116, 50689064, 532647549, 177707461, 757817807, 505813667, 207373386, 796632240, 802522240, 907123957, 51881847, 279956140, 921535939, 573841236, 766315280, 920234919, 757005215, 872763637, 704196636, 494744117, 396277975, 296307374, 591765299, 346181866, 192089689, 851202199, 758848708, 689864125, 940790344, 383715371, 985040208, 309171320, 59707461, 957620305, 107645189, 117397342, 586312611, 129044029, 8219979, 372638351, 191712898, 994420557, 24283022, 945733553, 413305392, 989254409, 333325158, 607557234, 767197509, 802631897, 463425641, 582605455, 567497737, 515603005, 682016960, 59729496, 893627408, 314284828, 797076221, 670506861, 877439626, 752369868, 198730176, 810932189, 928770848, 254457092, 122836855, 308740091, 891617304, 191520147, 241924709, 387211005, 547900444, 937669953, 246395318, 503560761, 168693547, 228653723, 711913442, 540912809, 94545408, 557984583, 1245078, 881748022, 625176489, 761990619, 114587498, 647809734, 41564549, 227051085, 157593465, 374937241, 105319437, 909149954, 666234928, 359496295, 665351675, 133544979, 975813521, 50670530, 280697427, 276268456, 109654344, 483471480, 298461461, 30643742, 535216927, 157460244, 268673226, 461080498, 272884373, 519031517, 609705266, 347445915, 451031591, 684196823, 537168525, 636681222, 528079541, 696493420, 448119539, 420583408, 642707458, 579304222, 907912475, 984834876, 267924670, 305665158, 869013869, 493496057, 707287934, 367297916, 242878119, 787763095, 692888343, 848194649, 522947435, 510252688, 691614457, 5653558, 725038474, 267917982, 970927080, 714560775, 777596539, 780114500, 128418688, 409984131, 966177155, 161811944, 218581729, 605950122, 696048715, 902192611, 48333221, 300108585, 849556709, 750081974, 531519311, 921586454, 169151282, 780706253, 54591706, 297551124, 513178521, 538794615, 549290163, 624433306, 585924518, 831558064, 276977174, 195390212, 243881931, 694618000, 460886935, 224867618, 19826687, 624714273, 208481210, 388312684, 334899037, 438323225, 981308760, 634520730, 263165737, 53200597, 1999394, 398618132, 401117491, 848815533, 484083432, 133022798, 126527304, 604519033, 354197048, 160113250, 535921839, 572438013, 853904729, 666394680, 4314266, 770035920, 60962035, 646284342, 148076328, 9481806, 431096385, 957009534, 261744060, 258044038, 215682837, 184819378, 568475105, 695673757, 81071933, 87992935, 400223151, 601186170, 717231724, 759361786, 24563984, 965552671, 287563439, 509356160, 735036164, 989412056, 817451223, 159743982, 800142601, 766503143, 81138167, 263344346, 27174536, 675339570, 248550925, 673136964, 746818768, 616594570, 306895125, 136576321, 782373803, 705150146, 583620182, 567862320, 423745907, 458207929, 267297415, 523519994, 20883895, 173086686, 823159483, 732596739, 273341881, 464529049, 240337120, 657974679, 671685743, 864128357, 444296668, 295842489, 133278625, 164737244, 221793998, 267795811, 369622611, 731203091, 482744217, 951847242, 977045648, 715219632, 874427308, 621853896, 526657220, 355094824, 917958978, 622075444, 569638030, 422447367, 690482898, 496339618, 402822395, 726689102, 417078909, 477323880, 151876663, 967053765, 147585035, 274446150, 174440582, 949203388, 493627212, 441544324, 697511244, 488194040, 90684532, 491471055, 707225173, 49033074, 662840348, 62026736, 665474651, 234210580, 985181622, 371061990, 55316251, 897767753, 524518235, 902804690, 329753286, 796531734, 483671824, 642764181, 587038958, 800256519, 386519747, 473850033, 969562456, 56843830, 829295437, 183344344, 624343905, 200122309, 997594741, 701610342, 778061639, 935484432, 635825790, 29787310, 185721997, 616876062, 808267554, 244897277, 697516215, 991922124, 488158531, 842977923, 171956098, 872659942, 874419473, 949136209, 908983934, 747494633, 389936595, 574246956, 911927175, 550388511, 658667973, 529139130, 400774404, 157530372, 64840786, 18995673, 879854357, 144819528, 901819707, 296111201, 710884687, 500237251, 364789162, 692670691, 781499559, 647742203, 136057253, 40877760, 432984110, 605546624, 401812327, 704075525, 943682816, 760415810, 488372329, 204276621, 780909155, 549570579, 324639664, 749962609, 362747852, 630788010, 561312407, 88553019, 935148001, 990230602, 33878177, 429790504, 783518949, 917362831, 269126631, 581220219, 549660531, 286570756, 927915484, 551822462, 539855385, 314750297, 297349519, 884721085, 223396889, 915065779, 176719517, 378124805, 791093421, 161382912, 841208577, 566933216, 454194914, 400917539, 134359473, 370969526, 739567083, 188876560, 317570351, 38065736, 379774550, 627353681, 387315004, 843069633, 208493545, 975294447, 996583705, 680324362, 151573017, 814310345, 974838269, 716270322, 570704860, 284109969, 784698763, 451045254, 895944912, 578827172, 393198947, 256579217, 9486253, 49790293, 381073131, 368145613, 650762095, 441007810, 873838384, 516696725, 326284337, 376396166, 527600180, 328813165, 101098978, 27193588, 239113048, 585344710, 354519745, 771897029, 920810308, 357894431, 468701469, 323919924, 82381194, 270464915, 431102890, 474901893, 436831797, 717243102, 727272610, 499276539, 657652769, 984908923, 47820084, 595719203, 482593787, 165856697, 967152153, 258371043, 565456680, 934093210, 653863281, 625176882, 272983646, 828986218, 734260347, 587053686, 120861324, 647043694, 596054062, 817413149, 465503714, 794080482, 310764316, 356874543, 118988530, 927568839, 403592799, 683321372, 706546719, 472737378, 86278876, 570060712, 307381633, 922471570, 254892079, 825775244, 970579456, 97702277, 708321031, 450421085, 453908375, 568497951, 747547610, 186236313, 648418646, 263353769, 247624271, 649564737, 905787261, 602709702, 620532995, 876488484, 187268405, 335680693, 830748297, 120991470, 90766553, 87948162, 111164151, 661328858, 312584865, 205898626, 822234884, 258531061, 357321364, 15164890, 928068383, 527654226, 414124011, 469832469, 815568, 848217544, 501545418, 67828443, 478410850, 13804170, 419383259, 237761910, 852420614, 422570665, 52350656, 293458628, 726019374, 29800534, 486958817, 14611692, 293978275, 214327063, 604667431, 143696079, 312889213, 325050671, 441677031, 284641740, 217726013, 144709716, 661620621, 949974702, 616654709, 299253040, 255499578, 284238890, 356537911, 86666320, 18958339, 275766219, 326616788, 243838931, 419136753, 952840052, 753741988, 985432100, 438530732, 245318829, 683782613, 628400481, 97889651, 340929468, 598224890, 745027202, 887595874, 300041789, 89590584, 746881228, 31677482, 1671260, 350723593, 11478658, 755803856, 346982972, 536993738, 731222607, 3045300, 561531385, 243423534, 19694828, 371561834, 359292423, 6137966, 352565297, 750484461, 778286239, 174830098, 881976152, 817305520, 598730326, 882119068, 104434305, 264522105, 915911725, 651516330, 51882194, 258305683, 343318582, 867581203, 971367235, 554004515, 304882651, 581331579, 311171959, 956371301, 942065047, 883986420, 321343475, 166843811, 467443638, 446409956, 459454543, 821233981, 753348787, 716214481, 74814624, 521713797, 564221662, 548688728, 733523165, 772429959, 303027483, 751146472, 350507755, 900042491, 934164836, 649105397, 596894103, 604472121, 44997183, 552196020, 83341176, 189832205, 918969369, 658979630, 27463498, 712985190, 752041475, 759393617, 504075022, 31835944, 295867108, 102066641, 43739782, 6950290, 316864104, 454874777, 757219644, 431459876, 394988537, 438443278, 199908797, 418897106, 302260162, 405822694, 987452674, 882352364, 134529577, 104081811, 176742229, 46630185, 611113397, 635298988, 479541344, 521782234, 299698442, 104545091, 99472373, 228319205, 285593215, 219999405, 85790495, 114622808, 85754571, 20761188, 165738126, 99063222, 802223371, 911164144, 978227523, 420603159, 740212910, 73420065, 880554502, 615546232, 627412622, 639541300, 647905951, 326794209, 235885234, 296250347, 786875846, 657286213, 320377820, 580938474, 432808441, 19986775, 358112824, 610893222, 818524154, 254985542, 453417629, 964618298, 106928950, 600374427, 630381545, 579857459, 38545926, 78919135, 237655387, 386990325, 324700885, 996694966, 248078569, 411790864, 692828411, 85340667, 710443923, 592476510, 380934321, 471225513, 324749250, 12484976, 60242425, 924517476, 725195365, 280177397, 794475745, 353518343, 989614164, 197169163, 872111081, 464834761, 776683306, 532554150, 768895915, 62869182, 452437598, 219001840, 302541444, 752835269, 952071863, 445535387, 289310155, 820429782, 237361532, 989877333, 460144375, 448923055, 885265985, 633254895, 530438231, 831244218, 733687778, 27712070, 848740918, 993504663, 326699861, 836103268, 669664479, 310513539, 901522397, 33051821, 632303991, 893736302, 923543055, 834316875, 321325196, 476539145, 685930796, 814224836, 510580591, 459580425, 309047467, 577895036, 597971480, 779788374, 243019163, 923014934, 984597985, 67056924, 439367612, 652797075, 358248243, 444896865, 986724080, 180089626, 397066861, 745639543, 589898422, 365061422, 819781638, 305903225, 757187552, 110266511, 102322451, 812443420, 37885197, 58543760, 91403883, 885580294, 358392917, 987515816, 743332916, 690056805, 360650568, 599156247, 944232572, 141153279, 656226566, 272734265, 334372738, 698043819, 339198059, 237481318, 370691039, 960721406, 523963782, 85646309, 647916149, 861437208, 551171026, 801897193, 597759693, 986657850, 491561650, 430819533, 771437201, 278117993, 853266521, 72943770, 415698551, 660575225, 956009553, 47209912, 634774852, 99368383, 356706988, 95262621, 405257738, 661414312, 713407022, 224992567, 236352605, 876469325, 74205017, 760722341, 489660432, 736971762, 301957772, 918015742, 386751640, 118676310, 331613324, 806378526, 991119333, 593728443, 530840802, 555648938, 845670521, 83163100, 797346650, 132946833, 655597678, 344513189, 148440544, 138896691, 232922268, 758213332, 408550671, 461099053, 299025174, 238560055, 232191711, 1817987, 191828530, 591381649, 291595061, 997659071, 974940747, 414518428, 607302492, 831543466, 286269185, 673441444, 64915778, 832420948, 558000905, 808296411, 296622409, 735203197, 255503385, 616408978, 704780680, 204650250, 492329154, 823257201, 501111114, 335221540, 161848841, 348499147, 540446496, 934363143, 560759148, 448972119, 91870200, 439129205, 667378390, 358492301, 931836913, 614808805, 498068309, 40702231, 817865615, 121361620, 805916696, 302956795, 409829210, 631374752, 432600906, 16225006, 219746147, 580116788, 576951983, 502908113, 675032410, 794783231, 489115197, 270454797, 341424710, 82427102, 12855211, 356104287, 745167169, 103714166, 303830227, 628476707, 599909630, 909435511, 978357249, 804868352, 551400054, 773403665, 571123889, 79267629, 875155648, 624458785, 368702020, 268319424, 670361846, 915551526, 708150669, 183895296, 788572939, 316523138, 526885426, 609015012, 131181436, 344558250, 249463386, 742971139, 710367342, 97922659, 118216772, 112696560, 102920246, 990022819, 412639922, 846961571, 752910939, 819055905, 762407826, 342471250, 100494311, 396911798, 733284191, 338053677, 822649216, 126067517, 492540699, 428338411, 536334948, 742189389, 782967532, 212382670, 933395521, 901020231, 325758943, 74039394, 557012040, 885526621, 222480012, 567430830, 516582770, 587380566, 804584563, 439101688, 247174651, 440394160, 491387855, 536762402, 142136988, 497189014, 316247101, 473509937, 916064608, 723190068, 58576229, 759957252, 943010084, 772799896, 112940466, 739103203, 578289787, 996387609, 735219686, 509621400, 136028973, 897877063, 775495150, 480810759, 21456674, 298360068, 132260492, 205639385, 735230457, 370313102, 431106531, 414902697, 405312500, 633716945, 706694374, 61062593, 293440740, 413103381, 723431885, 78557431, 193508899, 142796466, 897931095, 977088725, 727424382, 284129366, 213429680, 669577682, 158738761, 896511902, 654983007, 755551218, 365390358, 423199925, 351521066, 664859635, 978183364, 839570727, 13018644, 764468793, 629741049, 979086714, 58299830, 117247277, 53050370, 601946943, 178398783, 619087532, 579981564, 482287625, 405347032, 847249780, 99950865, 635527867, 208752096, 139516702, 845189799, 837760564, 894197990, 576706128, 1544651, 325454808, 558457532, 866949605, 790867268, 680683165, 240412774, 414506321, 885108236, 177497100, 555598409, 612299243, 286345659, 108997001, 7773857, 615929085, 910150531, 139658696, 917447865, 352813357, 652501142, 354992648, 900788601, 10386914, 267864767, 479555947, 535870439, 324964127, 93857234, 699776844, 877086745, 642988654, 901591058, 412690853, 4016849, 312797257, 556808620, 804635533, 572467759, 388629834, 182375879, 946286683, 445234670, 79206191, 602483018, 114170466, 134084540, 60512861, 660698410, 378196515, 344604287, 229186154, 333514303, 709149537, 900493439, 510253153, 41697119, 320604531, 693025086, 213796286, 696232428, 235262964, 220208411, 55090363, 800596863, 24931813, 789831587, 952456683, 178613560, 252971255, 330469562, 563181734, 88397059, 173455298, 152663144, 16123814, 61627819, 485448465, 17291296, 443794865, 674778668, 775234828, 235410832, 135808733, 647723151, 134904600, 855135072, 568273508, 762926453, 709695281, 585287750, 484390411, 323261426, 822870619, 182892591, 897287353, 504661456, 444530447, 924016961, 728081437, 243664984, 924572486, 251025638, 338724191, 686212498, 877215406, 111185204, 826421747, 641039418, 74624956, 576053786, 558520109, 732727343, 179533292, 284458619, 257867879, 308118898, 320969317, 914787604, 802078583, 538662584, 680261530, 233964208, 206444647, 581670513, 570088082, 210478276, 62324988, 639060238, 273029911, 775335885, 272463913, 417524545, 786242319, 710805201, 833965016, 72351902, 108426601, 892239017, 905517815, 344827966, 296253042, 620177899, 23355657, 459263251, 606255083, 146112029, 787966483, 783653345, 160214216, 159348261, 968087548, 983867297, 233784630, 184477489, 323759084, 393730436, 151426679, 305904842, 717855455, 211870954, 389512887, 939967340, 827464686, 292841171, 711858746, 823849237, 280035419, 733310668, 173480353, 780896755, 50072720, 301099132, 422404581, 112283209, 573892974, 626579788, 269545204, 765693483, 24323349, 420955892, 65021042, 495388143, 574461368, 271208700, 394805507, 662498604, 221243389, 540635752, 11552555, 437757035, 468935726, 796395116, 487656707, 676163936, 957464568, 36341008, 600765927, 22269158, 457774320, 288374091, 684238912, 849092960, 920036957, 819668243, 800336675, 499168444, 198746084, 817569420, 928329969, 970952489, 371589027, 338448022, 322666312, 519717851, 836959947, 9907794, 164097761, 568042632, 214802858, 678004381, 286430637, 992570100, 19181444, 328729739, 106912533, 606890795, 514694449, 727331789, 895839911, 133310644, 282861013, 623071057, 321350826, 69212367, 211333458, 580717296, 812997605, 81749728, 892522850, 768767813, 425503954, 409886412, 822138490, 433746007, 869070715, 56420080, 592697351, 107561631, 514005366, 38650225, 84139808, 768754096, 566777322, 177010647, 137383859, 385913398, 898303587, 121173656, 701421407, 909058585, 789727755, 977834284, 897310004, 728118369, 335470792, 943511050, 187218921, 22237963, 199497241, 248501038, 659575342, 104235320, 707879807, 720256815, 245061071, 785113114, 537970925, 715267859, 379679188, 685593418, 327450899, 392708680, 920630492, 733288766, 300327675, 476548537, 998639217, 923660646, 436439263, 324205976, 363175755, 403534005, 306883173, 824310396, 869879941, 667146023, 280031840, 796016291, 635041725, 658742833, 491657165, 355680472, 951726916, 989540942, 836326717, 939833070, 776847186, 193289702, 294461967, 82619850, 60860300, 928043127, 477977493, 165710566, 914365462, 995980341, 343136032, 90233426, 13611272, 689526356, 35978899, 463981796, 140801006, 248003145, 835321405, 185337412, 108398161, 548024918, 989149461, 645307252, 5380836, 807797564, 579106795, 568569866, 380465425, 459356618, 73767856, 677892960, 80498669, 195360366, 426103484, 175682630, 437987181, 935069036, 538799809, 633909954, 572302817, 915471643, 388207255, 521275395, 337693106, 457889018, 563778715, 652140907, 179411958, 698562073, 240774992, 248786612, 127023438, 545360499, 746832250, 18170699, 884502093, 37303660, 908883082, 571785310, 411771820, 872055033, 844081775, 704275894, 824096395, 219399712, 378445714, 251395519, 477617293, 671973887, 241518783, 131090990, 840446445, 301177165, 156210240, 333022958, 3192731, 774861298, 155986388, 453267852, 711617, 585630619, 92659602, 864316340, 848628522, 666863156, 830574466, 618944857, 425474008, 505299663, 815220718, 740041383, 816214145, 316019340, 804849617, 420827506, 519546947, 876049795, 654902817, 876630641, 700978326, 61530120, 330465435, 333651301, 566284668, 592549604, 959626515, 583213159, 66395963, 568617965, 686315155, 453132358, 857906068, 687295088, 294060863, 799289154, 162757154, 790002739, 454480043, 12666978, 679801166, 599229628, 468751706, 762738123, 283672244, 977248598, 356951064, 571646189, 264068791, 821903212, 410640238, 256179732, 63594737, 600067230, 207051349, 182029658, 607358483, 177033201, 997899168, 500069399, 168505395, 629110123, 420424144, 949551131, 824165771, 962777584, 373208997, 104090816, 478923170, 221077798, 128570961, 145912960, 981899230, 60583643, 613766096, 1704574, 604542383, 337869993, 174111551, 410613409, 155887035, 686942662, 419154768, 737721345, 44890188, 916593602, 880865502, 799817608, 558378465, 588022829, 569707550, 272090928, 175588406, 299456067, 180850149, 736410209, 671269631, 242134254, 906977065, 841192968, 199781523, 967150392, 865105712, 131942856, 666160659, 537660061, 701040502, 858137778, 88251599, 59142484, 497908243, 420562638, 249311640, 332130815, 807185532, 863987388, 947179332, 127268110, 518677718, 161060094, 359466166, 718661099, 727113483, 511171308, 903610218, 462561052, 600765720, 635185715, 276648126, 590569311, 681268148, 438630396, 350231744, 445486599, 443257589, 788480222, 762991224, 810693551, 896158308, 855827168, 525317748, 392913018, 882761310, 374639594, 232477023, 715726557, 436772744, 358878379, 17279390, 718235166, 551026601, 16838031, 683542014, 67677216, 456065639, 59106736, 66888627, 643899384, 388907818, 965992430, 26921542, 666826256, 105915905, 888572779, 840736794, 863811043, 832441302, 720893853, 79070635, 342743427, 94954376, 642699742, 554968969, 205747997, 871813874, 810011651, 506289750, 83954973, 580467563, 920314194, 527676354, 731374748, 844149064, 276493967, 834314076, 153922382, 807715001, 863117700, 765815888, 961303326, 43293397, 497534953, 693587206, 576753720, 827608656, 167038898, 983166250, 940898066, 580051199, 295106261, 936367460, 983087843, 390323296, 774586152, 959280941, 50388562, 17108282, 218667944, 37119529, 860389534, 504823166, 334476837, 581242659, 918610637, 915545032, 576129172, 800041069, 888808157, 506169091, 514238320, 192770097, 742851950, 653218561, 862601942, 937673048, 673646485, 528496788, 276167648, 318434198, 404859828, 347834846, 841740970, 261598341, 709685785, 158665761, 210610216, 974277618, 879362040, 223843324, 257566788, 536845835, 889246647, 871100347, 946409423, 538941836, 726499714, 660724271, 541179202, 555749001, 328444583, 718498314, 297905562, 841721146, 514883199, 654448574, 448772690, 463082476, 707397089, 437957552, 582806768, 424830342, 56561623, 915601750, 845299336, 768261243, 635349170, 531202771, 842805375, 912631756, 729413261, 566015887, 203395006, 152084576, 90083875, 374147403, 720187669, 688348814, 916734377, 629750449, 95008013, 605543380, 120281466, 494826355, 466611294, 49826449, 747315403, 327553847, 305504744, 139454721, 888716440, 43628456, 185168169, 836217622, 934062024, 31766705, 798153732, 101884301, 348885886, 514183471, 455548953, 107462261, 808531539, 280852421, 628700475, 84435132, 611261531, 989400793, 884409089, 692742388, 204609641, 882063510, 881441942, 753210155, 940651702, 24763471, 195303566, 576116323, 93592586, 832954372, 339386750, 237905318, 117990678, 934190248, 166452142, 818701956, 119401173, 232848221, 920740642, 857001042, 34081986, 524146605, 857196076, 827946374, 906377721, 698001261, 552206023, 97130879, 462926775, 264444091, 546330635, 800180925, 198396135, 918926477, 701060133, 752320110, 734785984, 411488958, 971484854, 383551877, 752918602, 941569865, 883207445, 548485186, 449031696, 462537437, 333062187, 954513523, 483093646, 374966365, 480652023, 225744180, 374507797, 202142202, 448806093, 907710935, 334208402, 919195597, 968577397, 544733620, 56788784, 816525405, 931349200, 659904337, 629075944, 425844170, 806175794, 788368617, 235999955, 309925724, 740664421, 201650903, 495807744, 501844093, 628316455, 989669215, 175739953, 31203847, 719606206, 455665501, 428689109, 851849941, 852443290, 873361332, 181885293, 955514550, 988539784, 655876606, 852593033, 293481642, 847715147, 276057490, 608727799, 460475235, 313040815, 705197766, 210492388, 750709646, 759695660, 430703017, 989648185, 868221080, 808064785, 899239079, 704999950, 660618662, 761253510, 509031607, 847917617, 70558722, 335503018, 477792329, 866245981, 401683292, 212256839, 844122200, 714694192, 345986851, 96248716, 127350197, 144603685, 79181316, 858694947, 753769716, 26220105, 204871252, 672392670, 82522465, 164520551, 957209211, 553679097, 580854539, 277878716, 547693500, 514218627, 818265363, 600319116, 747760708, 472725428, 391037914, 412128248, 593680918, 891532586, 294329528, 427822056, 501022770, 295664308, 943725404, 755817620, 535354008, 11017185, 336883678, 280146552, 54079751, 588111275, 15992588, 213874832, 808488789, 406348796, 97034570, 108947817, 378397859, 690286005, 954829816, 99157173, 166689078, 854331783, 838084576, 435662454, 612085307, 673654662, 75147846, 161548628, 326791458, 477813933, 647331091, 577296391, 295952584, 66197318, 393128935, 696336717, 399292929, 763429637, 310052515, 215206090, 625221014, 684133843, 331354319, 603623268, 994760022, 62016666, 458400282, 219704557, 369903352, 800805722, 233454352, 175605277, 711727316, 179686051, 761614073, 479787393, 261380186, 960837742, 816343412, 634394062, 157288630, 352983269, 349275055, 26795648, 954228347, 629550368, 598617059, 181374741, 230060676, 424802287, 268551523, 807032535, 379967023, 590771285, 935025334, 993285194, 882732089, 861216268, 304980336, 986459522, 365875090, 86237315, 770330515, 522400230, 113213622, 533150057, 290428017, 779254994, 749132961, 203101591, 699463446, 639376477, 369639288, 201884237, 976639004, 256689264, 851438110, 174283323, 759321804, 308508794, 2641050, 356309950, 62656215, 591763680, 463510183, 980362619, 799784418, 597425837, 37984058, 313691434, 32715280, 741132545, 260536552, 17692658, 893581230, 911043662, 471682327, 150964071, 707296484, 98052501, 741516705, 823661758, 298305573, 123465009, 136833896, 954182432, 874997070, 899589771, 993801240, 57841530, 774123521, 844648525, 745311138, 596437631, 375887082, 351162903, 398863250, 429145734, 171314145, 206421469, 553903650, 64749430, 642456760, 929592674, 690225230, 912568402, 677796653, 473081415, 712345919, 539176745, 877420683, 753714876, 155390656, 634734065, 841966671, 663571948, 259134339, 656289662, 959329587, 444615906, 803538188, 376463781, 973787486, 168961667, 129840203, 195854600, 550443823, 255236370, 869376438, 258788427, 624853363, 939937060, 362521401, 153930121, 990859704, 791213959, 747086955, 252210545, 157643522, 449629804, 248982371, 787803669, 847305837, 460872674, 314998004, 233270851, 69826095, 647597278, 862799271, 679105054, 614067195, 591477176, 917113307, 904348797, 139575754, 750499393, 371469229, 66394491, 370339657, 538376813, 327033342, 285305454, 674643841, 593921326, 978741197, 948105338, 229476931, 278774346, 250151123, 910213313, 53520620, 665378284, 63779821, 214883571, 906262472, 356464534, 673925836, 196690955, 687592524, 863874764, 652928405, 398135640, 834915701, 625643045, 652912977, 814090269, 766564535, 224234676, 971335307, 123171080, 307217403, 557644892, 53264559, 971389133, 876581401, 934745648, 555155525, 963435006, 195775102, 682907985, 981717791, 94216379, 310740026, 404780160, 160283648, 95444782, 169591799, 281603326, 275953513, 921296683, 970219128, 553537263, 298820940, 457694561, 951979696, 541214003, 510519365, 413700148, 931129961, 243335180, 736328971, 233261882, 439446039, 882547797, 540764542, 514526339, 134850776, 200391646, 651868592, 382279479, 935875724, 877617759, 572595896, 995052720, 973295517, 964110182, 913612007, 102135949, 656121827, 422993932, 835829017, 166092249, 288776127, 276690713, 110058051, 603842075, 113472297, 68366535, 938477478, 829350257, 290639243, 619537103, 558708497, 768801187, 283772683, 987982459, 408636947, 745899067, 101782812, 431655731, 437527820, 589871400, 214773545, 460094607, 171243912, 980061389, 803633262, 237370246, 483819720, 196500613, 521653090, 724829968, 205342455, 656874369, 354589005, 277684221, 928931955, 465169941, 910125235, 701348885, 110193431, 672533254, 334598773, 877982886, 577317872, 791911850, 864131569, 710977516, 581038246, 99642295, 53434854, 368818996, 919064064, 999272409, 539745108, 919349483, 774944560, 394732037, 588775784, 619090295, 148962539, 284064762, 75930070, 189345958, 453694351, 338475981, 794522173, 30917910, 409265335, 36401356, 375160600, 112189260, 837124875, 619673644, 543635791, 128664481, 616156163, 780678526, 345225407, 734551172, 642137234, 960791972, 507574085, 906359548, 703741823, 251593303, 791465404, 682577470, 116071495, 193186232, 144100028, 387970188, 637741797, 391194007, 264099691, 763042454, 885469609, 138966615, 47472170, 205178599, 934606528, 436997396, 408573265, 234388636, 388670164, 886064864, 444064101, 593700672, 155433530, 860604663, 697938220, 361408630, 421064305, 460528208, 847190525, 465306373, 289005051, 553608264, 508705405, 349737155, 286720847, 955998673, 512047225, 117862021, 695433571, 394540682, 594578731, 547698104, 78411406, 11493245, 665670925, 608491756, 714312296, 845651833, 555416905, 640037140, 821199064, 807146291, 864420857, 831675931, 18975897, 460196759, 729804047, 503233402, 136500313, 365918038, 178142829, 731644862, 143216052, 256243121, 424978755, 620407129, 348125360, 755308440, 994655435, 122086927, 732262735, 160658739, 307139475, 215712208, 387534532, 973153455, 218662538, 477037678, 448459119, 240755316, 141469232, 817266399, 88893301, 827487831, 203218335, 524202113, 147686094, 279580288, 450705682, 999701291, 252787032, 359752382, 551463117, 348869899, 536654088, 762021601, 682483285, 531960615, 325348244, 698974225, 707341267, 780686446, 378759295, 892857197, 499865853, 74128423, 650841757, 11907721, 929160190, 680647513, 792946797, 500886976, 373001739, 616475234, 430181532, 674267633, 256704073, 795616101, 980153184, 28357814, 385254319, 38800672, 333785017, 315744598, 191529905, 86877308, 419636228, 390248046, 936795001, 825720352, 423938340, 819543810, 279253135, 469582583, 38516615, 197309555, 381697150, 488987534, 393770102, 233908674, 778804400, 103432168, 403538429, 121930884, 847646392, 774249070, 980666671, 922083956, 892228514, 102457242, 300730026, 266614747, 682893084, 691866236, 580610436, 814269609, 512681673, 677014933, 550276223, 637680963, 684434163, 619834096, 245857594, 714265123, 856733739, 246256222, 248592283, 979515763, 303611908, 988574077, 887467141, 19373924, 977772746, 678706289, 66846674, 534594219, 743737393, 717946681, 380924214, 681173479, 713076473, 438389436, 421190702, 818266030, 667186569, 511428236, 637970608, 499092406, 882281418, 767926321, 988423697, 694833045, 197643368, 202505976, 61947449, 336469873, 785431239, 390533053, 423575093, 830222155, 883806455, 590968376, 256537761, 655003821, 486095004, 575759617, 760315056, 960952087, 923708018, 452704159, 825949596, 359810359, 49493162, 420856954, 266520268, 740202125, 559410631, 650852982, 24726626, 316216951, 24244661, 240596452, 378454289, 881536202, 567873759, 734940375, 934396077, 605892189, 613151050, 568926924, 105894907, 263593499, 231652026, 251039401, 671649415, 125004997, 95815095, 996413544, 687288362, 2399173, 823134991, 513047985, 379720803, 410861277, 802922596, 106074314, 174011761, 930638222, 677301431, 405367220, 115095629, 423101505, 376896422, 617607859, 69144422, 702808142, 776313913, 153175789, 654898839, 655286068, 733291151, 36206238, 737928218, 159276284, 690424534, 893896569, 613207822, 878724738, 484139067, 221190027, 288314688, 416084474, 606936568, 526090221, 303598561, 767242888, 743342646, 724223412, 871641745, 1359147, 144477282, 941808716, 537031096, 27317344, 720412871, 349578755, 637987232, 27701068, 184347079, 4786174, 846021676, 630418072, 80726181, 773739771, 276705764, 363519261, 11512557, 820838869, 547395246, 13444223, 144909261, 637822178, 639890846, 281278494, 584124689, 410382350, 469194336, 995146579, 281539541, 86175915, 39161265, 369630055, 200525863, 893767504, 556201119, 445225443, 311572532, 973592667, 324496299, 744744951, 660424814, 876678148, 431769353, 909736814, 493832122, 387633548, 58660654, 788948124, 82107135, 328907354, 79146663, 835693550, 720261614, 142307710, 944140810, 913452187, 884212592, 929337701, 894418998, 757154956, 131082993, 688083262, 687376628, 790080686, 494345503, 897813780, 797428220, 924602452, 47814769, 948076101, 485364400, 619155838, 294327034, 338201043, 291419511, 368283810, 70206647, 637553876, 35365943, 526242086, 981154520, 713814138, 594943956, 27327393, 487465426, 892648942, 376915531, 157583370, 639277155, 619652717, 216921520, 811392725, 47111942, 583162248, 602902227, 409084591, 86603101, 794997606, 169388884, 861716407, 979949901, 778877503, 956745577, 573844662, 330943889, 126631974, 616273247, 196812767, 856687346, 732757928, 519791431, 164296175, 770960496, 192578975, 144300610, 885950222, 739681293, 167644227, 184526169, 159088228, 653750573, 572134596, 698276287, 127457217, 559150521, 741590131, 33941000, 273629097, 228065917, 878810163, 520024570, 587907099, 846466038, 485151134, 947548574, 648666688, 886042641, 203128122, 699181585, 898831122, 385185567, 388284692, 562487968, 186433825, 51217373, 722018921, 50310262, 73762295, 37942011, 297786429, 196729063, 886638967, 238658656, 181219359, 371951954, 466281427, 684360955, 476516807, 267869140, 43592724, 318663536, 447577144, 940021573, 426513430, 627014655, 801248963, 976887832, 859104733, 715180943, 672502860, 145372525, 7587744, 808082184, 878689134, 486669326, 346028367, 83158926, 261715493, 642791974, 666754414, 712889664, 582420031, 862331931, 255664453, 734193000, 812613141, 93631877, 951058179, 395614599, 631192176, 820988680, 760497259, 407274243, 740216507, 691389562, 407577658, 304974010, 699405243, 14979927, 974503185, 923084548, 815387539, 920182721, 65929804, 202016378, 585405688, 899511295, 277254326, 758456488, 356541325, 661452959, 729807051, 540698731, 301357818, 808206170, 787714140, 823222657, 758326, 489501282, 992665762, 548692956, 313877546, 453418512, 838587084, 530027872, 269832277, 654506177, 114283323, 265286235, 377194629, 562367442, 918629767, 845974478, 126932906, 751041799, 662812209, 886987394, 70915417, 426904323, 40182667, 76393896, 315507838, 626794494, 867229843, 697541710, 212781647, 494560644, 586082943, 869444833, 64529997, 903233421, 265272640, 50641756, 98144061, 516309639, 561354276, 1241060, 815840353, 285669350, 222757985, 737037860, 690493989, 678305246, 189567894, 523068873, 555585169, 276541045, 403824355, 329346905, 265401828, 993860252, 31730864, 530914274, 999463212, 929372114, 336226354, 547197870, 976121914, 377710750, 676899270, 456367935, 965748398, 565689751, 246932079, 213280792, 778280483, 466551591, 687657822, 866343691, 758805867, 700999127, 949583872, 810656148, 909103020, 493586026, 124518593, 652633017, 571090595, 488751804, 259726970, 44334406, 445736121, 964206945, 357597806, 55348884, 889926562, 513527036, 529719084, 113590076, 550093319, 651523523, 551968830, 215140960, 61621264, 484701539, 263782843, 141735988, 836449807, 586756709, 481318146, 415294332, 655546062, 429270980, 563960029, 544430013, 474670294, 775805750, 712207997, 854762086, 241102115, 280159460, 119563747, 633998234, 310632073, 409370322, 670403338, 996972397, 578190057, 905592068, 627600500, 682666375, 756095951, 899016185, 161607268, 570512200, 442615821, 337613038, 799628100, 532445407, 256432506, 353305096, 287124812, 746365215, 814014246, 245247540, 543071564, 207049014, 798409292, 489597702, 648298216, 54320822, 426258908, 837313228, 135091074, 723387175, 143528304, 321308667, 702518826, 336658910, 234579543, 582784995, 846504844, 824014809, 999321984, 756845481, 842017001, 548883982, 171782161, 531679989, 379890992, 600141213, 977138498, 581120468, 402231604, 833787406, 434343310, 491502611, 93770247, 37631531, 43263409, 281776637, 935502493, 198269401, 702353909, 673771829, 413687828, 658862922, 533222996, 210185529, 50632319, 991493715, 7004163, 829949828, 934300249, 230711221, 200794950, 835193552, 568835271, 636927687, 859713539, 719663912, 122565904, 561737258, 979270477, 504060841, 435651578, 795750278, 365286032, 404861357, 29374393, 375782098, 154680545, 699710683, 944541068, 349368795, 555927942, 145463214, 371532782, 131871177, 242958410, 198517255, 485133651, 527707346, 41042364, 730569357, 349388230, 843206665, 367635941, 746358043, 139788526, 223772271, 123877330, 294425124, 854254920, 523848778, 360481945, 211217421, 549351937, 802355802, 242469909, 711416224, 825197371, 905371525, 591566851, 759871153, 857783078, 735303743, 269562034, 228372153, 18364031, 375681226, 562280279, 124985374, 961273928, 106751295, 34710970, 487938415, 802949307, 826592008, 657032380, 425482637, 243985626, 953205725, 523006441, 464963779, 775542741, 658529683, 777323353, 434972761, 560217221, 71832268, 691211741, 558005844, 282638332, 844142504, 652415037, 717303812, 217240466, 288818332, 846088553, 57580257, 765574394, 53885671, 599604101, 420474104, 524659312, 30553438, 884351708, 109328534, 910647625, 358185870, 73987102, 229496598, 534177476, 757888590, 731649855, 429648858, 787601976, 719435874, 526184065, 511776042, 259622198, 748465473, 811524339, 783158461, 628188955, 211249512, 460759309, 314649882, 394187580, 357163156, 111020311, 301203040, 551455298, 358476241, 136398143, 159077166, 209772568, 734266334, 933910745, 134348501, 267015447, 191834955, 302160647, 877641974, 457885199, 315488877, 784373067, 457952867, 953928713, 14227146, 672402766, 822389883, 906764259, 705414997, 27013677, 792408410, 979764593, 190214166, 684633560, 684601098, 697069139, 422981239, 476775166, 993910660, 543528162, 386953677, 267846200, 108898458, 123580342, 820218190, 147768419, 91801463, 708357973, 482817139, 736551990, 289925336, 116971302, 182927790, 63407470, 209471088, 669049020, 941128386, 30735245, 408490791, 3907014, 150406015, 719620746, 31831897, 186415387, 15010954, 851726842, 545401636, 1061595, 260266439, 226863414, 748056551, 368062603, 545826171, 830410778, 783681331, 340584944, 835329710, 941446401, 283184656, 241722169, 308833460, 960005550, 272646794, 374612865, 148167146, 312454619, 487784796, 891176216, 106505593, 315427404, 731972321, 243778675, 985640602, 90309819, 433529001, 582098231, 949727249, 356783478, 719452198, 665264143, 244422805, 149246914, 996666078, 95224846, 809873695, 254255447, 843504264, 121878560, 526104920, 670705096, 190589707, 648386439, 125353749, 63236637, 867200670, 241432791, 252974335, 583940404, 524607408, 762382843, 203959361, 507650136, 191215246, 395532935, 661318259, 310271342, 997187035, 184757833, 817785248, 680017810, 788476255, 132230152, 327865162, 396471444, 260061700, 591118063, 324818262, 130051462, 598576959, 888312510, 919013911, 498673820, 171388611, 729397402, 500823731, 317594831, 905056636, 762233536, 270193105, 718828879, 735623051, 253345552, 502411444, 83972171, 269752228, 68994413, 966763679, 692149605, 137492797, 244069944, 961435949, 446558148, 617574735, 245262491, 526298357, 98802338, 360104749, 683632015, 246158883, 758500140, 112307794, 893531231, 400226798, 525487316, 765188822, 803969167, 978987436, 234338605, 477255301, 780499236, 748416215, 549887236, 426344070, 250649381, 491602365, 645959900, 522507577, 107317277, 946273306, 272095517, 521975296, 308446610, 692043909, 23748453, 312184959, 310148759, 776413426, 768560778, 532265386, 482244843, 291029624, 779855267, 268736036, 146393241, 181997807, 912570425, 752656334, 867357611, 825091054, 740835837, 125985114, 244449188, 721722408, 871975219, 298634433, 177580640, 32925673, 687462229, 684060438, 475402774, 303047455, 521132371, 765511786, 196370431, 382269368, 152708521, 611058046, 572527464, 829689370, 441033762, 379227731, 946707049, 222291890, 682016904, 935416592, 25671644, 528056136, 73368238, 995687522, 533759792, 539434133, 428585946, 783533652, 444814075, 831217225, 287898744, 99431486, 262912120, 198849987, 869884693, 563445718, 737420484, 818140263, 989100375, 710973559, 9252216, 5130747, 398282759, 366063040, 332291531, 45768850, 959943933, 31335120, 598701297, 389189947, 385757933, 187387056, 332310, 160748489, 959682373, 338386105, 137287338, 883389119, 689876352, 314729437, 657021334, 979261960, 107449043, 930904206, 807590296, 922453176, 734153532, 971276235, 765817794, 797090236, 340405868, 530972905, 183253970, 114585716, 222115108, 431012093, 647369474, 669344679, 569085196, 375567660, 775970510, 721916531, 729344373, 906072491, 88603136, 491297163, 682371120, 214612920, 123673103, 825541371, 842079180, 107784489, 246027068, 469416843, 192399675, 241544226, 580744227, 27177043, 496959334, 490487155, 945831092, 138071151, 102960491, 699087652, 286314031, 103417266, 410087329, 417201823, 182316670, 670290103, 622755892, 525694442, 486026872, 556383025, 322312625, 34743112, 14320643, 157587079, 686078404, 486821809, 297519644, 237913609, 758638609, 803381736, 6080624, 560993758, 989518697, 120793681, 289992266, 171079899, 475755469, 390112420, 949771270, 125859907, 845514253, 48484200, 145488666, 368398426, 307209228, 92885278, 542449224, 436064108, 485594860, 284240332, 33699602, 75246796, 231958211, 356672655, 455582018, 374034293, 200461198, 340624063, 997155511, 648087626, 666858793, 450077716, 40746079, 63796507, 143921665, 182438762, 733218927, 583514074, 838299714, 39166921, 323719461, 942450321, 91070488, 284196760, 865172073, 432852250, 279993823, 791538985, 532034256, 700415783, 287994390, 73492940, 348717436, 529017756, 870896681, 917214773, 413916241, 41856566, 646143104, 62299416, 451718045, 185485503, 953447917, 708741762, 369761225, 341417818, 430621847, 154774977, 896609762, 822205581, 545675251, 796514621, 665819708, 889677251, 708851578, 80147835, 588546166, 415870577, 893155126, 879011177, 386757210, 848874017, 934123973, 147197377, 424273533, 589499875, 578440681, 6964109, 793625609, 337967185, 809814615, 188726984, 558071747, 639178521, 561972153, 726730842, 983135540, 2081235, 879284471, 655033708, 767757225, 249231267, 79265248, 749978881, 259533640, 179433036, 140538681, 515794177, 200457670, 680764716, 143609110, 641866525, 476932301, 236755911, 539515176, 116264418, 634053582, 57144860, 997881970, 437243723, 12714765, 791692154, 688127069, 535806545, 107638375, 935151876, 732803384, 907840686, 393087822, 847402969, 346267216, 254734569, 876849878, 841113036, 608367597, 345094706, 781897674, 956234853, 887605863, 250009302, 400585554, 85949680, 579245272, 622863366, 112067211, 62209796, 30014330, 348441414, 899454508, 786308330, 256787752, 549606925, 526350735, 796728684, 523894677, 592034884, 35143740, 561224653, 395765641, 23966086, 821570352, 944838230, 150944462, 690227106, 170911052, 690070288, 753374713, 338005657, 861597927, 595595196, 488362955, 43976271, 89517478, 601893084, 144622608, 94229513, 689266509, 691666613, 794870550, 722878901, 744170154, 500608235, 874269136, 189032448, 388230176, 670274735, 960101893, 653734062, 436269266, 320534201, 175400475, 503643675, 214029342, 155717636, 910080848, 565475509, 77912777, 68135389, 254624705, 326451334, 741136630, 263110111, 806045676, 494212789, 227212256, 587000885, 880924939, 328699997, 48505712, 73942177, 894452173, 932775493, 689822875, 29714712, 619289015, 74799073, 709419045, 837376264, 151113971, 450229339, 417470505, 680272047, 295353685, 164843334, 799340863, 715779216, 479778783, 19904260, 437709233, 531419012, 638266498, 234817123, 387528303, 874016316, 624452229, 336784171, 207090673, 461678711, 540897196, 352168086, 99904403, 450815152, 234159037, 775482149, 589577422, 974673284, 917538713, 533343512, 633369107, 404138498, 879132426, 862242479, 897989840, 154760470, 103299465, 332371258, 99732054, 18281397, 160300561, 838747316, 194107377, 427177743, 126615857, 700019034, 993276356, 972115407, 838484213, 956018065, 55476684, 347330609, 503111515, 986984970, 138162465, 926072760, 505061305, 52666810, 979756838, 925326109, 214731139, 842694911, 338155808, 837670785, 474724318, 835846570, 547003355, 647322791, 831906599, 201659348, 174527889, 846962649, 852282039, 18974496, 395477248, 601682022, 671303428, 626467046, 310084851, 784616394, 212654772, 384217618, 14361168, 109264045, 570916841, 412275987, 688475336, 360353914, 87488137, 118016963, 878957106, 812465175, 599600261, 415174659, 531428694, 154790002, 286614759, 28608188, 214529482, 936390648, 165554782, 339484286, 773334527, 557239519, 739255933, 234856274, 675835949, 768575760, 939726303, 369730888, 413386830, 6981849, 944504715, 296302349, 357976490, 570588673, 280872680, 406421258, 964055629, 103211165, 957763774, 554260424, 471451211, 511550985, 657495785, 21239963, 737955568, 125350060, 536128852, 684890347, 832296231, 534235617, 73336188, 144466064, 976738662, 361311321, 53261981, 203912186, 59993215, 37822164, 598695243, 447458634, 75822046, 696465340, 151167326, 484837784, 700700248, 635715082, 937199336, 116093508, 408718130, 141865086, 30242427, 882343778, 107509795, 549084528, 113031379, 827957260, 207447611, 79160556, 157206423, 325604057, 431118524, 332570024, 132828109, 194153390, 16285683, 597337757, 141537578, 597164954, 644819414, 548487574, 676439973, 887155066, 408766075, 374064251, 627280172, 881583908, 686476007, 260488690, 459543401, 234501636, 767151121, 767286150, 304516992, 899451753, 413666127, 81381068, 760811276, 11682851, 229369427, 443928257, 348920485, 114412414, 824639638, 320417292, 719604033, 208099192, 661792873, 355604755, 489208379, 720177760, 767727266, 801967834, 697934799, 373979260, 625449082, 900819067, 524569770, 968677400, 959519638, 568653859, 889318694, 392277899, 572394329, 563721391, 78280642, 277687371, 634812929, 383653244, 1616646, 341182599, 767499673, 977704935, 455950979, 797182583, 692821049, 903203194, 740271495, 894536712, 85290179, 42844791, 644749591, 757718515, 612949254, 458091034, 831395515, 944748208, 536173620, 812307699, 869672483, 715601222, 22982600, 957516465, 130948594, 608865699, 431473383, 633367288, 151337003, 715567693, 831616464, 250093093, 343893741, 147873990, 367153030, 315137205, 851098290, 443492342, 41075170, 721717104, 461908009, 987971305, 968100371, 71306484, 658917665, 447461343, 198329190, 742103031, 403801750, 547559475, 270692480, 244243852, 958002533, 605012317, 249605865, 627489474, 558646379, 436918545, 758600232, 863514135, 680991348, 102358884, 100736632, 944869588, 864842023, 239080140, 88617790, 580786333, 398371367, 919695901, 569156348, 125404541, 60334877, 512654382, 361118584, 332195569, 899827025, 315075125, 32303356, 159523070, 447797144, 412457883, 59537268, 468789987, 400367419, 382445870, 847229782, 219896709, 35280270, 519209758, 524822066, 3233310, 547716377, 953918557, 620592083, 744937048, 666580151, 884822616, 847930429, 633681921, 358278295, 315886561, 952205226, 19912593, 415016144, 980881829, 189853511, 917642325, 631479521, 576068353, 844964085, 675816850, 435696466, 663350028, 121972998, 346292047, 482300635, 89532418, 406226974, 186090623, 462572278, 669375369, 5408488, 752244415, 850143099, 592811818, 877360436, 816585041, 267807363, 928359340, 490279915, 879454965, 140047357, 162866020, 521186048, 686310037, 896098661, 145718718, 910491459, 239452718, 864690449, 283246290, 256832224, 712164024, 292750308, 33461981, 936339733, 443340585, 621803616, 215827426, 404292443, 578464817, 864099455, 673847716, 698485360, 120501175, 254883510, 23893532, 972265483, 166773984, 688026346, 903074196, 139340168, 903871254, 915962556, 376194413, 239215062, 747637726, 691450567, 614536958, 632279476, 313162116, 946973310, 914098190, 354101917, 333146126, 894716540, 499692257, 695303328, 671758223, 269663143, 553832402, 109829107, 547498364, 959396616, 936494093, 267398087, 803502298, 444148085, 186432654, 568443478, 128036394, 869405998, 676956845, 323497183, 368841210, 331874643, 468833548, 238938311, 727440452, 352338021, 196183083, 923794085, 647620836, 423128551, 566274816, 942898140, 595533634, 373591247, 503450648, 301916466, 8708120, 642390020, 960366268, 417079708, 19505217, 718437283, 994272337, 576266953, 267978380, 620876115, 560503150, 104881744, 588577337, 853021532, 92773150, 331318249, 40110799, 537465878, 99091266, 715165496, 143295717, 559433274, 232148910, 646022496, 753034835, 511186097, 666038148, 21304319, 640529253, 189355797, 348960957, 861505285, 772465162, 106856831, 276835068, 553306661, 594996372, 301654227, 572507808, 78309419, 924568234, 98232032, 793021913, 711613980, 178313275, 248950636, 175842426, 635103927, 648551638, 149175721, 106929333, 681295125, 195268085, 777020239, 545394095, 952433086, 431032492, 33199450, 639097493, 674713037, 373250856, 965884177, 808755756, 799244766, 874813906, 288041242, 972752016, 56146326, 570362108, 935808679, 262328559, 215709345, 919935644, 833924640, 221800020, 449290613, 324667430, 878602819, 535946140, 808444930, 230631535, 674122035, 266791111, 60396163, 921155403, 821742062, 476924890, 361644767, 72403480, 49853218, 747630009, 328061877, 417439488, 441033656, 632159512, 507820721, 522538070, 402865791, 855645408, 573952911, 283054350, 765745744, 537792458, 839929118, 554073294, 59924421, 136721373, 808381582, 364457444, 453435390, 402637446, 753919866, 960999911, 119331766, 251289717, 436669280, 182959411, 756668304, 200061312, 639127990, 595742744, 442025654, 763865471, 45364622, 984634075, 24386047, 285076211, 553281647, 36658000, 403978309, 146293223, 293518758, 39242324, 602427218, 955698155, 291735536, 425142178, 75573636, 460266447, 659879658, 544628691, 943659730, 491755148, 584904449, 414747421, 65881365, 976418335, 361809044, 328089179, 964390969, 950865970, 17441554, 991030273, 339159023, 590015895, 277362288, 697562806, 106295843, 390948291, 632721428, 185630689, 897951902, 142045815, 558379476, 444337643, 44745411, 161987194, 226963391, 911420654, 976080276, 893233652, 868123763, 333580982, 456166449, 553226012, 429155676, 92484550, 307074065, 410004017, 889360299, 565314544, 241794172, 436631745, 174423984, 852262193, 710263851, 260431951, 546490030, 785215293, 503322380, 109051541, 311081459, 531805277, 831672011, 457192453, 741254711, 618690461, 58033924, 458754281, 361402738, 428617505, 171527688, 86775423, 517784449, 258114637, 258639601, 747565466, 130007837, 3824845, 93132914, 233111935, 259801548, 149413240, 983993691, 797668615, 918119212, 64008440, 727563489, 312748211, 806530225, 866354155, 445614416, 903652120, 203652303, 886830107, 140246481, 263444821, 487926631, 642834126, 430543872, 797090506, 318096696, 507881666, 913908099, 11604038, 127172645, 357073165, 927274288, 707900290, 399462925, 207720041, 369532459, 713115912, 435903218, 890799763, 359602672, 936757949, 53399469, 863989773, 753734723, 212994396, 614085, 891786927, 370823381, 566691107, 718646251, 442898749, 452139134, 320961586, 354088058, 468086759, 706349926, 53032139, 599933231, 446990631, 444222755, 372571834, 698225119, 695399666, 773574399, 357184755, 776504072, 732137473, 709119495, 636698340, 844173280, 82185779, 539007567, 9446286, 83539706, 442043065, 112979215, 770200179, 968899491, 858582385, 360788009, 591691548, 389559186, 336045146, 534624429, 59063331, 715080752, 113577201, 987124861, 641187180, 724691310, 213828395, 360706711, 719910163, 856165805, 996203522, 952128882, 703174068, 232818133, 634861302, 251314743, 576130620, 891228599, 486125878, 347373354, 52345979, 128590367, 623188252, 624162653, 962840768, 191294364, 913331870, 154984041, 100738988, 965337639, 66372124, 819650510, 474557643, 236107285, 789901808, 228091145, 557034352, 973535882, 299116824, 586760351, 919651985, 961388014, 543399430, 766958569, 894780133, 82087971, 590419346, 925531041, 579062029, 720235956, 296886807, 807992629, 614995145, 598264088, 243167457, 397911710, 61253677, 91652372, 379127543, 273371304, 873818489, 180069344, 582614778, 450787111, 439930485, 301994391, 172207571, 268398348, 890519151, 324178453, 49325071, 167737300, 469953303, 494682128, 863564786, 379510961, 689764652, 920206372, 84701663, 536313610, 238050325, 839640831, 596351160, 167564077, 982270299, 970680906, 516740209, 680315547, 485981814, 345284543, 46138708, 260154757, 951418001, 87190965, 684993063, 407087809, 182928954, 86958420, 785384537, 598499837, 497547438, 733147693, 996554609, 483929121, 298046403, 280071453, 182201137, 258234946, 519357495, 775316726, 481500777, 378576679, 213015413, 925743368, 27325096, 807576244, 479734205, 258359972, 967227, 911207975, 265318437, 476009591, 667104769, 186032845, 659780186, 875108674, 354291436, 126810023, 820601994, 295726725, 724979290, 567579013, 122925213, 332448980, 890660336, 194800023, 796117546, 305476044, 132448718, 297922480, 982015526, 926552629, 329339295, 880758407, 955707493, 404114257, 479776440, 416277834, 665259754, 967297698, 895668877, 765533058, 644604533, 19766440, 937495159, 374871503, 759097578, 898219041, 453288928, 940326167, 596071104, 213452496, 251154939, 120981557, 143450911, 729162194, 916388434, 915918014, 636253694, 673753950, 737828766, 253480748, 611332843, 473403153, 83130062, 186440894, 862301875, 709879494, 155794511, 309553452, 583303847, 373194393, 997182042, 534294410, 598556869, 663967431, 53656262, 780834477, 953191418, 713183738, 35773636, 206857349, 960533711, 530527494, 737030882, 697351356, 40991260, 489215176, 792718472, 606782076, 542403926, 724173148, 238621950, 435022195, 488311403, 436226960, 314979943, 193558304, 374905406, 870519144, 981998494, 693000922, 988395328, 797987201, 564663247, 883618478, 122371689, 275580554, 796079454, 598785764, 434225902, 795750553, 393578899, 750770899, 686313468, 822126843, 782545868, 832183920, 671106083, 144341797, 700451317, 682448248, 286482938, 857962572, 580347433, 654803229, 20331307, 192428094, 241231025, 666908657, 640002483, 488858255, 307392177, 36891839, 759451533, 278546701, 413682854, 538439375, 791577454, 659576628, 468769084, 24871781, 42851931, 277370287, 942962095, 940436075, 674662222, 223154700, 389087925, 288949462, 956671979, 784701640, 605593367, 992701530, 486496081, 305008458, 758641137, 465275842, 956463323, 939876469, 610897834, 599358067, 415940385, 504626416, 328576710, 17217047, 419754822, 671319092, 932054257, 984890464, 806855482, 417809640, 177148459, 440058847, 539278363, 653060463, 955068168, 593253126, 887756207, 787136554, 361893918, 354498579, 150772784, 31699000, 84003374, 169566356, 429598682, 87540963, 71516326, 447912785, 792729602, 848795911, 944124125, 251091054, 590379615, 237696705, 287462036, 417933260, 848542971, 487557133, 74428201, 485713542, 513593751, 336148722, 448567158, 290922947, 939599864, 299746508, 76523942, 75042446, 736253934, 994781062, 171272606, 699574402, 435585880, 851279441, 652000345, 474764919, 397625217, 163742404, 693953240, 861222428, 88102557, 986263237, 508710000, 991568119, 578697098, 193714424, 387517530, 992330945, 63610347, 912565908, 990635183, 290701184, 454301595, 403512639, 70307908, 857107123, 762394623, 841902486, 666159582, 366230066, 221898371, 542082790, 854669158, 965136461, 202492638, 793340909, 690142410, 231776610, 926449425, 910977129, 230300040, 750549056, 419675764, 110247652, 945269000, 970911039, 63396117, 424771911, 741862566, 231717581, 266119486, 326694898, 745798081, 810752844, 230616021, 254245882, 186054504, 807808752, 453254538, 328163355, 713796846, 711538019, 551722277, 923601592, 396731197, 197256270, 231184816, 915983645, 484609966, 276340230, 664565909, 555698194, 741410215, 94295545, 245588591, 933569526, 108396010, 72166270, 957300702, 673149963, 688732366, 601669809, 495959351, 701770904, 263323826, 275253286, 124367722, 2734600, 420488510, 80913777, 326269489, 106918400, 613319399, 934400777, 439737807, 680376019, 799638715, 707167213, 955356673, 157012925, 551588408, 419059661, 873550859, 491599467, 941527032, 727612131, 139892498, 949157918, 757483275, 624436025, 529363734, 143406928, 909198936, 748072490, 634327877, 18104425, 379430137, 118084030, 827048088, 710799903, 623524562, 991691175, 358492755, 67591133, 241090140, 503549537, 457175122, 350921434, 750497064, 64988700, 859336356, 237058357, 137144775, 343793704, 326505408, 497189043, 892983307, 237131281, 935311269, 359309429, 80239012, 24801479, 501307990, 624878903, 265940849, 306422625, 52500088, 482848509, 132717108, 921646677, 513754830, 439585270, 529799753, 245920117, 657433183, 387778822, 935556434, 377164569, 773224679, 391455270, 917325682, 805970655, 22766151, 531614558, 325602180, 428727683, 343339065, 326973139, 75700361, 914606244, 952587246, 515312109, 145961359, 997273968, 144564614, 908274600, 726530551, 655006923, 788305502, 473829797, 678169028, 813486710, 742409090, 248239602, 239286729, 343829113, 73181693, 596205035, 399138277, 449901593, 653701684, 851323690, 812905215, 536834390, 251498622, 191559987, 429210439, 333664263, 272405973, 243333569, 816625282, 394969278, 526271870, 157390056, 823739262, 174032266, 53097163, 546286788, 934054524, 606528329, 604306554, 123031184, 66519386, 935274240, 322720622, 461829036, 971124327, 283023026, 313003892, 600600973, 619035885, 973374058, 39825, 200206299, 42347269, 73732344, 273228295, 532791109, 847358537, 361338355, 371344527, 376952847, 306044107, 857936433, 257853609, 4139262, 880192936, 946227645, 277191246, 984270515, 384483395, 554834928, 579025521, 279133744, 44418629, 177523319, 933508740, 239194651, 224648962, 956979983, 555467453, 221553626, 332609125, 914506387, 115189144, 119353705, 301683539, 925350999, 985227683, 828707860, 293511065, 721566560, 841822295, 889991993, 404259123, 787204592, 512681495, 459844120, 114282188, 254653429, 211636413, 555080057, 469882947, 87028688, 221499898, 17167209, 516576539, 547609455, 581198527, 857996296, 653031600, 679175475, 747692458, 755721184, 725398568, 747772763, 345131604, 617778793, 984802228, 658791631, 533883228, 989469540, 362321013, 612477206, 563470021, 417577705, 936512024, 246856648, 167541860, 186272290, 734169420, 941479057, 523255211, 862427987, 489019477, 549742769, 629794235, 1145583, 564674985, 459175465, 341343488, 748692303, 391698902, 759073987, 214827023, 225939692, 672683471, 260578935, 602733683, 946632319, 3911113, 534103402, 449077264, 132129961, 389758864, 671513637, 439904258, 190170600, 685417699, 139894268, 258040904, 200334579, 693054931, 895493180, 114454729, 8972787, 341758372, 26343267, 555367778, 690765421, 580958384, 337409685, 149366458, 276875064, 695048460, 36518971, 734884482, 831110138, 764364067, 86060433, 299543698, 636158625, 720725846, 160792987, 88725375, 923786212, 657934936, 338469792, 834367976, 156012032, 388862765, 493568946, 373442644, 748626922, 992931962, 79694534, 132985725, 431510537, 60233134, 948127898, 457540049, 345597233, 985695178, 780191773, 605334852, 632780312, 48939293, 273148917, 120368028, 516598947, 785875825, 551225051, 287247270, 218549497, 732195266, 970082344, 327083142, 329278064, 701551283, 161785731, 587128510, 821944980, 30556133, 273212081, 827874491, 577829261, 253863588, 716825404, 149417073, 212947487, 393458078, 570170768, 158868666, 21531319, 416836166, 94155425, 375415448, 848378056, 64156827, 291416978, 666546806, 909675659, 495715432, 586548240, 881674190, 345839218, 143007099, 327952575, 856311612, 976111976, 625108241, 76989415, 651451962, 273090621, 744577107, 405200504, 176434506, 956103016, 248645083, 390437760, 867778426, 19834824, 181686803, 372485690, 189284301, 526122275, 572375486, 503178770, 963761103, 971635904, 276050488, 393037525, 754309357, 680312567, 596724844, 719467883, 614914612, 905901249, 377493859, 990639316, 154190033, 670432958, 274367469, 313081679, 102418800, 26694346, 185660012, 218877287, 213852814, 441499435, 72566398, 899972694, 641963663, 580545800, 990874750, 199883995, 351599201, 487131143, 457229429, 404670433, 4933619, 898026554, 703484347, 535581311, 9286018, 144353800, 260261518, 566325691, 970513587, 768310366, 889023785, 173601812, 535956854, 455093153, 87811404, 843076176, 473985374, 420067528, 990636626, 740993649, 157246543, 188195900, 712200246, 374142337, 901937928, 26928655, 653291552, 579185920, 277247977, 785834624, 549113930, 517204936, 498616755, 59710653, 286059960, 964334576, 565856428, 6669806, 352360630, 965718402, 805245336, 243698995, 523587938, 577110944, 689588996, 331265609, 451742345, 788536690, 947479573, 871534312, 719926444, 233402639, 238195113, 246449268, 265230572, 953230183, 491446333, 671197979, 7047587, 16671666, 240888335, 140062060, 706895620, 748977270, 492530109, 434987277, 337162560, 470316883, 933383345, 252244776, 618959246, 827493296, 875942867, 970282902, 626057245, 96970027, 849099662, 772759510, 197098674, 306681007, 709803829, 836488570, 273442000, 115598660, 488702261, 870194750, 57652682, 997416473, 529183324, 75867853, 972531095, 625177687, 184421291, 330967023, 664200861, 358399965, 604445608, 882599504, 752623657, 496937357, 59750851, 621788307, 635789161, 275679622, 827635235, 289610650, 494972688, 258562653, 737295809, 226287271, 645231611, 75192320, 572911455, 60717784, 978696221, 682879037, 677786264, 948675474, 339238334, 589041248, 549125039, 485298582, 883874604, 864965847, 765296099, 948768527, 30104772, 454492007, 914855627, 861330003, 842381341, 226726667, 929845260, 980551468, 762214052, 489320256, 798487203, 662900436, 469331233, 161680823, 417168944, 669871431, 127392157, 250111371, 35246008, 126868351, 93711287, 305079419, 479688972, 304702453, 811415452, 658185243, 845080895, 85843304, 155536938, 118173224, 315968584, 766146962, 638927549, 813042777, 855183675, 271804840, 40717076, 885105410, 899857241, 434664830, 568735871, 657738442, 737943427, 328894351, 301572190, 696956033, 921457996, 561507911, 179689599, 985087370, 113010601, 341805605, 388225361, 829519317, 417724430, 699915482, 647193869, 987594114, 453600658, 266979551, 447159341, 877716100, 925427966, 300958648, 518439270, 727859569, 103708812, 28678347, 180676360, 171236096, 894703194, 92730318, 330297317, 91761973, 299039419, 148694167, 183039391, 748013797, 384273839, 845895751, 248195479, 18678431, 910423700, 413743872, 640810030, 33029132, 759135589, 949820960, 707188691, 127782889, 38798486, 470943920, 479633874, 702175842, 455659636, 126615266, 914983365, 132614214, 110470652, 761578387, 406060959, 11665895, 945773959, 90172252, 231781073, 493975115, 431388485, 905854703, 887223348, 496936186, 907649222, 584330727, 947129128, 203553671, 131425463, 873114819, 55013211, 407245658, 214762788, 365795404, 306691043, 568516961, 883138457, 417862974, 103583370, 596659562, 230376807, 676145482, 124273327, 33394490, 592164444, 602580791, 38801531, 556212389, 458194518, 622410982, 69369731, 653380598, 136528398, 618185117, 653364674, 513255390, 623933430, 442731736, 30561095, 981128012, 366784173, 159083276, 497651837, 175107924, 580012839, 547417685, 253066693, 288801627, 534234275, 880706689, 300143322, 564726276, 275553459, 406040272, 254495329, 987048813, 64676769, 441978557, 18678310, 525394761, 704736501, 432613354, 138851392, 122731129, 268766057, 569006584, 92775041, 948529335, 457619443, 230544756, 368515958, 342035753, 544229607, 238065117, 778089423, 806268241, 804874619, 263830987, 796610254, 117971509, 409630931, 829234682, 170183232, 63611100, 290135020, 525840971, 841288283, 95450998, 331723279, 652540450, 145016640, 78754803, 499886419, 374588182, 763217486, 72985237, 631031776, 213628056, 537188227, 306985253, 270297719, 497551303, 130823181, 757229236, 434626408, 719231760, 2107453, 970337367, 561391641, 19862835, 926180724, 407224549, 599014735, 804131798, 187969252, 731515992, 576234532, 175091503, 847989924, 39441746, 144149740, 399059542, 347267207, 576982081, 773749599, 905394895, 762226404, 56316634, 694295387, 746469779, 588676842, 290428562, 881086864, 474519769, 395301284, 994260220, 219811629, 855669593, 423365268, 74956469, 41087431, 676564891, 774949322, 596125750, 361071408, 293807262, 59431982, 662741489, 238317414, 45635406, 78701409, 848233728, 389037534, 131990294, 385753469, 894296061, 127964148, 6961099, 926257214, 13606838, 288864832, 580484331, 328777804, 151793963, 46476220, 717619171, 476688550, 290763997, 133169100, 709318920, 817205736, 371308225, 216511838, 654058190, 766273647, 784750066, 82277349, 659157946, 671372437, 579478278, 661691965, 665452412, 940904569, 378404277, 124143660, 285540609, 445198491, 715025402, 850832303, 805372353, 906635976, 247592222, 422041744, 339962339, 685210079, 294849456, 969554398, 707248416, 415851669, 657166265, 551379698, 519306776, 942357103, 479494570, 330541528, 707175884, 889531663, 765718562, 410643499, 411120600, 341595009, 857973460, 426088457, 312090874, 233046156, 102203318, 483072844, 70452268, 855440285, 636070837, 289213814, 864401731, 614773833, 309532466, 136241264, 909955027, 768283164, 398899747, 143498127, 10298813, 638856350, 859305241, 988444009, 553679392, 475625993, 296683191, 899546659, 862473069, 965182355, 336080293, 406807507, 206989007, 111164919, 942654374, 790947806, 29288221, 308781338, 386575578, 345191776, 441499348, 656157602, 45399575, 12743002, 896705128, 427461829, 506017903, 413800572, 367078252, 755163095, 370222472, 32861513, 217123679, 665714528, 778019878, 435751675, 5396732, 538597818, 309296166, 427362408, 723109521, 205558549, 10610330, 157850236, 422076531, 356313780, 344014077, 834857092, 531728948, 586868394, 777699105, 650567871, 142441761, 40357451, 865195956, 25812897, 543373533, 272215813, 894545126, 506504452, 941189035, 270508314, 691194995, 107465562, 444367467, 292883603, 26355706, 631607108, 695896801, 823593707, 902125059, 723540215, 165724695, 820874619, 1119028, 220427679, 944854213, 596428505, 297812539, 487328974, 768779587, 42776395, 140933790, 806931407, 199274019, 410057843, 346808765, 11902656, 343786525, 235822876, 68536062, 813750181, 739344538, 276362132, 290445247, 973832303, 161741708, 945622133, 729389152, 647446385, 62055997, 951971572, 269529971, 861423586, 701857641, 646959077, 849836966, 221631558, 387410648, 737522450, 928832683, 441161933, 623747643, 161135186, 679325491, 35263619, 34331665, 296900038, 315174268, 709532697, 857444952, 72512175, 615048453, 392760515, 251000549, 851653551, 812811299, 916002590, 807064686, 352749903, 769492970, 403130321, 186472067, 358201062, 622150681, 102217839, 634077878, 112464426, 678527775, 424136870, 612871883, 624841866, 176953403, 32662543, 242967993, 413587288, 407687239, 701741126, 170231212, 90688079, 787374492, 170743596, 99814796, 522138546, 197913327, 634617715, 409077045, 23232132, 710881604, 979691352, 335427626, 130980036, 376549076, 363894247, 863224224, 39887408, 947612893, 591537483, 579071448, 547420641, 176961251, 593533372, 100710319, 197905558, 549243433, 487560458, 856012353, 92858828, 268031614, 106561053, 292479019, 137705667, 38404934, 263993986, 270623413, 252996443, 261198080, 81505637, 483192496, 822114071, 417973381, 12363819, 983149243, 262883037, 731770525, 748984846, 214008342, 997477368, 21451837, 82987402, 246417397, 539365511, 303200603, 571516278, 213313155, 844034031, 27068144, 47654270, 704165313, 5384975, 885909595, 685370629, 843713832, 138090601, 642299875, 369579267, 203249845, 897606310, 406097082, 461930214, 193067956, 158444122, 369010689, 102676234, 719861112, 454469117, 242335545, 367778122, 124727016, 408437834, 717868072, 811828370, 449685984, 106915902, 675324413, 67966548, 958085392, 983324420, 846982732, 799102816, 632107202, 812521382, 6998837, 220467774, 523992766, 552145359, 992499811, 243564559, 176672883, 286572572, 727676748, 171912138, 1645269, 975209769, 784444730, 238364676, 161502667, 643555889, 603667075, 161313498, 561586229, 784095248, 961994337, 199183995, 112401305, 733356380, 164698451, 943972660, 465760920, 937304417, 482886930, 787641689, 487364624, 492325445, 560881066, 626720879, 478409260, 442604523, 510307711, 142144579, 517667013, 225046983, 372928109, 109478568, 5788372, 133723643, 331658583, 630888125, 949172858, 691176458, 244567106, 440356186, 454866234, 723047150, 589394822, 568253074, 379032528, 557491456, 337743229, 399478544, 824716973, 543623412, 929415675, 878487134, 717395207, 766758713, 463256069, 416147906, 692932119, 743175440, 640141727, 195213756, 283555840, 503475194, 31297715, 105694466, 561557824, 603800342, 264398298, 118003881, 229860239, 242685699, 280313003, 261067443, 975932615, 612370496, 893616279, 114660049, 189880611, 836947636, 223925977, 694134179, 61714093, 103070592, 256755548, 690693090, 744634665, 669541531, 364361776, 781067906, 359337672, 524759852, 681700560, 911258055, 258043379, 266175187, 985376969, 973589039, 810404231, 686681047, 344323092, 469777972, 781698442, 883768045, 511900378, 403479762, 612375921, 458905518, 84941273, 332013534, 232007092, 467249726, 954843340, 578832620, 817841058, 444936974, 238492450, 531495949, 287668354, 675127408, 646579508, 80899172, 47710479, 118710441, 529475683, 697062486, 499716447, 140216163, 579368545, 207863190, 454328013, 631060148, 333526232, 454390932, 578440410, 886593987, 407485147, 82803372, 872483961, 172429053, 937714213, 169899755, 912122690, 666097923, 300399522, 145558576, 322040263, 661984132, 869977213, 77359005, 204741640, 625345479, 897462625, 429576551, 818925970, 641675195, 509518216, 486297409, 935212456, 255407310, 46810908, 124824973, 701999199, 77237166, 743433009, 825580231, 737510583, 869565914, 207196350, 239076253, 160854101, 703726033, 596463714, 482311055, 319622580, 251834275, 438756723, 798803795, 930329819, 653482262, 583085529, 429994051, 164509089, 524286169, 96527711, 273608107, 679359232, 461050380, 711903291, 957720900, 794623679, 247518526, 210325577, 178762415, 293406800, 572166436, 299455134, 644264207, 51068042, 358068888, 438503499, 583907627, 660873371, 153415752, 654644497, 673441363, 274571347, 932774038, 858751290, 907473082, 770924045, 603891004, 543392381, 72989159, 144240368, 464481639, 567576461, 208811886, 110025818, 344615131, 504836743, 689126601, 549317663, 256536350, 495055434, 637044827, 755680189, 710441033, 147463796, 72866024, 198066979, 950410639, 536920136, 817741101, 758811627, 894788114, 71371132, 203049376, 469348813, 244252933, 112978402, 593053730, 885617757, 251035480, 54924876, 976775716, 584502941, 845294171, 859322242, 327093806, 300595057, 762742782, 521255506, 366648418, 892252027, 843135189, 336375028, 87809245, 277515346, 423947390, 670011693, 602620390, 988534805, 100529074, 297622636, 128738783, 344608450, 518154926, 205357396, 647386568, 11413129, 273815071, 605745772, 535735529, 780955902, 238803305, 72160722, 488308642, 254210590, 719264294, 919889283, 282888952, 764466204, 84447424, 562552172, 372458069, 653243988, 107784996, 777947740, 525818672, 711547447, 610787417, 801221002, 889581736, 948028183, 841614516, 983296831, 187685710, 977272772, 280635424, 961847129, 998115970, 111650337, 570073136, 384637571, 797638626, 203603489, 875974552, 840444424, 5022121, 214667817, 422601550, 700425990, 950332521, 359699644, 477349096, 607903255, 408628230, 454876987, 925057165, 849290208, 844265666, 110547659, 564221413, 633072914, 459626433, 756990032, 247348989, 594762037, 251297917, 579784396, 215609723, 359577477, 429290021, 415521575, 220837271, 953900640, 438301732, 713833296, 65149534, 698800827, 595362851, 494746879, 262815013, 144840150, 265189890, 566926127, 76993334, 898333765, 17835830, 452704474, 301650402, 663567847, 428298444, 253914148, 809191640, 535886960, 479435984, 844894150, 487345423, 933498496, 181134868, 125345268, 42389657, 131653715, 807251423, 75043296, 192499230, 950313524, 249016569, 433675012, 413811030, 585822183, 609598034, 998802123, 970786381, 88230554, 855761103, 715802736, 741668651, 199019742, 300470243, 103541565, 46958035, 949825512, 19901023, 665694592, 398101488, 360291240, 479347567, 740914572, 325984764, 96515375, 391140858, 760356982, 162065718, 514902097, 13446798, 934842282, 47446945, 643481845, 650916997, 274827440, 60466703, 46039594, 622732027, 108310410, 374054937, 232598898, 463676976, 689682400, 726709547, 100101887, 759162856, 854559174, 970209121, 711617925, 223297725, 200010650, 855372343, 266700872, 186143668, 861030039, 578932284, 136075211, 13860939, 264400199, 416497929, 267037432, 83928378, 334419797, 51877942, 475756272, 778643761, 567767252, 279837233, 31567238, 936661748, 705028642, 763003623, 689505706, 907169773, 526676541, 981787899, 707360774, 305123579, 362150653, 32104807, 43551195, 994610608, 507210610, 226904779, 801658538, 592341185, 196399429, 763328448, 91766588, 961581196, 275225487, 610108454, 593106130, 566955320, 721662006, 692080609, 671707026, 416583738, 630245801, 124823101, 374487246, 248869401, 449615721, 257812372, 265633643, 390390413, 586517514, 546500372, 134967171, 768898918, 818241403, 45291630, 472610130, 390205777, 670852219, 167555627, 297912798, 770570567, 189748836, 108244698, 71445472, 91384760, 477716838, 854112346, 735945341, 378570791, 839134244, 275391526, 648385503, 911909974, 497615668, 186615245, 91037685, 592780235, 853572035, 9797248, 342681649, 164795852, 813142915, 233984455, 871484828, 428615449, 984751343, 814144315, 511943614, 468913955, 14762012, 473617234, 797719504, 634252201, 181911721, 536374860, 102497828, 790226011, 961068722, 908762303, 192125859, 5152282, 304090475, 617042054, 333542195, 329466202, 740960306, 655430558, 126815976, 498936276, 695104874, 955246424, 639659030, 137529027, 81802103, 232412960, 701096386, 974449929, 270228346, 186699289, 609632173, 487581217, 743996948, 985671186, 332634022, 485147903, 581478281, 219301122, 214850589, 475346600, 163073452, 854253371, 234509338, 496502069, 468855818, 349503909, 110610291, 381766387, 430080980, 842068923, 810841829, 10534682, 947195913, 844034129, 388075488, 512926636, 769590924, 641646561, 695462610, 27217796, 741867446, 650039840, 571763822, 595958268, 989627691, 942041751, 488620850, 906725490, 738659722, 171561129, 270150340, 157114286, 617892299, 196453740, 159775636, 294108940, 908735610, 781733846, 822314023, 236389617, 403793850, 603083633, 150720172, 504899484, 56707488, 757139369, 132591128, 854594007, 321310475, 96085648, 542789368, 523808403, 191853681, 688341705, 961825771, 44470840, 922087614, 110671299, 423160459, 907832378, 482389967, 126433630, 96027281, 58882129, 82663174, 601514573, 762275316, 971256592, 425337727, 668207519, 799665504, 234432250, 627014335, 575123149, 798932362, 76338584, 965156190, 176550005, 613917587, 546869503, 343050890, 424858864, 447827426, 347840103, 378296488, 136556931, 70633094, 846911428, 777655324, 991601292, 455291915, 789130000, 54330637, 837202109, 414406718, 993938425, 858559165, 703477429, 100808944, 77327735, 928953259, 561548283, 623227478, 951048234, 365643641, 252818517, 167510814, 587699923, 625586777, 473445632, 994728525, 284061703, 618756217, 816715560, 195231343, 421210632, 399800135, 694306088, 867095275, 74757158, 706512125, 866273470, 823656937, 894998246, 946362500, 189757114, 763717318, 445776142, 704467706, 516233296, 826183297, 570029020, 45508413, 399693792, 487298899, 872720635, 519724819, 605201757, 297021988, 444368982, 791740706, 592337095, 970969186, 257972710, 34630406, 983503446, 958825765, 461389725, 516812538, 249271600, 607004560, 167402967, 745492167, 196462803, 593822841, 371790444, 781601286, 838974108, 60304934, 501954236, 892339806, 695512128, 448888016, 844962805, 159162079, 31990836, 74774561, 141762230, 985045977, 85428377, 631563270, 79263494, 122317028, 83091838, 487472966, 177744204, 658507978, 481550271, 671728345, 305355193, 278568645, 502350920, 408610745, 568870957, 904104068, 733082030, 899456087, 200404018, 815058429, 171510374, 390681569, 480670329, 239521505, 772637339, 762848247, 26204659, 490997674, 153497037, 302542444, 547208525, 855511510, 17138392, 277672652, 74312849, 105069448, 483708873, 564390146, 711522650, 581005579, 466510771, 674519362, 173665206, 774365810, 976059071, 979769339, 261729816, 276408921, 534494439, 912640083, 880942367, 744850414, 373264082, 74809778, 989715410, 814604227, 138669987, 65617468, 283072707, 655117604, 290440286, 547721166, 799753590, 130111264, 764268253, 880385360, 438926761, 191066578, 744889889, 510646920, 35113863, 669821795, 568044641, 502992385, 844332774, 720124923, 935836626, 141884343, 83388794, 240776551, 673604019, 556412816, 408495480, 832511325, 864094512, 177093337, 242878916, 146080110, 706429040, 742829728, 517372071, 802578300, 30021023, 721027265, 367952682, 700566292, 337412108, 921065223, 2134172, 809038105, 179615095, 854005182, 650837734, 76771753, 944366236, 681807780, 94304479, 886226586, 979297603, 91047196, 392854741, 156791855, 60413431, 211564522, 142778973, 114485690, 504550092, 635733822, 518684238, 582214388, 319006625, 355831293, 286558341, 126340568, 940496988, 507180674, 763622231, 216451034, 837564003, 496021460, 393563231, 683175185, 975147219, 888744232, 937136627, 558018917, 141731169, 159826664, 512908375, 140343606, 473158324, 996338101, 592530785, 27061833, 250500901, 536192559, 69167655, 12488416, 276469737, 230188923, 150194085, 308567598, 808723012, 540153921, 635674218, 34364258, 573138692, 840083591, 246611605, 195674985, 322082282, 244902852, 254271007, 959404815, 374370074, 826457376, 617986086, 116498511, 57472933, 972365849, 273791633, 455945512, 523848134, 690680406, 824296987, 154743246, 238173559, 384393062, 28365134, 232912843, 300847628, 357572239, 889225029, 226717400, 52107095, 405474347, 427066161, 79890213, 103008317, 343414535, 210740736, 604262010, 679861650, 958056075, 946064859, 362162542, 221470715, 457854510, 118285399, 381566030, 792770094, 18934426, 142471862, 311487466, 836564918, 572520080, 671483489, 742321783, 687751958, 97064296, 756175661, 241019977, 154957972, 775471998, 304130498, 978405073, 501615246, 631332944, 64651642, 641029548, 660936550, 714033081, 500707835, 349162421, 644670177, 771160647, 872158566, 59207420, 671681386, 205747918, 518145722, 566827151, 34434070, 979169753, 559716998, 178410760, 100358641, 201318003, 439958104, 914645294, 233640120, 363985409, 840947238, 564881364, 257260688, 623440134, 688218924, 424506755, 638716814, 391362324, 600646935, 663237090, 694453177, 444767053, 384869803, 163063315, 425525399, 227105528, 94246437, 773703429, 49415571, 136116233, 400274283, 761034313, 220459831, 518975605, 435626073, 503711042, 224520753, 172158033, 169688476, 900391298, 457214657, 671655332, 92602477, 980673671, 404061464, 935534236, 849913394, 180425345, 934883624, 61880852, 645318303, 146641092, 86538392, 433500179, 359787803, 874144540, 139718242, 854425290, 23420694, 660818224, 644037340, 313731579, 218062397, 102161569, 28606413, 759825581, 248199165, 586678882, 914699551, 452648297, 515957833, 761562738, 233162044, 346326984, 853862644, 830841070, 425014203, 562235498, 49060902, 553788784, 640501662, 108346074, 220109081, 939152917, 239228713, 751798769, 226135237, 140376977, 399425437, 268426567, 764260268, 916098316, 809768337, 716730684, 681816095, 783870310, 817266580, 633543718, 860295118, 926929740, 679169149, 18285285, 687416226, 10675125, 655258309, 327587502, 992508473, 776465403, 423853303, 490551611, 84446753, 960494381, 959501583, 593455111, 434439739, 168520694, 1727406, 908945848, 803095277, 125371173, 334499687, 426374081, 902787252, 440197190, 333120704, 390014263, 807200810, 484971867, 157120824, 283844808, 90210200, 947611324, 494343818, 587813812, 274427504, 852316689, 667398766, 346655400, 740140061, 509352436, 636311733, 793205157, 183270123, 528821580, 83135772, 29784188, 353879407, 698287736, 463055531, 564759558, 261309523, 348463154, 188680933, 278609499, 288812098, 850382605, 978769896, 689671583, 370541353, 815874615, 42891369, 670704124, 988952538, 361216582, 200377097, 600601899, 403660617, 603939276, 145915267, 806932541, 353991720, 222739090, 368586496, 173009804, 541341575, 346398930, 233248410, 887591769, 755018233, 972094345, 420828019, 538842465, 251467951, 352864990, 895353714, 827680807, 381477155, 602468267, 937358463, 432578363, 389537277, 876644867, 771044036, 734977046, 412657570, 760256673, 3778120, 11409995, 62626762, 691073698, 807698748, 224926476, 129902797, 656649283, 259687750, 741591549, 595472273, 444741943, 80897351, 768544839, 596249585, 695134512, 651476099, 798592604, 459952429, 49958669, 679208948, 95615299, 940424773, 945722672, 910918817, 77983391, 98843349, 421638127, 489044821, 870903145, 783663356, 309232266, 609634888, 442417798, 722235924, 602236470, 752705151, 780987207, 743293532, 768550702, 674024795, 211633468, 353267069, 2192426, 881314049, 33473358, 518139082, 952775281, 681579622, 270065564, 616703943, 246953786, 428995132, 24565273, 167351238, 148186602, 174685767, 52000683, 476069772, 361436109, 585231658, 563618451, 469679252, 5357701, 89196354, 519323895, 685961090, 673888732, 286132475, 828058982, 112822276, 946475689, 257905571, 513023089, 984656276, 262605252, 779796802, 234689154, 329092184, 859106879, 474501900, 833568449, 993043778, 18201492, 529381955, 566675611, 981534613, 467270010, 872478329, 587798813, 879023023, 374380701, 670120309, 420572517, 346193120, 667691642, 586359520, 760217374, 191071261, 621641053, 194159506, 155133331, 995699089, 373945392, 760431064, 20474637, 345412485, 876654472, 247775530, 21134216, 292794244, 70881705, 17033248, 916658589, 147444337, 89432692, 414386538, 881071270, 547837434, 473533446, 563950592, 431464745, 973951109, 540099399, 297605937, 855141676, 811451846, 340000763, 95076030, 850913523, 429587891, 430009729, 671013372, 390731447, 347090843, 205520092, 108405652, 8610937, 898419346, 679778687, 823005918, 435834196, 666083490, 813686475, 657076421, 96022775, 511309328, 259539729, 586430999, 454335009, 51128306, 163494169, 798637904, 663557173, 641640227, 315750491, 300951877, 103033855, 558307683, 171414822, 547080870, 130034656, 139351265, 952833102, 313882127, 23194626, 723498128, 670016452, 863901018, 65330993, 149852124, 46095124, 966692630, 907631208, 179131687, 782141004, 739706942, 921071125, 580715527, 494175560, 250520200, 947503187, 935725320, 624974152, 932145690, 635108473, 583925009, 943993525, 732820609, 732185565, 205759698, 971483546, 818437156, 883818758, 648556857, 160853073, 347972701, 411936259, 342610326, 1583739, 260789691, 705388948, 411638707, 341823653, 201611905, 59596742, 19420395, 829664336, 101542335, 926730051, 647207668, 822562499, 830575229, 357823481, 67082947, 841007040, 19199736, 629848131, 785178192, 664795997, 650479804, 144711375, 969495797, 201903980, 469031270, 101126290, 601811841, 414972091, 707938410, 134643942, 316648721, 932553373, 196677635, 135823324, 285873888, 314258620, 849644979, 372485299, 144800388, 636534857, 486838965, 718959822, 609313283, 705527210, 386171173, 331314174, 927358422, 207060650, 411448579, 32060993, 82457790, 288165960, 569773236, 353415590, 489710214, 64054706, 662995368, 317744951, 133556477, 855690340, 76844890, 349078405, 636207779, 623873857, 986020275, 642789184, 775474463, 652034446, 412764484, 974653379, 219073536, 996179841, 579599740, 544736897, 622116016, 752676433, 253468856, 908940458, 631694511, 115245490, 961194666, 636914407, 120024094, 191172505, 656609393, 439224085, 662729348, 447492693, 546350823, 549068015, 255372250, 507793347, 168052206, 858606855, 38444516, 921628436, 509294223, 828094814, 850712306, 483075159, 349290839, 25623876, 748647883, 29941391, 862166371, 801032138, 617966500, 820599758, 3845746, 966326335, 777675275, 929792510, 480798239, 363340941, 800229477, 213124118, 206806288, 131423021, 2281237, 97345993, 240648033, 389015100, 997747899, 356757178, 821534044, 594625898, 54811103, 39965058, 853597808, 241375544, 574128743, 11988362, 908582406, 385618665, 157134844, 738833123, 613934601, 384663001, 322510831, 603178342, 293491005, 460701176, 284882285, 729110766, 42822167, 391564854, 562866607, 162115114, 245214488, 246562286, 691170784, 954382783, 678736710, 806486448, 314522524, 93013353, 599971230, 652909220, 964715955, 537175757, 445585318, 594260771, 843813462, 106748220, 716660103, 215228868, 200074526, 523646807, 597740086, 632114762, 972274742, 835482772, 703219355, 321798326, 434651574, 517812114, 204509924, 20101817, 227375654, 945639057, 926993978, 892140081, 33971387, 54769575, 343017605, 934533237, 652359679, 815572911, 946344014, 672916635, 246297237, 849036821, 914611642, 950759803, 859713779, 929340752, 654393783, 554300867, 336981082, 483922886, 248419390, 480989368, 417067735, 762990504, 835987161, 414281166, 638817093, 327949304, 6159449, 107960857, 850376189, 962053620, 99700399, 758889168, 988237055, 768654083, 631850309, 88507752, 96261689, 366891115, 68309398, 408303516, 46761286, 54054152, 749430428, 634462018, 487034145, 486095792, 293671586, 151810236, 112682459, 875405756, 407312380, 873856218, 903341692, 50900359, 643802165, 146511745, 308666783, 808686714, 297501769, 695548678, 843896752, 381994355, 56600070, 182654381, 573560643, 841926965, 664020617, 560814054, 172709570, 681490423, 192108237, 303946857, 60149072, 987681057, 604468031, 457280141, 277267148, 533965698, 800619727, 76691781, 92257236, 337794491, 239052716, 626317700, 399510502, 251704325, 670752218, 927152936, 889038015, 626736644, 275265385, 515648766, 19125327, 175166090, 568750119, 625501153, 470793115, 52455375, 801639694, 175190757, 316077270, 523877302, 955136331, 938114465, 726979426, 199636440, 608250040, 108896504, 595174659, 792356602, 463936211, 851690826, 238053897, 392791052, 305774738, 684591519, 135386936, 346051059, 183362569, 75586124, 646353433, 488679784, 832989845, 205664941, 113532124, 450993716, 187949277, 256063970, 337166613, 199202670, 872612406, 553546333, 903170555, 69845615, 660588872, 671122490, 563659156, 801725995, 355501935, 909118553, 939839093, 644663952, 347383679, 253593685, 523963999, 557203202, 826147604, 194666331, 861708858, 87952087, 883309353, 874998483, 91830423, 897276229, 129328519, 72811858, 770422665, 461455678, 485809884, 494883436, 837186598, 373830270, 631622730, 773475492, 275179508, 650861145, 355000439, 91562598, 629646276, 552922439, 713183278, 240019971, 175753795, 635093383, 584349041, 924850517, 54904519, 376147794, 210923883, 509987679, 441078164, 827377036, 698866406, 587171652, 575786123, 31433110, 365428766, 760895433, 43030326, 347978337, 886647197, 512325820, 691911219, 404955085, 289301521, 520045940, 237563121, 184761742, 89310806, 64570804, 952769912, 182768669, 819422692, 110269467, 527506347, 893625949, 143027389, 24016234, 199928619, 744422043, 702035798, 712667944, 289662759, 964554929, 933993721, 417058552, 210486592, 481812223, 666167156, 873934605, 411519672, 852799097, 515744464, 480268034, 16742969, 878069178, 33913, 648360237, 336920253, 220617059, 574545230, 566016563, 505981993, 643030446, 695159288, 255391908, 23004834, 176898507, 618476019, 834890391, 737275058, 417092945, 747097167, 834541403, 210034475, 216034830, 379246087, 809542926, 29333680, 292639856, 383070222, 570221408, 530397967, 887534051, 328850434, 15819775, 572402363, 47665037, 521758585, 623235406, 559513937, 398928652, 912874491, 932348188, 914108299, 727804030, 999497402, 113000817, 568451540, 798657516, 64214238, 13480936, 433132202, 730799475, 546728116, 823505447, 123465792, 833277600, 524947339, 935537821, 408657250, 445931457, 227996233, 111001807, 607457728, 22556178, 412910714, 647256143, 682939959, 807986364, 453424801, 155355381, 853278697, 868267312, 671536125, 716790991, 690718391, 24556365, 800422475, 200713387, 776949842, 640329486, 539718390, 892073081, 751106587, 465603578, 350979859, 392774049, 737668400, 337781649, 570031836, 166894659, 213634696, 621884176, 101687818, 647970667, 32660175, 407636294, 751408893, 898195838, 925428591, 491078134, 263892285, 693472314, 647131976, 432943337, 475860198, 741421708, 654638364, 409628361, 598518393, 276826709, 397764515, 829935787, 932166470, 929454380, 291181797, 239800944, 656409758, 828442922, 218293656, 715363236, 395858827, 656528604, 376428430, 910174862, 382446756, 816261707, 474529246, 254393697, 850736311, 814969485, 76623738, 807265106, 567179003, 852666402, 26368387, 243255783, 862174826, 437660763, 825663719, 153473943, 673815575, 885346838, 749354633, 227944176, 593180822, 883085309, 679358201, 101516744, 648517780, 558709793, 904250848, 135539008, 985417751, 890798682, 216080864, 160707469, 212818325, 936020194, 301272013, 917294257, 317856443, 845923707, 743588957, 452575338, 377267369, 180952367, 66228360, 637335141, 948476637, 273905796, 174664111, 775529891, 42269585, 389061649, 175304981, 791483882, 551138888, 981290016, 933465151, 136041626, 970828595, 881805865, 530659302, 131673355, 468312513, 966230113, 220075904, 574202430, 683756221, 691183272, 153652951, 391769245, 424822563, 433437484, 50033463, 582763591, 253174742, 497131125, 714012973, 544521248, 328421815, 259113998, 466040839, 361920263, 173139588, 137616624, 400261575, 427515164, 4512961, 626158842, 34495521, 938588464, 756817567, 112550928, 304678185, 47448887, 585855690, 709244664, 543616341, 507125650, 595913468, 392626496, 918477618, 303981209, 55545944, 327167138, 796348769, 999784642, 143124515, 869754010, 167008457, 540184879, 309886119, 810775485, 580121227, 621495520, 877405498, 978263781, 103176482, 521872626, 329576518, 21608418, 429930262, 61735471, 149962604, 707910970, 469969808, 809872010, 472286967, 604093798, 425499879, 937162693, 422644279, 128594315, 204673093, 102980943, 835177027, 502096004, 937961657, 258061152, 793960662, 514271535, 196523326, 541852562, 873091852, 536280675, 941856090, 665958096, 884888438, 887931749, 874413065, 850801270, 850663872, 51879632, 541168347, 293326047, 290895036, 874140601, 621956792, 52275751, 921478781, 941246745, 618333118, 445663310, 77091212, 655318097, 873077286, 267888560, 408025260, 18981265, 353135826, 775806289, 864073917, 603167328, 68268439, 856966592, 776452587, 716263954, 661943485, 526717345, 572613561, 984853298, 51022864, 389549047, 656088993, 922427077, 441440945, 653224936, 448980070, 623140515, 470763907, 599722944, 635319127, 159019238, 529939552, 270046392, 748818360, 14437834, 38036377, 744026374, 733758616, 589084785, 895697964, 308267335, 610700181, 417220922, 268299169, 517658714, 800494851, 790246018, 323437723, 419380138, 784530573, 786311667, 477348032, 886514368, 603053356, 8875265, 923126023, 67859664, 2263262, 81564628, 637668245, 405075398, 530065509, 516342684, 15161318, 679283480, 506446342, 423948098, 429864327, 225407091, 168705688, 822101875, 79145248, 588164816, 939238422, 472687075, 813777170, 209361154, 279961691, 426352515, 625176354, 436604018, 593656104, 385132221, 27457216, 422052678, 599456011, 977122858, 951149860, 134405162, 785476015, 683677143, 616292005, 592876387, 894096286, 788352055, 295190069, 262693923, 512958449, 653249094, 671314977, 563751364, 295612299, 885434715, 958402259, 327361439, 388685829, 190462685, 914374511, 37776931, 109622274, 635931261, 693618332, 737985184, 326378667, 771310969, 72792512, 121082634, 638910178, 738663801, 966524305, 886428042, 903333549, 139867712, 329635506, 454807900, 273652613, 948204337, 306326077, 680382991, 701957252, 709181371, 430040294, 646374135, 743138503, 784354119, 397902614, 980888582, 943024409, 469558249, 537402058, 365214551, 519765683, 902709049, 553352164, 137637347, 907447972, 492351595, 500016349, 853610680, 60210362, 555343276, 803732280, 977608150, 493311126, 667426308, 426868627, 876886125, 976520541, 340188918, 74523507, 231073465, 169232856, 977317553, 763305913, 874597984, 804314702, 365008874, 605724694, 166357858, 175474443, 760139402, 857101038, 880885333, 440492653, 120547624, 331179985, 598956111, 36961273, 382329770, 61313774, 903809554, 945582656, 603250083, 949385101, 101043564, 434069502, 741951612, 916167639, 41246808, 611429570, 796742463, 550610914, 855229128, 433359938, 395193663, 77778212, 741047582, 176850694, 948623426, 952477399, 117484004, 528373876, 126617977, 367414017, 354475843, 67433983, 117429056, 476800567, 886396872, 891911371, 199448852, 441790094, 66946428, 443042301, 508711359, 229056599, 82673902, 232183014, 199336346, 457468359, 422866886, 526609574, 123733560, 347225114, 923271917, 657287052, 401006520, 847395918, 440452473, 63820512, 861323514, 758565543, 371265610, 517960709, 175129097, 117311493, 635797644, 17281900, 429756483, 506461929, 144828127, 859719673, 644796141, 827465377, 580456718, 148887143, 17429279, 907614717, 163853720, 82475201, 308587042, 981207329, 187793974, 926167332, 86726967, 888737798, 67019956, 375639746, 597475322, 786503026, 402902817, 262568862, 960353906, 866336899, 607091050, 590957068, 976463473, 120265767, 644839530, 448102962, 54295965, 477178996, 52989616, 190430595, 52011201, 586395626, 68785690, 601268903, 642317723, 314572997, 891545643, 983947537, 901938810, 736840262, 587774671, 54152973, 214586270, 861629380, 375888993, 792128660, 758805434, 610722348, 652260583, 482882316, 609175648, 884684702, 767347504, 336326620, 980888766, 151313345, 144944714, 160879586, 348325435, 220761873, 292399268, 74509641, 821087756, 249138467, 57586107, 499141761, 681909765, 895343661, 383998405, 385054846, 697772610, 264686654, 537728762, 927037010, 337109270, 45063887, 995195801, 618825483, 58929949, 276959075, 23587876, 914564694, 339702450, 604099902, 393966428, 376107011, 851587520, 890345473, 258642304, 932864771, 158665752, 339652727, 650186666, 270649104, 65197338, 662303000, 15858541, 569732331, 866185578, 223798270, 825764245, 843024789, 101338031, 834345592, 71544288, 904700599, 118338327, 964307475, 594438972, 288590904, 214853027, 145110207, 209897947, 939130459, 421663399, 197831322, 324476394, 583048009, 917410219, 60561505, 641215483, 574952656, 886919000, 816078377, 65318921, 782841805, 747501604, 676311251, 799133890, 976868059, 877038081, 777666581, 739769252, 10136799, 241979462, 722892501, 857047564, 404427106, 832677272, 585390712, 769285413, 906031543, 349457511, 721635917, 927345330, 772364528, 209577357, 555120129, 4695168, 474495672, 143482042, 932472003, 745430531, 458513346, 651362574, 598785325, 353207018, 93314772, 603236921, 979520041, 788404896, 560078389, 780473405, 296242445, 752161002, 220526906, 539137168, 907574311, 403478485, 805337219, 58598089, 878742722, 549395077, 315942498, 749481217, 135708856, 667148767, 259852233, 984878579, 987103894, 976269887, 303403900, 808792230, 600338356, 652246795, 792897565, 650428497, 762615000, 738791701, 688806767, 590832939, 686630628, 507938485, 572952486, 825552348, 919231805, 452861061, 483028085, 217349787, 947455678, 364148776, 56493453, 316277170, 31574773, 595665536, 239736705, 549376748, 316952644, 284495528, 212114030, 813421410, 116411703, 523668683, 786614230, 304726939, 150842231, 948448954, 34737850, 493604710, 731446594, 622597283, 332155777, 364083193, 193205747, 954212009, 117648665, 974856949, 327768384, 330407921, 762849413, 140293167, 434601332, 973565189, 627083534, 653063100, 634332653, 386853928, 116191635, 940640576, 258620498, 114318003, 853979089, 91719532, 692518439, 792326132, 937904356, 529723730, 490990931, 277067415, 86607700, 677037103, 434003989, 201599970, 649445958, 324970611, 999537882, 251090903, 11342933, 516918482, 941334890, 415313024, 95764654, 413128439, 108701547, 368856990, 972235813, 675853728, 669950736, 267662711, 822747576, 945139068, 996580991, 589168745, 359273257, 594889446, 824721692, 390361406, 223865396, 471633036, 691222512, 471409414, 523422718, 98001234, 498086030, 948552917, 489569846, 23669927, 557800862, 692740353, 373568236, 755027028, 982277692, 351987067, 196035754, 61130376, 975378300, 222823560, 242484661, 460401427, 793609977, 537519358, 69276576, 712146486, 307076371, 995253598, 633919947, 580086650, 606929191, 48353269, 783009465, 721581714, 668116121, 153850855, 626082663, 840705934, 594125188, 500923878, 448800818, 185831989, 704189761, 868088451, 380692905, 863853789, 656449090, 324476482, 60254016, 837900799, 452725656, 659128754, 101539499, 109467980, 155891588, 12668296, 450520351, 707603304, 762377913, 118543020, 819422606, 224953226, 137940282, 157114551, 688954616, 248333325, 912805632, 98708017, 651095395, 664533352, 744976589, 573544711, 977532380, 80194429, 908798935, 744326218, 455044147, 971540534, 451000305, 943542245, 963557281, 582450696, 215352592, 488474896, 378125462, 397348884, 448842889, 142377177, 661147398, 445673740, 15200016, 998593620, 666403862, 742124295, 882357119, 840293485, 247896681, 238510772, 72077097, 790191782, 29349972, 444514156, 60055191, 357220223, 979465404, 213448912, 93620179, 998112855, 904557816, 726980458, 662114361, 820709172, 604268576, 488994209, 322008906, 834762719, 932202560, 740259420, 184447499, 473221960, 334798983, 665080520, 24273087, 784268332, 533649868, 530197265, 205873936, 206599033, 266021515, 998694492, 469589730, 42437456, 28871806, 763044667, 873180659, 678279234, 837553236, 14862073, 271226825, 113309564, 281589712, 739389790, 889650511, 208213166, 110841140, 252055549, 663348023, 477732817, 7429285, 252607696, 131403048, 701598584, 497892468, 188471695, 611866056, 826896571, 572974253, 127095626, 724147526, 231357599, 31807592, 24922946, 688294501, 53645973, 154082972, 396763680, 773230225, 830184377, 78574159, 355007890, 44038892, 27804658, 633282355, 262090439, 743135846, 249950277, 192811674, 757764405, 62917549, 703165987, 980510195, 792376043, 180718987, 661013269, 526504162, 551175253, 865845592, 212475506, 477412448, 724187955, 842055161, 625270760, 956331704, 517596657, 97916410, 739193309, 869802411, 528315079, 360053809, 791207767, 882453767, 665452919, 378750740, 797041299, 862416661, 935701931, 821397038, 753651411, 841721477, 234942511, 996583632, 408198954, 14034632, 461612983, 188296368, 949255785, 332549182, 819710392, 807244647, 305828812, 783388050, 607019126, 99353559, 257546142, 689457037, 990133928, 894447613, 545445656, 653747779, 676054528, 217278583, 124993572, 997153662, 937480216, 39349814, 595138638, 337393021, 211550234, 504307969, 533248999, 129438619, 108570227, 708148417, 772152503, 267364797, 524640969, 325993560, 998351111, 469229862, 730441223, 655163648, 868649092, 518031005, 541225412, 270251999, 548125803, 10425728, 525185222, 9204728, 131213515, 130379067, 446123568, 927010661, 155732318, 203909777, 434524902, 100554826, 526707156, 497831019, 262196685, 437719028, 179120960, 392856653, 602082239, 323312790, 913478482, 894886692, 554348994, 463452016, 649855437, 144865710, 427376073, 133240608, 594239105, 322230373, 613679652, 510444121, 460603812, 111683891, 945694476, 777131582, 843885076, 257664933, 615111746, 267339385, 200872157, 146316667, 142074036, 370236263, 92122618, 225056129, 87570433, 571232247, 381912703, 940394360, 593327812, 567063392, 676159957, 234989543, 742841948, 166529760, 225086103, 913079762, 49515144, 967645431, 896918959, 196011864, 584923654, 570315000, 150408083, 822732739, 537686339, 408592887, 783001547, 74518797, 373960945, 244844335, 330536997, 226264460, 721909404, 247772145, 441264015, 131302296, 527771816, 785797208, 212875804, 365168372, 208349576, 608825116, 793684232, 433802337, 39697415, 384438798, 388853826, 49701207, 398984205, 757659637, 796349181, 994312700, 627122121, 82435278, 493069702, 515248501, 546603785, 965834786, 526914898, 115138670, 985842370, 909078792, 151634822, 321788442, 906852944, 987383519, 49132989, 698976144, 672622668, 721046966, 729027142, 263197472, 249512040, 137370994, 521026422, 364426817, 195958050, 16299585, 425890527, 625702258, 335822777, 424725500, 488877154, 685813074, 296319954, 565670800, 287696728, 167066321, 992409332, 934496703, 99158810, 900312339, 97498111, 169685884, 521937130, 765513359, 124571992, 203584265, 672693836, 972858163, 440771082, 989344401, 588486979, 656400850, 656739676, 400164013, 335522317, 957086244, 66512514, 358881508, 292329301, 847231903, 887585371, 492071164, 306445174, 289743471, 969552904, 979238531, 166750197, 197863223, 210045584, 684778819, 508077053, 598622997, 465773284, 892792175, 965069659, 945623383, 882285593, 689327749, 479874469, 767695076, 527297791, 876383747, 518501490, 236982142, 907826709, 654711977, 916402673, 431452070, 562261673, 472069762, 359557263, 64810834, 109374255, 478650822, 467004910, 658094620, 491274748, 740460451, 517543485, 170765760, 67514164, 189397661, 897754899, 698916301, 257869149, 585911865, 291081959, 355807935, 627699562, 672697863, 378153285, 310892216, 905756458, 800338532, 100750514, 262183716, 385726789, 515212062, 846988397, 741374778, 935501440, 537816412, 314664588, 644113669, 805423838, 667183662, 133982075, 16537263, 833930839, 805432347, 894702606, 670328405, 721316608, 203701296, 647642986, 766493404, 833396174, 206548314, 914613230, 464595404, 773892338, 176327344, 9907258, 501134437, 119424939, 960574421, 346776928, 93566189, 128288733, 347961755, 811468230, 877106073, 644907164, 710382873, 869396556, 562782076, 271765576, 150138418, 519977004, 311698311, 473295216, 558074020, 902864750, 63041947, 167981179, 681493415, 922625311, 139430698, 384836998, 244776809, 107743744, 758449660, 916446839, 540753121, 278640466, 866749835, 629090566, 401081817, 572463831, 841700278, 848981752, 237392150, 725968333, 710444778, 957935789, 644064172, 223760774, 318145713, 281506276, 898237029, 323892409, 159059807, 190134405, 294689647, 546793765, 415166119, 804075443, 573070018, 905183941, 218117932, 530716709, 652063303, 548801894, 927902568, 808006137, 920933209, 500073133, 647776322, 659772860, 591719804, 403266533, 762923556, 73290294, 234330065, 169646963, 32726695, 276139069, 619517579, 94969208, 573126573, 475169877, 785419071, 91259602, 925628376, 770823169, 731619344, 397469737, 394041073, 407440988, 400544707, 508555515, 622476745, 631173025, 632188256, 671261913, 491096014, 164228752, 35354379, 425967024, 583889894, 823660279, 660854351, 882892134, 634823066, 683965824, 610667142, 911936924, 833326313, 574395477, 648618034, 38695149, 812640761, 47975790, 43669278, 221004393, 611878368, 972110440, 638775488, 940561069, 129650387, 862979767, 37892033, 592547251, 253500791, 96549002, 851210732, 799875318, 42775206, 217785275, 839517296, 485435343, 301341764, 699605206, 954809569, 831990133, 725019958, 845531437, 366243854, 516759022, 74913138, 722525954, 486903351, 760142955, 371742760, 955699818, 574118549, 686924598, 257711843, 428446660, 766898099, 809633088, 630538084, 734137233, 286724018, 461627394, 870153680, 165372175, 345946907, 209163746, 910524368, 863268309, 803113671, 497557351, 926003720, 109385640, 163507920, 714769276, 182892738, 899213809, 516621674, 289514672, 848715525, 84721576, 753001950, 350550842, 812998504, 610300904, 523736468, 817253803, 336975471, 371593140, 785989146, 497109701, 206544816, 766441671, 99786593, 133215921, 878373245, 58170562, 606637933, 315565907, 850625031, 254982504, 2322375, 673931608, 103146591, 889791634, 53859513, 236213539, 754138773, 546612172, 941402980, 592443110, 86066893, 277639763, 162332751, 86043732, 212529565, 441213095, 360491824, 840785602, 190393423, 642379966, 80721313, 402355242, 927781196, 469799245, 590172299, 606339937, 5413578, 146423737, 148690376, 243111532, 829420215, 697815025, 636806172, 743365981, 460814626, 871812196, 504718439, 862071287, 252586500, 993619929, 479977191, 631733445, 52870513, 743593306, 741570060, 777667534, 128151224, 771329306, 41041332, 10597413, 352729929, 251188185, 225372418, 12479020, 752477331, 3942053, 125814946, 70913120, 720200933, 279271291, 566848753, 858073122, 940910986, 877798775, 871508440, 614062856, 815594058, 876059723, 823279457, 480929260, 40352357, 988875365, 297921063, 731759155, 603935241, 729487379, 817871668, 668187609, 929237989, 449086970, 186122534, 101142710, 929675463, 135089418, 552210928, 315426627, 5233712, 917921754, 657055609, 550266139, 470265096, 883827453, 729646435, 357677816, 845952811, 571117015, 913977204, 601693284, 529006886, 932917762, 481693141, 698906180, 387959675, 260035439, 842171277, 824516600, 518015700, 542728175, 577998960, 101069416, 805388411, 766447926, 328929560, 751656721, 544965822, 760463448, 198196402, 842324505, 804735228, 462418359, 335418143, 242105522, 281665241, 659291071, 347839273, 356046462, 533799667, 828569252, 512190786, 702549287, 260895952, 381315749, 769239368, 882609635, 584481294, 388448206, 407451586, 293198400, 270174447, 120208446, 241748147, 483462515, 776793722, 622388507, 200330775, 967010761, 250576677, 726513472, 726069485, 725439316, 200261002, 718960545, 34542321, 549026667, 660725122, 5422737, 57121478, 842793349, 291340232, 287998312, 721236850, 785406424, 748750705, 439322697, 517353480, 75322660, 585021555, 136739227, 145850185, 885888503, 422838996, 50741698, 48628260, 839771517, 39389077, 528131123, 14368544, 350171894, 238796002, 245854429, 947070820, 45132283, 543993151, 836508620, 474595641, 558050520, 782193545, 156670437, 234184698, 892054889, 145761990, 704569628, 224043634, 206824689, 393141268, 723310233, 832981496, 387984497, 40052999, 104574663, 813746006, 817384975, 63898040, 486318506, 260064465, 592943084, 23240710, 847527467, 376923286, 259246087, 494098014, 782663012, 329419024, 342227885, 62768921, 611248875, 246285944, 402000507, 442687545, 975034547, 207136541, 191403959, 529045989, 572879496, 165786144, 493192255, 847716119, 119224490, 627518886, 323209929, 315718783, 916494290, 585702839, 841464216, 520932310, 348489811, 132390501, 413377524, 540371257, 418168873, 955036878, 920608636, 540154184, 508876743, 920740995, 757782801, 310874249, 42913631, 242879670, 158677242, 738144214, 344828545, 939390462, 197869905, 17670721, 822852448, 368984731, 258867973, 23457688, 387258074, 929339415, 509717426, 951194537, 644767317, 425955444, 636212887, 879960645, 710756791, 669166455, 179292324, 550357170, 948313561, 476945344, 194469336, 106095815, 6855386, 418771434, 11548757, 192304716, 354748364, 979469930, 915164147, 501698129, 273809447, 946197186, 829167286, 6569904, 915403236, 592658407, 779327442, 965554044, 201160114, 626496382, 143101120, 467741750, 83550289, 957113319, 796441276, 403558241, 452000951, 501480131, 370959945, 467091176, 206068140, 873309189, 662471285, 293941493, 925133724, 927881663, 724887858, 128222908, 665734342, 101477207, 573121739, 62293481, 140592987, 838853678, 192757746, 659024968, 961526019, 719306213, 425334014, 877597363, 23620544, 801210194, 723505418, 512102487, 442685714, 167435703, 31418071, 836770231, 480734294, 419979204, 635484044, 908139479, 176554736, 181825074, 322968209, 139909800, 253322862, 490170426, 136350592, 649358312, 302574281, 282348063, 155512751, 307954016, 473817489, 654207331, 5436170, 325483422, 300442500, 456426061, 159594368, 535209988, 979458828, 985836157, 807354866, 983177844, 879879653, 868855174, 572852449, 263839686, 898635347, 109095469, 719294624, 593498332, 365882058, 871630404, 784843924, 944376771, 417073129, 990310588, 925143393, 666279219, 23486219, 283420257, 103641855, 518238127, 922990123, 95033471, 361689283, 27046571, 750803698, 664675800, 929772949, 835429007, 448952546, 329167451, 940031872, 730000965, 55981542, 705416127, 212837235, 36334507, 358262807, 297452244, 190474851, 892271380, 397812639, 840169239, 661632956, 341583785, 235284456, 792636700, 993381847, 409644560, 231217622, 676533253, 335609291, 206675057, 273249101, 688936209, 499971347, 903352428, 922367950, 953126803, 587591703, 45969420, 291330793, 624972603, 603655752, 818893524, 64714672, 380762708, 906415028, 876498239, 699719436, 484929292, 609934802, 296958649, 23073869, 709142303, 408520799, 111061964, 803572874, 711826541, 166166274, 594694644, 350363955, 553825098, 632161490, 94517549, 685210653, 944398116, 38503506, 453895113, 667927695, 645246018, 752596372, 181454665, 331458940, 10102572, 123200794, 438733782, 328987668, 141403688, 59458490, 516081376, 642431121, 941952532, 868287545, 319415044, 49122833, 757057612, 708357766, 790421965, 5217861, 66414072, 924885090, 304545843, 459822034, 42465726, 387934381, 785675694, 920267660, 537434082, 576966922, 813718009, 166029160, 794120106, 516643062, 60164841, 564372781, 459717578, 722913673, 161064642, 852147205, 579346661, 953891836, 588221117, 136824443, 515520010, 313576656, 714496605, 328882696, 860464743, 724643122, 302908750, 872755722, 336438801, 37660795, 380446259, 651591349, 607672690, 992932972, 951372211, 386124193, 140953678, 992674336, 427825601, 198394579, 508789731, 340662251, 906587698, 228275429, 914005210, 699733997, 768483920, 336742232, 103303366, 573215799, 316210908, 892578609, 539215582, 895428114, 928963798, 219288042, 501555439, 478176946, 276956746, 519471578, 334295531, 926375044, 345063213, 23875692, 686149556, 367625240, 923240099, 982239442, 741830844, 971996363, 91092087, 125816144, 438264806, 645522119, 995380476, 204340647, 36511733, 667260736, 568561194, 971218134, 178918322, 949928767, 789381313, 509264196, 10263012, 476890522, 382824839, 3218061, 999536627, 700400549, 572949255, 57886355, 487664935, 731446068, 322009859, 210070872, 635250343, 760441464, 417263317, 220352282, 304817437, 315068744, 446843190, 490017609, 343743367, 105476786, 434737547, 994554761, 125915220, 258844933, 593206606, 992612478, 460559537, 821406314, 120308316, 125228877, 989891967, 763247003, 730689118, 750112393, 269886315, 861612147, 629495284, 995271377, 913623282, 978957667, 380748574, 530486543, 167045933, 937239766, 160580490, 345465742, 740087287, 199648178, 653218537, 72489425, 476356938, 915030851, 369847305, 488603102, 748491983, 668414874, 588278894, 839084007, 313513944, 823900588, 528754019, 465405229, 119394206, 764564499, 781682760, 768038805, 283974265, 919991884, 286246575, 411639386, 718738709, 942980697, 605508594, 829933671, 195292656, 217779951, 859693672, 454573827, 890381626, 358387257, 123208115, 784600970, 242228379, 521302177, 108688846, 257769185, 170722859, 611742154, 454304626, 120429193, 638727409, 712185096, 99864273, 982797992, 39289361, 802458098, 735885733, 138084382, 672038835, 429532229, 755424421, 11925113, 541359535, 3851220, 710612587, 859049326, 226824303, 378084817, 880905535, 512639926, 398079207, 476111746, 465709568, 111165360, 888093349, 203252506, 723749908, 203424701, 825026113, 444412103, 922233310, 560210290, 263342011, 185902702, 374098121, 714403466, 579892033, 926077980, 881590611, 592431918, 535563527, 660205382, 321451635, 650161553, 188291674, 475172216, 432182421, 136427279, 8881214, 33065180, 980582541, 830169402, 897741831, 833919490, 388757005, 209625960, 562298219, 841198286, 387086913, 28416165, 536234169, 936261092, 869795200, 633732255, 583690402, 912909935, 139543276, 295173807, 369212592, 128305827, 496678049, 601911890, 430842764, 192944663, 744982815, 458347151, 299367511, 841537730, 896767969, 590883800, 853102476, 291073748, 38199782, 169877189, 278260782, 6151558, 538848297, 3269711, 778799547, 216863126, 877732019, 40211908, 395565875, 848362778, 943910443, 960162466, 101405102, 355603238, 135225239, 557541527, 904773738, 342712166, 246845344, 699751661, 911194592, 648096980, 202600981, 321991432, 831954226, 405563561, 235136064, 101066582, 925943261, 315656633, 802292044, 755633593, 70336119, 692592701, 508200218, 340826610, 1750178, 287346399, 582669040, 18613000, 603477370, 429182991, 152439405, 548373113, 941685992, 122525121, 311596229, 677929072, 686740419, 551174646, 975646265, 174912871, 332086941, 835188258, 104665797, 923155760, 690799581, 463316525, 760937361, 408402794, 384524154, 238999250, 664811069, 34623069, 99809581, 791750190, 540255705, 831495122, 664024318, 467793965, 687662630, 505195105, 679195454, 712640518, 404407807, 18305707, 408796821, 94745392, 987122058, 359243208, 940404516, 349437398, 700858946, 245834038, 960239156, 804893602, 414277640, 524434576, 937737849, 862822848, 241356490, 448653891, 774625363, 700047766, 858170727, 468696270, 371169750, 812305172, 407078248, 319459080, 14575559, 869916696, 605051064, 458270927, 381614459, 220493295, 669826685, 76699142, 742313538, 578655087, 99348549, 638289611, 424994279, 483573056, 266479939, 311283706, 809813501, 306650477, 651105684, 111914806, 693116795, 906857002, 399146430, 786713284, 58050971, 804773502, 737274400, 334221521, 525382798, 480411780, 64547304, 830430168, 613743921, 810720079, 711016591, 587876780, 227859896, 79903628, 337415814, 766925192, 413953085, 968071044, 940492735, 859606382, 819704046, 12571521, 514887247, 43987415, 279859886, 994722731, 328252401, 976037706, 275183007, 230168557, 828639678, 605959544, 734868936, 388402530, 134605131, 34448834, 907706720, 474480183, 909648787, 296872443, 281198647, 209099299, 150879910, 859487805, 614744388, 951273151, 488629713, 747176645, 708701155, 770402504, 82304468, 272665620, 714995640, 183339898, 167226600, 992408582, 762936226, 656294115, 598872996, 13998339, 6350989, 532873732, 937248614, 778562626, 897640513, 615948966, 792820661, 406858956, 546914080, 588869072, 426952889, 598364892, 191297659, 120704582, 644852405, 708465877, 775149887, 945605391, 506612855, 717259397, 191960151, 415460960, 995152594, 53517496, 635862395, 783703951, 118419086, 333273658, 202619752, 956842788, 828608954, 247594391, 486314327, 935831027, 622762407, 341722913, 626166471, 453606090, 687925155, 509417196, 294712725, 604592055, 421356081, 9058670, 779205232, 392055054, 362551501, 426148834, 860250353, 519977462, 906522317, 930415726, 552084938, 616437629, 576705321, 7496740, 121488452, 161109625, 378495403, 107966941, 269582524, 873652229, 963390414, 360032608, 680211738, 30528034, 975781893, 947178499, 795226803, 723332746, 644660874, 505460180, 974723066, 17769636, 496865400, 88582682, 702819664, 450199753, 52486241, 905400247, 324565347, 897553650, 103472998, 88298964, 55675070, 349775971, 544690673, 731527179, 698848609, 885487562, 265062202, 18901143, 680267630, 598718277, 421330350, 814137289, 263434356, 841012098, 153092659, 667394861, 772141886, 945357666, 951279095, 909371941, 748956611, 6518243, 267842858, 85476437, 328802615, 800045310, 808027768, 771030694, 698097889, 430292786, 19650646, 404998264, 967260041, 712251179, 181992048, 347634203, 816234379, 117822975, 127505309, 747563181, 490934013, 557395675, 211291887, 223154085, 485661142, 711988747, 490386362, 668940330, 114222388, 21711786, 15885505, 498726207, 673204654, 71176026, 542442118, 161717400, 299082634, 995073525, 328189, 92569138, 997852171, 908947914, 813913506, 124349194, 789749376, 769205401, 269562832, 186636431, 426218102, 987439960, 544658443, 479448402, 359333995, 648863668, 239938482, 976105248, 382163585, 656693477, 622243287, 504517466, 190659743, 860406322, 768925516, 511815339, 458942205, 678796225, 416040575, 156452195, 964068510, 842839309, 905514460, 11144761, 432563059, 176911966, 456629418, 532858206, 34590659, 214199089, 147703879, 545256018, 978060125, 65582640, 149467035, 918430291, 379345633, 622068290, 396545312, 977416432, 63842925, 184455097, 204992624, 510279037, 614875420, 428249734, 841258722, 408456495, 647480238, 261208502, 65797812, 14725872, 816263207, 946661533, 542184888, 684113035, 84437586, 894534273, 254331636, 796284355, 672810683, 819989474, 500256200, 459552541, 28567396, 214257117, 525729166, 150776706, 586271576, 790295716, 626619327, 209071485, 489447744, 497595435, 155169688, 445608984, 776099390, 524387058, 852225576, 159753875, 813052077, 402968709, 762130352, 186273743, 174523603, 79216871, 192007964, 225019178, 35652806, 230036032, 948807646, 303228740, 951629767, 536049215, 966846327, 692095613, 340057254, 603574174, 915550365, 825315163, 882691915, 608723687, 367601953, 112038743, 13274181, 831989424, 869841685, 577819159, 259189514, 549749748, 810136887, 729113868, 690884449, 317160218, 823033729, 758518981, 307563808, 309914537, 459685973, 969543661, 663381326, 540739901, 212920707, 561781550, 504426141, 335301075, 955692024, 927550140, 405804021, 434328713, 59782753, 778018240, 984942164, 289451232, 634204391, 832757962, 121992967, 385449186, 344371929, 392184443, 365252327, 236371205, 878550105, 49434950, 261401138, 139863554, 334960475, 663375380, 449522204, 628030918, 640126330, 153095079, 274176702, 17137094, 622718747, 198225209, 896215535, 196291294, 788104982, 360945542, 482199517, 61780664, 804733709, 842723295, 533175212, 193714219, 146606031, 554831158, 740931736, 981235034, 385101037, 324038389, 98081803, 209652112, 524894538, 556906949, 598381091, 365604455, 818344672, 145038560, 659478050, 260009568, 319651343, 954795731, 280146749, 853755722, 219352039, 953565398, 90255264, 393981532, 346642972, 532744470, 310389855, 190245913, 328470773, 424054072, 403575815, 558839948, 334518467, 769231832, 12081507, 997455998, 771087184, 259508275, 868017645, 605782230, 686114316, 59878676, 512238943, 400104445, 321510643, 462025001, 603044277, 328512662, 600729499, 686569708, 81202808, 827955695, 90701616, 168089048, 683429175, 156114411, 604926801, 151662587, 499929537, 493827720, 509738148, 301464705, 501122521, 249712851, 30187108, 710309730, 586920958, 927459710, 401474459, 301164580, 633391583, 257401333, 259356285, 754962158, 892424132, 219763360, 509118939, 750925801, 861610700, 327005274, 381364486, 100711487, 347593386, 662209524, 172152635, 476244143, 322120484, 871870739, 719287612, 868609561, 651082445, 73636870, 255939116, 864788918, 733371060, 477885549, 447515979, 260996223, 132862823, 9583465, 559904138, 842922601, 327726928, 775409066, 354271631, 886723820, 420128334, 213515576, 647417009, 230672650, 454593239, 726203152, 936692197, 416445300, 456949911, 221639320, 685988178, 394522022, 262465314, 685031777, 902499325, 967273575, 719722451, 477426687, 462064336, 240435241, 808718934, 185781824, 832888331, 366910820, 961004930, 86059875, 956313269, 784726490, 953237198, 837845776, 214144929, 701312907, 262779831, 739743531, 892270841, 466574750, 1215306, 768824917, 746555034, 400290052, 559339803, 949538691, 969212821, 778764948, 367796259, 971832334, 318690822, 152208137, 488621157, 198313074, 638012602, 482728992, 803205947, 359705174, 410867432, 228602165, 352547701, 471210182, 908030487, 543127353, 296263554, 970864038, 62671823, 792301093, 70880162, 385321664, 97480719, 55827638, 477772880, 658189900, 120651222, 674288129, 333015276, 738755540, 405660289, 688503710, 639721734, 267102902, 315516912, 355321378, 389200539, 305027369, 787939731, 964381539, 451299247, 617738212, 670213495, 218233848, 832899665, 766846933, 898597988, 88124389, 680213005, 556496917, 451665291, 656825152, 185894453, 32044409, 901205796, 519326973, 960333651, 890480591, 434446711, 257679847, 830873669, 760349119, 603681116, 122837758, 320013743, 534585140, 873829971, 525098623, 505708863, 440206900, 323727428, 527038408, 649288459, 142139231, 290935411, 691579108, 198133237, 160094525, 701840136, 296034162, 563056640, 190092175, 139509085, 540792072, 344486466, 863838282, 600879284, 179593093, 187047607, 26776479, 168378073, 899360405, 828269168, 465261643, 781888369, 931994288, 834939308, 426677928, 647208354, 402244955, 730435532, 959581419, 996373017, 667014808, 657901092, 190731110, 711577958, 232526504, 333247853, 176727046, 10180409, 724262278, 502265987, 329312512, 18124509, 282124519, 630989209, 453709216, 177263908, 413111933, 289384921, 970880912, 182489879, 339211025, 146656008, 959513366, 629064580, 352030355, 414154639, 496749821, 627145848, 223333156, 821016984, 781966258, 261044075, 497500688, 16667341, 824170953, 597569546, 521679983, 400713508, 542701004, 357782139, 465914297, 927778533, 753680607, 257000935, 626393737, 965286183, 920432992, 252504013, 313553372, 107790045, 418907980, 510190789, 891476421, 769614677, 553500633, 199432169, 197001773, 365693610, 457245626, 366300036, 592104168, 130404670, 417948251, 603475688, 752343881, 323385396, 758556261, 220260721, 43169261, 846445454, 217129972, 639523751, 249537432, 842533304, 715835564, 368029558, 966763665, 196600356, 808554525, 630966134, 964575832, 175975053, 198385658, 691905999, 82557518, 650962536, 371470137, 733322132, 212450549, 598348818, 277425049, 625018232, 488610139, 806632339, 112046032, 490099843, 668142910, 8007771, 926932865, 137644597, 927858069, 967603834, 808921704, 447448488, 553292832, 75358558, 863777398, 386448049, 54718169, 18590876, 984857428, 6637357, 849668307, 966842061, 298091282, 405675764, 215956096, 302894366, 373660859, 427050783, 994494367, 123461746, 34863209, 320582400, 228039657, 227350705, 66932536, 927138285, 960435012, 777500193, 841763461, 958742419, 834611620, 597628234, 310277554, 549557507, 286537570, 168324710, 382027750, 480056019, 474276066, 964016314, 662968498, 466477437, 302044787, 385988225, 283093622, 134174236, 901225469, 533357237, 66107851, 932033817, 918427370, 682193199, 303783850, 536505584, 378436218, 884577741, 928760840, 756449245, 868856148, 146924578, 347061919, 43368932, 759003892, 254700498, 525319813, 167652958, 576862186, 568230661, 808175752, 681090647, 517335221, 115744491, 360093158, 195548411, 138863758, 255320134, 140781891, 3355627, 539127692, 477485984, 279642756, 212827439, 32411215, 375957696, 168360979, 827721473, 765078939, 519684530, 594643045, 608411770, 145571995, 624288942, 623497818, 686964868, 865361812, 368261800, 281062241, 676833381, 748659474, 63013760, 888319126, 273041799, 587057113, 890313461, 436125113, 334011451, 976651848, 641666783, 166676911, 68324818, 912419925, 885991185, 179084112, 152067355, 967964379, 665223433, 99675017, 940652080, 857890798, 241337956, 631334966, 554356411, 798617746, 462884304, 810305103, 865743755, 918301077, 459666900, 390159346, 861328577, 156938956, 924210844, 563610348, 675733506, 780882061, 254902242, 351884033, 218470579, 979702960, 918168918, 320142815, 510354946, 569524481, 831895169, 219892530, 955291933, 963487946, 593756316, 751803878, 235933334, 137372912, 701414471, 350178797, 840331820, 292255250, 778437193, 855730466, 949950907, 974426110, 638057666, 682528141, 173960658, 974426050, 130942661, 3680728, 781900206, 791752262, 570788434, 571937500, 576024615, 403075295, 325671507, 190549184, 51834131, 118931851, 777112959, 161141967, 431933896, 742318868, 966554051, 778590512, 595387941, 278276709, 369364210, 374910175, 732931033, 201132020, 816154433, 78344512, 171281219, 451949233, 95938798, 254429112, 495235180, 512190917, 788661771, 834973721, 769191113, 555989504, 634697822, 324023915, 54262728, 308268164, 963956317, 211215494, 965265015, 402168919, 942494763, 878356628, 665355169, 433200613, 593116082, 236650719, 610998783, 898596515, 820072024, 236299123, 32817204, 411369606, 660294239, 735398255, 828308462, 132688742, 860263456, 541041009, 643348793, 814442662, 57362740, 11329437, 926012197, 663274395, 365912189, 533682378, 86778572, 135840991, 804220326, 84048633, 567340831, 192877861, 878162670, 447153359, 869405959, 816583136, 837220686, 181511185, 527501805, 416855095, 802090772, 415264997, 206304779, 782998589, 710677099, 223001194, 821648496, 270480589, 539379758, 488220563, 663598987, 631501906, 255877717, 782518756, 582356745, 885145815, 564724824, 621925157, 981798228, 91670940, 537759214, 197313470, 712428637, 623713602, 95145503, 444888862, 196619380, 325269265, 937493096, 115028125, 690774810, 239349383, 30821591, 409016739, 331354324, 890720411, 165657003, 27230839, 518787189, 159291152, 981547325, 478229440, 438859980, 892943203, 515654505, 963680492, 813241553, 640581525, 300261270, 710772181, 681939296, 420590285, 773339736, 793648975, 708778116, 163098082, 17549131, 858269909, 679839283, 689574744, 41315473, 985524857, 431721804, 643009839, 653751640, 366601259, 852967765, 922073647, 674259799, 761557594, 479497336, 503459487, 774387232, 521490491, 343946280, 144326602, 686613915, 47523945, 873439231, 728096341, 579807018, 324650987, 604209431, 579272279, 658101437, 206619557, 520861690, 665576216, 753652646, 106162474, 972830054, 380650122, 743904305, 595929529, 832318608, 371421576, 921277200, 255115094, 669431855, 509724319, 780262251, 725484202, 383474789, 633449601, 817609842, 640875929, 90479798, 479683021, 309961059, 185939515, 26995084, 123719640, 59608052, 891831668, 18880936, 744592664, 118473497, 778359442, 401075572, 991940936, 310032576, 85186445, 203045131, 10216235, 510378255, 648314933, 22414366, 331306899, 947770658, 566069733, 821178108, 192355461, 278916308, 868222120, 432043350, 927694790, 850676265, 960083044, 877113679, 231687443, 245894775, 161437782, 11446780, 527937160, 489252326, 425075925, 779636025, 449832115, 850345230, 110959884, 45759193, 396290457, 739906746, 387216725, 96740726, 412704644, 613663447, 233554198, 451393215, 333180277, 749381727, 420429054, 804005615, 365635367, 828701495, 897281833, 332289135, 342352660, 924863360, 800029429, 405197566, 852267221, 15553068, 739412884, 759207705, 225942784, 769765320, 352884218, 727240571, 673028344, 836647418, 997907022, 53270279, 615012218, 324285014, 188148567, 39755019, 541480765, 135301229, 296236929, 538053163, 43120328, 887568298, 558802393, 703220411, 14714989, 600393119, 786489169, 385593632, 485970884, 612301041, 762741371, 345742264, 965666631, 689308706, 620567942, 305606042, 970182378, 449966262, 240799549, 890693131, 776850910, 282786544, 837092811, 613365693, 108641867, 501198772, 136167331, 675371821, 414487787, 837312155, 707109856, 57098028, 9117878, 197390236, 42677803, 961767030, 594580270, 268121797, 126723520, 85771910, 341853516, 965550367, 229817214, 417947403, 500697139, 3127973, 992123677, 800478457, 296325601, 518773894, 326517120, 145740299, 459029650, 267194016, 809465484, 261813774, 803872925, 127767352, 913436581, 947878354, 143743839, 842286471, 343116392, 952213924, 338774779, 192237450, 376995044, 750862309, 490022394, 170341363, 904319579, 949974926, 167656208, 645638757, 417204586, 498857434, 906498546, 111267020, 454841716, 887414828, 399669462, 14472622, 433560446, 4800517, 251755819, 957993788, 855591153, 212887191, 150335458, 222265015, 415296976, 561171222, 291313304, 734067320, 304959534, 792179445, 433750803, 505166871, 269487290, 262894618, 722062083, 139053914, 377187456, 411579969, 646970603, 63988099, 873407461, 757701349, 971073433, 370404265, 51898932, 170839042, 820177162, 859478686, 600060624, 88073697, 739885325, 580288788, 501248824, 247700339, 219505966, 176127525, 663257382, 161345183, 576755242, 997958465, 994292983, 40527858, 458203678, 142412968, 874483351, 572490801, 708171165, 480409401, 573943067, 898066525, 940516554, 258849525, 79768068, 653383275, 260585182, 376002286, 612802742, 665570956, 989654522, 824911074, 810038468, 645987213, 62252684, 875075297, 920638117, 803817341, 926587326, 399611854, 378455057, 46132028, 732529522, 305644483, 543588468, 978831166, 396146979, 868783688, 671001188, 593845997, 682412411, 427829909, 643698429, 165816640, 718503498, 704548770, 937509236, 633600719, 938362565, 20962985, 385649936, 820187364, 990047237, 834243732, 831265717, 741746258, 642309471, 639253120, 350268078, 522002454, 731680013, 887979839, 248308010, 498261779, 964439456, 135903059, 904136862, 172702366, 407105093, 124190940, 170891629, 510560155, 940887897, 660722101, 922946116, 928230895, 171193876, 40525908, 900880200, 322980942, 638140230, 965109389, 874455640, 804546654, 461173153, 658915494, 990231425, 552623684, 589927703, 104317791, 837392234, 801606919, 275880666, 896884885, 762720947, 362319725, 509621094, 265427423, 295814863, 470904878, 714843908, 331291711, 119378391, 569770270, 672690372, 854571984, 6930962, 704917879, 501308132, 150619647, 397515277, 926500799, 571360012, 289862974, 340696179, 389260147, 94876185, 972722124, 968801650, 512124642, 974316414, 326990167, 333508455, 171899811, 71722612, 399245390, 257237170, 550216708, 166929968, 659861227, 388873521, 7574921, 817880396, 654219701, 818979811, 970859529, 594887552, 693413423, 383185351, 649108248, 433320235, 67318238, 755626199, 544734524, 902970712, 236756220, 402372078, 144333028, 371301172, 613373423, 892504393, 801666364, 182775731, 119064113, 763555806, 952994622, 798178999, 660123158, 250165799, 585344343, 872499825, 999060507, 423062459, 317882325, 543399080, 59442142, 519706369, 630732065, 742995184, 754971468, 625677186, 316509102, 421355817, 154805335, 651052733, 67636401, 483352400, 498687117, 777681639, 586993828, 113254447, 892925419, 556152862, 890165736, 520703448, 723470494, 502966289, 158973500, 665720295, 324304134, 673096381, 956537903, 850361396, 529352931, 68430996, 76060786, 814053882, 481355148, 884143525, 224951044, 71575982, 406687634, 158209218, 226719703, 691048661, 474018696, 852600965, 532151719, 581367915, 681135648, 409625739, 252464427, 242025498, 440473532, 995215672, 74304806, 652648017, 355491018, 202256371, 796190630, 34513888, 205112298, 884379361, 516820783, 54669368, 937038661, 535744418, 83012962, 243649573, 235547908, 346534450, 841621802, 573781413, 636037209, 410395845, 402071241, 363368652, 856680971, 132186158, 278627411, 121882250, 767962092, 240267525, 602007691, 647082928, 16748044, 773377708, 655518175, 800191948, 210916821, 266303998, 902594749, 536426446, 759124394, 528311637, 950374430, 229060681, 507075345, 394113195, 679179716, 473759977, 204073467, 762006714, 91939445, 282786337, 353467175, 624217837, 435593747, 790162978, 923401492, 240430545, 531845469, 750853653, 792449081, 171708216, 64959730, 440301816, 124966473, 814853072, 601552376, 706270755, 605835611, 69151234, 95449075, 326075238, 508418557, 495003661, 60411780, 944637723, 964802212, 789043752, 351186360, 179203322, 366785206, 151202005, 529457183, 106006515, 369173395, 131754091, 841721451, 705027357, 705610894, 51932186, 906589056, 996806869, 691096145, 855335882, 551578511, 398322750, 538652645, 521800701, 807284618, 9473955, 587426959, 765372820, 316041618, 509010011, 765008154, 637695696, 333506864, 225595067, 996669693, 923414023, 693195988, 437749955, 21223914, 530850116, 563713282, 193670253, 435899585, 117131283, 670997449, 258272182, 329835087, 746735328, 433308169, 547506901, 16507599, 906340384, 433715339, 954583768, 973927563, 223632896, 538169183, 152618538, 233327644, 501790442, 274042557, 738589732, 641856025, 61275691, 359820368, 79881906, 264852298, 866861811, 698393031, 891121882, 375257927, 71603060, 375498828, 674065880, 248667492, 591690644, 987037568, 860867619, 591458687, 75745686, 311555871, 974115710, 284735483, 72289402, 868887207, 334921290, 645731832, 250228829, 258864393, 424041194, 613870378, 608907524, 883559915, 64645989, 35852669, 224715684, 681674326, 497460600, 230633221, 838628204, 559890034, 544845073, 499553112, 407784937, 61516738, 251250268, 851089621, 798379387, 462192239, 211371140, 944817496, 833657135, 923595266, 920237252, 648236942, 888258575, 582578257, 24554175, 71765556, 854572402, 367164957, 780438302, 243338929, 139460243, 882815349, 525178900, 13212357, 62357480, 938576035, 164207670, 938176243, 861339046, 730695535, 122741174, 19199668, 995278601, 116982254, 360967510, 371654701, 804072300, 545377003, 562947735, 453060501, 818791051, 957116304, 386520358, 525223270, 814380764, 167954065, 402506840, 169559538, 287576956, 338543678, 753668107, 640640382, 128110665, 260277174, 625845840, 320070580, 344580130, 30059073, 698790824, 819551520, 476046245, 581502179, 144260516, 199657619, 931999680, 244616813, 692982318, 297691257, 55778874, 515023732, 286819419, 186762386, 426284061, 797835817, 828835999, 61275512, 260220870, 26019778, 193334276, 352876054, 37465669, 128867722, 224095476, 575347488, 120708878, 381987737, 613085063, 93434485, 98806168, 390682050, 20641518, 608602520, 380060713, 911366398, 289159427, 897086030, 273868219, 318976501, 155916481, 683586629, 450950520, 61507971, 442208973, 41896123, 662992686, 68024608, 9146796, 851996758, 982371110, 14351093, 425840877, 45261906, 519502388, 497018167, 208741213, 51582483, 722481391, 263391514, 160126229, 831636947, 178511717, 527956136, 852389889, 231997792, 981179597, 669256815, 901874374, 184997389, 141360946, 797994333, 537387314, 399748672, 995335056, 659323824, 979119413, 769669380, 81636731, 337603155, 837990697, 988464949, 100711904, 939143858, 943682457, 716681431, 972646704, 145893729, 573573411, 292712043, 548356851, 249812066, 861308885, 127288583, 587553940, 420004777, 582832936, 34668385, 496989116, 516319137, 368057363, 806013465, 521333093, 818490427, 157021662, 851633376, 837298065, 607834863, 954878331, 885610307, 913721839, 837303318, 760747588, 59341387, 382289215, 711530673, 406873621, 420813265, 665740550, 677370913, 422326752, 648600304, 233780428, 458690253, 327134172, 459998990, 443077449, 559522983, 884005420, 900499342, 792390682, 928977931, 999640607, 165364968, 346274691, 285425388, 667786913, 83354706, 916637524, 754438708, 756190130, 417057738, 490796456, 643431908, 179746787, 147350850, 588325909, 603595610, 573040056, 774788865, 919310445, 243661083, 791195574, 105948787, 840322859, 614425714, 142496740, 207383251, 134688139, 460713073, 40161181, 160492821, 687252205, 983906764, 604441736, 878866742, 139302410, 590115682, 747586754, 820272123, 292046902, 655449154, 236380682, 958171329, 511186646, 751673063, 129707770, 112959947, 34133681, 403886652, 182755083, 933093911, 523553878, 92341063, 366202319, 446744952, 244216109, 164822363, 229134110, 183955064, 932356814, 288967448, 662286217, 815197887, 705079582, 896458201, 141214707, 673608353, 704373355, 558596024, 342999057, 820802995, 288115374, 324430790, 860700036, 695891226, 426529412, 15074735, 164634624, 587041625, 776225742, 471022279, 745839236, 981995050, 772911100, 6517183, 607111356, 585542854, 812969548, 918468428, 533146941, 603112979, 96618682, 860978800, 875728393, 864903378, 732189925, 63253060, 232473509, 204045808, 944899811, 635869866, 242093459, 482215936, 237373925, 81747981, 845764046, 452006143, 428844609, 974599461, 25210292, 519976777, 883511797, 959066663, 135127754, 44953230, 802206243, 694079055, 775620984, 260411207, 879925733, 930797492, 536490396, 545262951, 153489140, 102675311, 303184317, 49732346, 846830842, 652308367, 445135204, 29173843, 907558186, 266647263, 959801368, 182740900, 598651304, 563665788, 805132695, 396254361, 881957752, 247418345, 123536641, 270170093, 118761487, 641777545, 908889640, 413935293, 649795179, 908301166, 110384506, 983431747, 88646001, 23614606, 356422024, 545478894, 844295063, 787357962, 319705864, 818388187, 775806008, 387502033, 809556221, 823402615, 872740607, 265759102, 984851792, 523598928, 552288213, 761844285, 542165323, 383373802, 90265658, 454803279, 218974847, 947340731, 47595343, 974948758, 808705530, 590189370, 16044126, 803789662, 863080470, 230785862, 725030443, 211172950, 378622358, 75201463, 571299534, 343959417, 12458275, 17461928, 461347535, 96752543, 184087840, 837631442, 922657290, 23914372, 308787395, 817812888, 796988251, 828982230, 788774067, 145922823, 748144796, 31722420, 978153541, 703883730, 201442618, 995441004, 133307168, 29299268, 925468629, 573331215, 194554362, 276237215, 5331475, 137273581, 414117114, 486589381, 549497388, 312915281, 531479198, 894776148, 239933166, 603377714, 405601885, 623728281, 334370212, 47269450, 418762275, 719711934, 346710009, 812891758, 608348112, 107712361, 881223271, 918535620, 376366986, 379989253, 548264522, 656015370, 400019032, 796166579, 477178431, 408333136, 569799737, 779092676, 705285158, 868627191, 56448683, 591095524, 879859368, 690381258, 973877706, 225479496, 697704665, 752637380, 508416197, 301315146, 934404738, 892909462, 300873405, 958968097, 318483217, 158952553, 15657124, 240452923, 795663263, 123537597, 376542338, 990934333, 429535162, 937496806, 658455862, 495991173, 236903023, 182138149, 40611345, 255176346, 268350763, 367637839, 877059128, 447738260, 900919286, 743796030, 336422502, 478383906, 9816114, 350453674, 303130403, 369753971, 500701621, 624363370, 962813474, 931766866, 455626043, 279923726, 90942495, 498308625, 949235931, 861148008, 113271668, 936390947, 959256104, 81152383, 597065423, 713698587, 922937996, 203065046, 816626482, 890732369, 210853719, 809311754, 988856620, 97548080, 505149780, 847145268, 619479021, 963031661, 866122104, 549543562, 956201273, 810867958, 259637664, 162797287, 976602300, 135987752, 385086066, 527908318, 399889432, 428832979, 955342589, 146754868, 913141719, 373545825, 620705621, 998408405, 419657690, 207634565, 417751595, 874822290, 702682289, 551118143, 642648365, 843183184, 45387985, 850288161, 248224341, 887999920, 374169120, 848448480, 515827964, 435283358, 150592661, 426093659, 645533438, 849968471, 145768982, 900174400, 460750274, 288532027, 167301535, 138946216, 606590551, 60801000, 551986166, 441916118, 566033850, 86215233, 6445526, 552309808, 388167880, 755509496, 250371316, 504131602, 777554820, 51575130, 518565300, 256175871, 46924114, 152510771, 49226509, 785781152, 467148285, 923443492, 97601917, 42984097, 193993455, 230744252, 835867326, 160338666, 662374779, 335528122, 773022958, 157397307, 391348650, 682289606, 731179123, 916216292, 9484551, 155076848, 152631717, 290953485, 439559259, 349899713, 548099413, 367194243, 77920839, 436072474, 82264043, 475307504, 570814209, 544018533, 933030607, 889607341, 662432446, 80929264, 816073035, 274529858, 521776000, 600819459, 991951287, 539739627, 239228828, 574429987, 357592554, 885757690, 149365611, 174880517, 787834086, 536418053, 737965665, 791477844, 971155716, 771594531, 240711157, 729172316, 497019047, 989407143, 971282585, 510567662, 628182580, 142003534, 215032880, 434638202, 446845940, 31138963, 603873675, 66146380, 95499896, 744572773, 721534263, 308323933, 662972527, 136269107, 388783054, 104569918, 839524051, 907653243, 600020884, 862541721, 590599358, 91511545, 405913024, 396061738, 66168487, 596223699, 554678424, 458611316, 362403682, 850265886, 467663210, 694535840, 62207080, 375384240, 804693898, 770211511, 911608875, 243961456, 78410278, 358778223, 225509058, 650314367, 880852567, 867724692, 604381471, 610352103, 261731435, 608079215, 893562093, 37565996, 563510910, 939837714, 988315062, 78005146, 677503721, 29719927, 214570148, 484475619, 936714362, 51338661, 624569961, 367826594, 181125765, 505918631, 806158105, 642017093, 744104480, 269775488, 860172452, 80842168, 233255196, 350548024, 492010950, 939676579, 64458685, 956858495, 484766956, 397939091, 192748820, 395312532, 21197199, 128161443, 730581329, 952150375, 201670853, 83308639, 196634839, 375919963, 800707170, 781780257, 823343747, 522904943, 424913835, 59344486, 917959064, 667608688, 966242876, 236382204, 410320911, 499503331, 956957206, 646126345, 724174493, 729864778, 520498316, 496658578, 792248697, 854884956, 528833893, 410515730, 75601560, 101892351, 461851802, 444409508, 223914693, 608818727, 735190743, 691144323, 909650044, 226554431, 155578086, 820990307, 732816182, 574751190, 203815486, 296860145, 262626466, 176659134, 929414341, 504895267, 529864002, 220186464, 521409615, 724796178, 86600674, 496316163, 840817344, 7501278, 837669075, 985167443, 164575470, 72101795, 83829206, 469843777, 672060839, 93050435, 832905072, 618941095, 691756125, 431431003, 973262256, 689859886, 127951482, 472532793, 961145326, 217595911, 428196914, 560021241, 858514033, 824943010, 904045119, 402392115, 647892804, 168616521, 414407257, 641198895, 516120939, 508782054, 38169324, 2282850, 18586565, 405918365, 249762990, 690109167, 212979142, 430455415, 730401489, 264720777, 961702435, 62493118, 653544339, 857486652, 45021247, 415968930, 966602309, 304563776, 832671808, 969970729, 248597259, 62274505, 802965310, 535440916, 767251575, 898576137, 875976288, 789486196, 699868753, 201391171, 72211437, 447081022, 837938631, 915315130, 615579428, 284761557, 667743056, 617911618, 121322331, 627789796, 378607091, 78819566, 860651293, 607609515, 76717090, 843949774, 382179113, 123256883, 806808661, 176765770, 268268285, 824219900, 28539558, 423039125, 826948376, 250588129, 250800611, 839614253, 172466989, 622890385, 432201480, 208443434, 976813821, 874521396, 431939454, 138807788, 116917263, 71465593, 927177425, 598897172, 1709462, 134111862, 492411615, 722524731, 591799471, 649089409, 70196528, 392992952, 566093712, 282599348, 270431385, 799168849, 70338882, 283747375, 756431565, 794008162, 196641128, 974796693, 526808165, 872767742, 335392724, 749386486, 489152078, 429493777, 865348061, 164614889, 163236818, 269580463, 702864204, 663365614, 79374258, 152018394, 885441872, 961657917, 392380888, 228938363, 109646974, 537854819, 249756152, 117340232, 592622604, 143236157, 396813664, 911803591, 619966231, 544925703, 406459285, 456503416, 97640851, 552376968, 515108972, 72531436, 894101302, 711785260, 346785716, 667692416, 895274495, 967714982, 913452629, 351293404, 568595338, 14245729, 605525224, 817301017, 223724282, 668494018, 373068946, 512943399, 881558684, 200108455, 828728729, 808671015, 538249867, 377302086, 90579142, 75849605, 697831390, 27084027, 207824870, 804450427, 278703640, 643267166, 375300705, 224857742, 198506987, 214682551, 48761807, 745862469, 402239956, 687334659, 575950247, 730101920, 579515959, 981182131, 338638716, 560856917, 46633298, 10690791, 165875041, 45796935, 971972506, 45065100, 87578479, 663374284, 163681429, 682357081, 481248704, 930273256, 181957240, 788300574, 223070017, 847216328, 107635730, 685727707, 151178505, 507049609, 383889963, 40023228, 996816032, 509741872, 14115847, 723062844, 264100379, 296588253, 68980736, 15385712, 90981557, 25143707, 413701365, 531244170, 586090424, 346268998, 611388522, 81095689, 343569350, 548336024, 557962984, 333296082, 507110664, 64774327, 159075420, 28321383, 782344507, 203688878, 58371119, 564110362, 900451899, 426557314, 19822369, 167748377, 987732437, 575764410, 406318239, 653294409, 665955118, 554522684, 159348447, 837380891, 171201590, 247364582, 641383340, 304813270, 75118424, 214577476, 619924602, 360076570, 359846465, 121606488, 444735646, 926309417, 745335195, 323960439, 361198042, 991925323, 556958627, 242915238, 31596263, 838311174, 950154603, 494863222, 207590688, 296701470, 959392941, 275981651, 102534808, 838179576, 251383703, 602245989, 458464376, 714183929, 855809354, 131367815, 30998289, 96736427, 251535086, 300787687, 562815254, 229074777, 505730937, 782759665, 928535749, 865539925, 335441926, 266981344, 397520538, 63031943, 889784797, 64863952, 970981522, 498160722, 951945431, 78521889, 530551612, 197490965, 885295, 459403591, 774776292, 695271799, 964868216, 617474258, 788132154, 594019538, 779960764, 640033534, 839126142, 329602732, 599146784, 100001430, 374024420, 666350935, 443308813, 375842942, 831730331, 962112046, 732410117, 166771301, 522999415, 381587655, 428996210, 713271658, 481031579, 451831695, 566570241, 332122325, 89932323, 462068757, 333523170, 176680743, 215264392, 873508203, 523245504, 621309678, 391191762, 459323496, 633106831, 25104680, 930558052, 87886622, 251630726, 945848058, 832710854, 75021570, 588492176, 910864480, 489651731, 872239799, 393134255, 73851295, 483278459, 623412685, 665970618, 906172616, 618340723, 959644371, 349028573, 454240721, 700924056, 630565112, 970768050, 396645088, 850710448, 174351519, 22501931, 572141979, 458440688, 890213751, 867634900, 508113257, 994571096, 631377261, 693091753, 519527198, 322544272, 927659660, 476743132, 379583920, 459462450, 177492298, 558976360, 994107857, 489224340, 150829351, 53527762, 637520943, 944076542, 308012624, 205693031, 354348429, 615139999, 406830855, 69620400, 159478446, 240172044, 766125364, 280003971, 904063705, 757968916, 325223380, 33270092, 667178987, 777484406, 140240865, 403617518, 467020657, 424230387, 608839231, 9999534, 966505850, 667035798, 812879882, 140122602, 727218504, 275826576, 91930415, 659644388, 222387613, 104649326, 633683778, 250055314, 92082319, 680397896, 225830032, 610976207, 862263613, 249349791, 192870435, 744740398, 296808190, 190019030, 391478679, 629189499, 297663965, 619248346, 340278600, 689370749, 806864057, 766408980, 47653494, 745385445, 462080799, 681332164, 713754247, 456837407, 368629709, 115270735, 502383869, 408010657, 461299316, 144410168, 414177529, 227499952, 825537471, 182489226, 38652724, 182129796, 571753330, 71322038, 260543706, 802113946, 363166673, 879557250, 736852393, 287759177, 876136245, 112206346, 175624476, 438349878, 238300653, 546370687, 281679260, 433318855, 514496110, 74260745, 371732741, 921536200, 501400003, 882234981, 238065963, 893916423, 644331215, 893843204, 207216870, 31390715, 459894111, 715880228, 401021161, 296067737, 653142445, 746432399, 497767389, 583953400, 915869743, 166993547, 59527503, 973031978, 668905713, 373235937, 960521336, 345548837, 82896564, 620000234, 798158927, 199586094, 784528988, 143253903, 344391963, 438733875, 705023834, 492217490, 273424259, 67979183, 721041820, 488779193, 476024373, 256420469, 393086715, 975785022, 844765083, 712069481, 371384848, 885012191, 326603804, 631719382, 122276312, 23676002, 449615410, 943241127, 783595435, 264155424, 752199756, 929779718, 793646891, 898145153, 378126969, 174052281, 967599680, 499306095, 724592272, 593255613, 47588133, 290378367, 80872648, 976400915, 409852479, 67992532, 179375748, 930906108, 704934140, 905770088, 82809776, 993812612, 69438726, 59721079, 898729108, 790201280, 228307218, 238076460, 576205268, 8394152, 50735319, 724979183, 813597847, 39021255, 255269817, 387015767, 502177797, 522877337, 822060945, 435773160, 677063779, 88761571, 698027986, 205937150, 58578813, 960293741, 224694252, 481375727, 822694588, 846431930, 691398141, 385445692, 290628381, 217417572, 400317471, 204987283, 197123434, 369504332, 713151480, 982392520, 174184598, 357800646, 713830313, 488345111, 536724899, 406111670, 799973966, 810700746, 274304459, 631559971, 146226204, 690883732, 244410549, 65277055, 969225359, 206011929, 147662570, 268262442, 346959438, 193756626, 550527814, 822849115, 554987594, 75060627, 775701799, 797075437, 232648646, 437377424, 520099277, 477666854, 839197092, 34802194, 860681417, 454945322, 362632720, 91482570, 1346922, 230788303, 962708553, 94826266, 178768561, 363537655, 998534124, 584344726, 535135863, 670328769, 109504196, 549790291, 841969102, 238469495, 362039526, 780348620, 890266470, 501505057, 965195944, 752198845, 180614411, 574975433, 746075606, 838581197, 661428653, 364046394, 538756117, 210331601, 755004784, 321270807, 384127763, 736887061, 88242547, 192784353, 430027013, 980545983, 368942660, 98004844, 451059443, 443214260, 324764340, 554954027, 800031013, 272353360, 583846982, 905706919, 30602417, 283464928, 753764772, 746138474, 2191642, 67545728, 848236481, 503884392, 491252659, 498786394, 789596057, 628477469, 163471314, 442873264, 307597734, 70001787, 644028896, 730818008, 950990853, 171129838, 482480395, 874755720, 466720297, 509692500, 836339382, 191861692, 77020410, 546115169, 80315951, 965807248, 884973698, 203167631, 796663249, 443378538, 187486233, 387990852, 595792361, 208850689, 444559175, 958699608, 754269044, 732852513, 973232506, 860290736, 671221142, 989265016, 878355562, 827162688, 340117897, 197360870, 618095799, 935776650, 155095604, 203001100, 183878588, 315034924, 964959547, 480245096, 604293435, 806387861, 680113527, 947373600, 277446092, 459596193, 992782556, 699619610, 922289465, 500660938, 886288531, 395470365, 944864205, 693382212, 367397318, 562985924, 629255011, 985303952, 940575301, 113364924, 546787969, 368299777, 406945092, 62718219, 14406436, 815741220, 61695158, 504669574, 786138553, 1505647, 588767777, 536290328, 203271294, 407160654, 388306208, 292458743, 364239542, 484315709, 926551691, 544939608, 58680798, 993187662, 27953206, 570945027, 598558536, 972392653, 295803400, 616576074, 220310493, 517732420, 937507723, 934923397, 764150042, 155552516, 489106806, 617535652, 504792994, 78663147, 132087223, 298743721, 908587608, 414771720, 556425128, 225995156, 796280433, 372261163, 494231249, 750619426, 705109896, 206269958, 839427919, 468672105, 206815370, 401090131, 367808305, 425509903, 923355222, 882653487, 179006901, 114165356, 712647393, 145883642, 319219949, 815931664, 902434750, 656683808, 495914505, 87688213, 948455723, 25679996, 232498264, 375699054, 793266369, 154606436, 49882529, 36510228, 108603841, 415908849, 840200131, 781839055, 704231617, 584065484, 155350489, 712825211, 913807777, 180279795, 207314886, 171920059, 45234788, 863285305, 306850155, 304842231, 693330369, 949055238, 399411886, 95996480, 706996079, 135642416, 592804435, 865112755, 890810142, 201049674, 374814494, 852909287, 749306341, 165279858, 808442665, 216373937, 220285267, 834053723, 163550978, 128628181, 938528097, 783198353, 357737992, 238206282, 182328752, 406477500, 517044214, 426846433, 16451593, 805641889, 866456194, 746755280, 246515645, 591142466, 637924147, 883621225, 19431642, 33304927, 179272394, 327130490, 894617730, 435187300, 966004828, 347019991, 150889733, 642312383, 494389161, 656371015, 70736358, 624825524, 333112664, 368305759, 414803359, 338114362, 717715470, 770372213, 347242697, 78539843, 990647601, 912791511, 331908920, 436141351, 870505515, 997020248, 738693718, 893152670, 962811096, 479666663, 593356483, 317868521, 604756552, 2295575, 41260452, 2065586, 866156248, 296479400, 618001689, 96658089, 929014072, 50353254, 960801390, 941542331, 356679540, 281066668, 531919265, 953791268, 504329724, 581815735, 371145517, 70379160, 280547074, 330575865, 745595141, 406849654, 759820175, 514496312, 825134750, 716279675, 811200868, 925096076, 746674441, 72766959, 920637776, 713982243, 100516965, 149019013, 639887879, 332345688, 258462146, 329339283, 448883052, 922781796, 786254291, 633497995, 950502191, 716798912, 573286347, 167515566, 191525657, 579828663, 842977034, 813008275, 849590517, 890029518, 422918743, 518019748, 876193272, 152299389, 814164966, 410192763, 108877312, 649183551, 155663332, 894205730, 846869777, 808999950, 548438102, 509958761, 484971684, 756304798, 313567992, 821134224, 992770039, 589815962, 468269185, 936397192, 42317305, 106009334, 192085320, 995086078, 269727360, 556512894, 999654650, 623696287, 131027908, 659367209, 492772098, 905798345, 56498260, 780504871, 174171173, 410468795, 404922700, 247293540, 300453819, 86771761, 241595061, 456803544, 908913161, 820962136, 818275509, 940242413, 195556255, 596920206, 290841155, 720928842, 962650351, 851120282, 747365180, 185482393, 341983456, 957165310, 182550305, 731238740, 90238917, 896413833, 459819550, 62008988, 394590462, 914973632, 654541539, 923567249, 128358872, 373740636, 265275454, 384030265, 181884370, 975870815, 664041056, 588276999, 231768290, 107343489, 473362139, 584359827, 864059150, 586456121, 660010961, 589952053, 90000949, 830707668, 52242640, 514408887, 802800368, 975665519, 733411069, 411023843, 150701883, 506867504, 233252214, 100543516, 699562278, 450334811, 474520512, 50414467, 152313370, 358058332, 576493941, 253785507, 645675377, 390847978, 360127208, 71701887, 506790941, 543944044, 373291593, 249016077, 548016718, 389787349, 863366560, 979715452, 849053431, 569109266, 899288899, 420529827, 225933546, 806681591, 711736545, 25284592, 591401132, 101182231, 242572311, 78668254, 694486023, 15386430, 574162294, 757340990, 502709116, 413448135, 448798493, 684933578, 897001011, 859244494, 855875113, 616624432, 480500027, 722811689, 876760576, 363217706, 297172723, 847547283, 248044217, 662313666, 858437893, 387371874, 921875135, 692152414, 874764355, 332573180, 451541474, 669732071, 512225185, 375471257, 936461671, 245997035, 199386951, 752318471, 689198019, 821418668, 766269485, 702534832, 733892321, 937537632, 202104191, 972415937, 974327455, 114146315, 659985501, 281339937, 24359203, 704270742, 398030948, 587759051, 458902853, 356199809, 856478849, 523252160, 220406070, 30365815, 567011699, 850472260, 825073435, 339214730, 583536753, 608806562, 594522500, 933528551, 303172092, 189520814, 814054381, 113387436, 210557480, 779263304, 811639170, 339573645, 331105385, 215218344, 679269381, 478353651, 350528157, 278106535, 507490191, 654326957, 343661653, 241930813, 727714139, 946088077, 794034958, 208707594, 602524511, 476419465, 956242291, 915356158, 887223299, 625445507, 569325623, 580242928, 838149458, 567403944, 904006067, 998985567, 684076456, 727913110, 715085526, 112725420, 482427640, 788897704, 969997923, 278065723, 506021059, 38298957, 496113172, 503777158, 997106999, 464128506, 571314827, 126911763, 475763612, 477759673, 737383355, 818641277, 727223930, 165430750, 137948166, 945317198, 354976160, 133375289, 590700590, 782199799, 169494189, 299575739, 951584377, 364982626, 444309544, 160243111, 456789725, 607930218, 225813748, 157773042, 76703494, 253989042, 736351242, 472007927, 442568329, 600563762, 92512244, 750184612, 851256613, 236864583, 271108420, 447281723, 62925963, 158503424, 491292144, 652857420, 279166726, 891017777, 373343801, 108209094, 734119784, 498003584, 892727251, 72506095, 488927670, 7450717, 506825671, 769350627, 162867061, 506181949, 42822397, 531232870, 765410567, 834935492, 297179229, 934792014, 706054342, 794823780, 84978239, 466899742, 993206581, 698004665, 330459783, 851702784, 95164086, 729101474, 801088659, 504423255, 826161712, 275217587, 97551799, 326740501, 333400229, 248217849, 883318318, 5523328, 419177756, 701911667, 822492098, 324613462, 269270190, 495917377, 136806735, 324222161, 295036684, 522843008, 554185532, 163757284, 134964034, 650972125, 668935378, 655882972, 886041692, 673874056, 386776814, 573941503, 25212222, 422331882, 561413515, 951170085, 224115479, 400072905, 194092773, 596921003, 427611729, 515891008, 498974187, 641612685, 157798273, 930114736, 456694074, 298959773, 743308512, 960247939, 133889093, 196134433, 469952609, 543586914, 495069289, 671781924, 446144350, 7140390, 378204170, 147234912, 3291195, 630273017, 829558408, 205668991, 546357810, 341337177, 874969086, 112654721, 531077799, 542684757, 40214345, 639659725, 739409073, 746313359, 8350195, 827020479, 778676063, 403495582, 197375135, 11786664, 941112542, 450008277, 774925048, 188271075, 821885984, 885784316, 743637794, 660905401, 971354369, 287100135, 604637885, 296412734, 521220971, 402828864, 51472792, 141426236, 19613888, 806539194, 736039840, 731564273, 143618918, 737354059, 236491340, 77263520, 616776772, 176546391, 381956369, 152912501, 262594699, 412179951, 897316581, 598328556, 20990523, 200501225, 396829036, 486150070, 237770707, 97376287, 679622056, 307680806, 792633934, 128585358, 257905839, 32307251, 581199715, 221515029, 784885275, 714876395, 945925756, 903250776, 317830733, 392940838, 963765795, 487003281, 75746729, 759494684, 822119460, 632128897, 946501222, 210437508, 211574125, 307487911, 91374330, 347093493, 300869199, 629918265, 863398506, 691727507, 556097321, 911245289, 558657907, 831742211, 6197548, 928754438, 394757287, 192939002, 54011045, 462322708, 141826995, 253602635, 676714601, 300398342, 42660931, 314048528, 924880066, 671947283, 365257727, 246002610, 856836338, 601401807, 81046531, 902273265, 580489470, 439173088, 713176159, 544965871, 583974630, 906840000, 334023962, 993048428, 227500428, 82890007, 357271232, 559050200, 500847662, 382909240, 41555471, 482606795, 392867781, 968094403, 614888831, 667021159, 834537318, 475406475, 535130731, 76173234, 897459893, 820027663, 745923862, 197222401, 656373933, 944473418, 682892270, 861330419, 330917468, 805107152, 529516787, 842157965, 758540540, 899195004, 192866260, 298251198, 911024998, 281642491, 366305018, 93321393, 933652497, 187369244, 994763065, 974563094, 286465012, 6876626, 123240400, 899041496, 891524093, 587219766, 510648609, 886400812, 717605711, 832639454, 456586840, 890305724, 374322663, 476948864, 714521798, 806081834, 154913863, 184507204, 565017645, 359360942, 226227207, 943805354, 879713891, 28300463, 844046586, 706503012, 15031623, 602891221, 449994011, 429292701, 899847770, 909535767, 865536546, 622078150, 66601641, 567722822, 828035432, 935175598, 935782124, 325407749, 463188457, 353894608, 749505837, 158440462, 702923608, 420501860, 989087570, 503460816, 271912181, 921980537, 87500768, 227684280, 351077163, 128327765, 836013349, 82461624, 295456421, 386637263, 600156233, 502322651, 645144639, 332803155, 139250169, 724016152, 740528942, 216488748, 298324999, 69466573, 838604549, 119698605, 835581445, 559518287, 77580012, 109155046, 609068539, 679255046, 782439433, 16960034, 914500321, 188266170, 959524768, 375096550, 3094361, 818577996, 88376119, 295387788, 937771268, 241726717, 19483933, 801713227, 38845511, 909129618, 320998733, 947880729, 274312683, 583042620, 327502151, 392250695, 938063247, 433806210, 320013106, 247561395, 304723446, 611800364, 577060365, 518782308, 952367951, 819385379, 203754331, 711291907, 290605789, 749869057, 733529888, 633003904, 594843571, 192144646, 342115005, 412233315, 924583709, 97759251, 432096176, 406625474, 60904078, 950288812, 720563991, 986529732, 27726928, 826628963, 330110044, 680618414, 750432866, 704987127, 349851229, 957446793, 994106082, 964714593, 339325676, 568810410, 185071587, 902279601, 913974357, 494139547, 446348148, 709195114, 953091402, 56379663, 367959861, 281772441, 175196907, 193158275, 591846189, 893584006, 900705808, 703748452, 924796691, 955182610, 886452586, 65435036, 635566900, 28855687, 443491459, 690061446, 556798193, 9778386, 460625734, 646822056, 716713751, 730066421, 477579974, 146209395, 847190339, 176173546, 40613475, 50420939, 551346875, 271525429, 643454834, 986743868, 370646383, 665033659, 924577549, 546684285, 938981083, 624381953, 527738628, 542018238, 2038188, 145725045, 237290896, 997676911, 450178420, 912688277, 118435639, 11486528, 705900202, 202431677, 192518381, 671602045, 524597190, 472156307, 798191456, 191013884, 934641081, 489337562, 383463593, 768395147, 229903967, 631270075, 540498309, 16900237, 929809699, 373270149, 248241931, 748287763, 377585869, 171386530, 720126208, 398399552, 746424329, 780422708, 263989991, 144150331, 345958011, 184078779, 849716529, 276430122, 605908393, 326539204, 130170106, 563687452, 588859714, 674283665, 773268553, 140985367, 442740209, 932840764, 803692213, 776248623, 102992327, 419190881, 323989045, 553359913, 451617740, 599999359, 949584992, 352146874, 8417860, 650074816, 636395179, 768103782, 682960839, 553435832, 98017018, 806524428, 153285580, 876112460, 709111592, 603725337, 82707016, 864503674, 532395304, 763740367, 320428443, 379729145, 206378202, 680903181, 310883041, 445254189, 126149027, 273461883, 790776573, 376515829, 490534546, 318491172, 588756105, 312761075, 842506060, 139182834, 951966515, 79500949, 316087467, 752278281, 351106473, 348364212, 649911847, 858572035, 849559195, 766230357, 961896111, 988444396, 300011676, 612853334, 455255122, 140179071, 619331365, 954812054, 800697415, 514517471, 699778998, 758837919, 55278400, 516027398, 350535328, 781676228, 478056366, 349769427, 915507737, 376695263, 736494145, 149726433, 410799331, 311719233, 336582226, 464149486, 521637541, 192169181, 442290372, 652236634, 479169732, 155712251, 721111414, 680393351, 420535896, 798964537, 514829309, 988764062, 666186499, 853508305, 280825326, 656624234, 907253455, 430487118, 326331827, 545746561, 827210170, 373350456, 880494766, 936340106, 709879081, 671019740, 615892470, 443164028, 123400371, 326315738, 95200497, 627134840, 991822544, 437718122, 592920007, 904605167, 905083519, 726598280, 597140825, 42194731, 232502620, 230014486, 395654696, 673026577, 34860748, 8399639, 487126339, 602543803, 183266410, 486233582, 622113033, 226354871, 513926678, 57608157, 838319130, 70955021, 858358992, 905682627, 353579736, 735788126, 273412180, 793891862, 724650768, 237352722, 220878161, 286383119, 873889021, 448770918, 571576457, 457064700, 808457106, 917436360, 98816323, 6170200, 728387901, 363854644, 252591279, 274048961, 7956286, 637650320, 256711099, 945972172, 579818106, 78260003, 827183598, 478105170, 515727903, 782298425, 683020935, 286579514, 456793959, 241673300, 940919299, 151633926, 479483506, 783637880, 744563278, 194826046, 681909654, 39401860, 871867480, 657387639, 352880111, 58648378, 558020170, 617722759, 318251790, 170015800, 162945446, 572250893, 609284472, 479951416, 334825495, 697419076, 222518413, 396625552, 215892174, 435841502, 979726838, 498656066, 50438781, 402675120, 904655923, 954618407, 995106918, 976073668, 274170531, 452417665, 494657303, 48000351, 623413256, 489764874, 705184329, 54333014, 147217316, 380916964, 982762341, 347752784, 840431395, 512502012, 827240979, 827374545, 988905570, 6691096, 505607621, 851226644, 941414337, 139757636, 189794485, 636226035, 544814232, 838057823, 246615043, 857037689, 429695095, 563521819, 700350061, 314791528, 759275308, 106136809, 863215350, 890722174, 513201198, 169588058, 18407361, 244698626, 849811136, 523102482, 988046602, 937782887, 198214237, 614732875, 630068637, 776909733, 423614087, 954107868, 971491122, 626364901, 782341807, 205066338, 211662798, 79759682, 771776143, 296281276, 54867662, 182304810, 456507748, 875738804, 38934346, 513924246, 67624364, 441174614, 592597203, 887963047, 671412907, 81132428, 371466099, 369507194, 791536706, 405337304, 86703244, 176293055, 999075953, 745554972, 204186361, 893201172, 902183545, 232118291, 783284181, 583351046, 462807027, 880136338, 397240388, 429481088, 935167180, 94816457, 835991466, 140864722, 480726275, 578198429, 856901163, 610851517, 525053793, 56521769, 819030192, 953111395, 380870582, 979283515, 451835306, 177019966, 106203176, 40984474, 458810736, 35062861, 94798699, 410892526, 757973576, 760225808, 144301397, 438487129, 458087910, 617841306, 53862063, 881474555, 648725032, 625850869, 106846793, 59103321, 130287170, 55858190, 106256979, 467609062, 733529465, 921660093, 42651837, 287224135, 331009045, 739351487, 59263952, 997062136, 25975033, 185527666, 792017077, 891541964, 20833729, 813291921, 652900308, 212233283, 154043146, 364259532, 839047024, 470259066, 944742692, 41438365, 431113069, 571174040, 442001780, 573198268, 878497441, 132693610, 902642512, 23692264, 852735461, 643391819, 665958762, 221963136, 749511817, 579518106, 5509355, 630358796, 910782109, 113100991, 192061930, 597184570, 716798456, 574838673, 76997997, 479259004, 234621367, 931318381, 608674963, 29866866, 975279414, 502991113, 434655698, 407023589, 411870282, 624474665, 274221751, 99950408, 262106537, 716845021, 337077676, 609345062, 519122507, 304289114, 719951465, 176110, 954987274, 815425092, 71039173, 710080504, 81802667, 591535768, 229776424, 753255660, 366725518, 165047097, 551944877, 80392950, 640999654, 841446938, 272892163, 438868922, 559793645, 171495704, 60344413, 243984976, 764656231, 158874348, 895875300, 270565635, 304699972, 354588864, 184701914, 893713292, 933071872, 45850169, 525883529, 689305900, 242554507, 57949580, 323918702, 101033909, 627515772, 406634322, 136135600, 527436270, 112688027, 171304360, 393831291, 586183317, 275121519, 263520185, 137794446, 28125746, 620367348, 504148197, 538271959, 175747565, 185043089, 986833262, 312234376, 319599038, 734318940, 351400556, 216417579, 990681532, 112333277, 41996147, 774213456, 300932224, 453811385, 266081497, 61674859, 585868369, 171763549, 673828718, 473270348, 702710701, 637874468, 464683132, 582244949, 806149756, 764639168, 513696848, 338291917, 456000069, 627643430, 298904242, 251893994, 293059545, 954290084, 295451152, 760257821, 72194535, 771892440, 100458621, 168583877, 843097152, 759290206, 725400684, 566933715, 967502404, 176293142, 994525645, 325106871, 783667701, 924375833, 483334099, 290840983, 442401896, 404387225, 470441542, 781870448, 699909558, 856628449, 138270830, 15404944, 265728940, 544184140, 233968399, 444536340, 993221223, 451426594, 503397701, 360556046, 323610031, 298766218, 964482359, 63537228, 869661946, 558806744, 818817797, 915391262, 482475944, 503546583, 390943121, 633746812, 279591874, 924859066, 208413322, 879899082, 317222003, 513817540, 606889261, 799186780, 730547604, 322327396, 431469975, 793382208, 173561212, 786905107, 380400206, 373707612, 880782649, 963531696, 667116659, 190112770, 993269622, 964146561, 767628943, 804378147, 599274498, 303043090, 963770167, 699452920, 407487594, 524024414, 121796924, 209262746, 754647745, 669101433, 579471, 513069676, 737185823, 418631796, 695520704, 234254946, 773037087, 559865799, 481101916, 342912787, 283825443, 562977445, 340069583, 155078035, 980182810, 488659457, 202466600, 803091352, 936976299, 297769593, 949965738, 957792076, 298368043, 711194837, 597086919, 95857692, 664946225, 271093470, 34373913, 328645400, 563232451, 548159833, 370578326, 341724629, 970549012, 591472013, 847365157, 114268571, 722927905, 502447327, 255313162, 385122142, 927473524, 979135073, 591906203, 39050727, 510464489, 614585705, 622637922, 420776640, 509461937, 161789328, 792251179, 776709370, 567866941, 785129893, 490536534, 921640074, 900064689, 134379550, 564983414, 178914109, 114331868, 994623611, 898404498, 561919861, 576618887, 627898067, 580860331, 20603532, 769682024, 199635178, 575226037, 279515065, 803439446, 424828341, 261990628, 23433182, 733710688, 139333207, 767734981, 433105596, 660640752, 278130782, 109192457, 839583446, 447875256, 998085433, 846337512, 117751281, 617136025, 723718152, 419778792, 955213217, 619319990, 44924395, 816057871, 743856842, 984688650, 417707366, 535204575, 932319570, 499027506, 757931450, 405807634, 198275254, 980132060, 396039667, 773943660, 926781176, 402287440, 629006096, 538452985, 404137215, 136426050, 741093962, 753989209, 257877342, 572462575, 540950406, 344324171, 70391687, 778181364, 955321310, 587315315, 701178046, 840234656, 225094713, 308147716, 838792576, 577487562, 428502981, 653074512, 590610055, 22598444, 21969844, 242033708, 200611577, 913875283, 21876486, 864542873, 466860493, 25129619, 25861233, 497900922, 348987843, 146526320, 542646176, 435079770, 372207157, 417808697, 177347109, 664264967, 731449192, 270112119, 619416470, 501592599, 945285293, 775436697, 64684103, 881390905, 891804122, 292170167, 118540739, 809761542, 342847561, 45686286, 17746520, 222267418, 530720762, 79757126, 253665319, 52359476, 973757830, 343395681, 349734517, 779132365, 633288479, 428790068, 735405769, 936327, 233381154, 235513417, 230466169, 729889208, 642147090, 264047853, 357577935, 396460793, 17007473, 905811528, 651024950, 770437648, 31356370, 949893395, 452004702, 607769622, 253388505, 928791893, 483206806, 15949365, 70764511, 337582256, 799890148, 50790079, 800223418, 421005375, 833478899, 602288424, 994690921, 844945588, 727969738, 58278989, 478667095, 377425093, 219545894, 432428602, 999338857, 678478121, 179889098, 623037361, 575912807, 90750292, 523987250, 774673273, 2931546, 399612618, 797302772, 8047395, 421356798, 196796557, 825496749, 591440418, 577121907, 618773777, 363632593, 213617612, 853018562, 180469239, 961617719, 310023263, 742673092, 655797100, 861038177, 797995633, 465619274, 854917557, 123935363, 443643673, 394051857, 90279500, 490194570, 83428862, 430037524, 610041888, 311163423, 520620262, 169446134, 808117550, 632459432, 381251382, 346320498, 161215196, 704184307, 688824397, 514266523, 66767622, 586999323, 306657051, 753063585, 74564118, 993075793, 872789450, 906304100, 218396656, 577982969, 610374013, 702670844, 256984048, 872185032, 208700944, 565405050, 209770397, 111430212, 145382655, 141132443, 952829628, 915578955, 875330929, 674809968, 891091669, 467382882, 402830535, 105814930, 381274054, 84882080, 555155219, 71716099, 81058288, 113633678, 429414773, 643478179, 282900296, 180887696, 101813286, 582886359, 926302011, 127830490, 974561999, 678979957, 675810563, 375230659, 251575431, 800128462, 589823166, 573359566, 708197522, 912006365, 251823052, 490901285, 813346737, 487054442, 588098708, 160981422, 590826962, 167504460, 136972197, 824608063, 475195129, 889909517, 110895714, 160321121, 552603184, 920553189, 125616, 137676272, 396242954, 130709706, 531011987, 114316378, 577851397, 885029833, 108135122, 152740409, 739150447, 100715168, 411667132, 402176397, 703079243, 545106065, 978705614, 126221092, 650389554, 313746178, 264361702, 412538332, 34271410, 820810110, 797295926, 180883545, 703461511, 539699710, 458898889, 15423689, 394876600, 756894171, 204056690, 692078708, 42292733, 25739014, 131211609, 674999466, 75862537, 503311196, 357686483, 760240237, 237647953, 535155316, 242230925, 326263516, 754612079, 586766296, 843895003, 651214819, 285752803, 931658651, 191339174, 203873908, 733326685, 872130605, 25673318, 971861256, 555079522, 84129738, 573747161, 355027765, 954081720, 418893878, 833372449, 720089116, 363921348, 925613852, 452403950, 284839614, 602996529, 974354701, 904221851, 218635168, 203196222, 71410642, 196847096, 172839711, 894622134, 709570724, 732459572, 832165085, 943571413, 760445692, 763530951, 217170005, 501593706, 198934970, 224464895, 179615431, 737325133, 652926420, 658044632, 829284550, 407788216, 928500387, 846501560, 832629424, 730184349, 748959037, 993263004, 483341165, 760577570, 766246230, 185966985, 899426837, 430861015, 412592063, 221554189, 592046348, 370745595, 147080153, 429956703, 204342011, 534758139, 477671890, 383591193, 649229183, 803175346, 543054612, 983774914, 755405964, 851439346, 475030812, 960070022, 347640738, 366119567, 81137461, 287914088, 637020556, 696062279, 600184316, 597550213, 307991163, 627140047, 33844861, 741156415, 174973638, 574924861, 502004294, 491152708, 371933489, 438599924, 587503204, 193675146, 867012871, 274780783, 941157221, 449928147, 747475818, 288524351, 90529330, 290172614, 70302635, 82436581, 199034166, 780273590, 637808001, 477744689, 700640330, 972326100, 644125193, 552632007, 96183701, 678074581, 325174055, 945207565, 301517157, 888945905, 81566506, 337123444, 83307725, 604189118, 408153267, 10114851, 892666301, 430660969, 282910377, 645991093, 975760701, 922491341, 563114517, 413834577, 608867809, 702678873, 93860474, 240074889, 287619413, 687601022, 587446313, 190697662, 66710624, 674239863, 23759387, 77500791, 306766612, 409398851, 627519898, 892641270, 346119516, 284466612, 336799609, 782919190, 91984401, 341136087, 668652196, 264866524, 894091373, 910411446, 305660546, 850604912, 368603531, 564185476, 756115901, 581148958, 596575932, 723098293, 810811689, 913143023, 151599645, 854619381, 889156821, 529687085, 198061242, 364390766, 284844314, 996488966, 836507816, 377375165, 487047340, 85104984, 342239169, 531699480, 920465303, 597966992, 890413931, 54449645, 405975404, 344339940, 539846152, 470593371, 982871602, 999770783, 687080452, 333132915, 995794614, 700662458, 657704829, 458172140, 852366457, 892033037, 16098443, 403744750, 153717031, 271167945, 319392064, 978886419, 807618453, 276595107, 210811421, 786015306, 723887375, 473100165, 703954414, 919750518, 559613824, 730762418, 464465081, 172686743, 797703304, 81655104, 24445208, 141972075, 727565736, 346267315, 704764241, 282371565, 566660583, 765413571, 302560684, 855886849, 327446857, 268072995, 848079230, 642483112, 240138770, 63004413, 420838215, 428052926, 689971987, 17735377, 40056281, 542960992, 240791257, 938461643, 875019804, 704770908, 500797649, 847535470, 24200970, 869316303, 164334954, 635671329, 436468370, 292969748, 756640174, 417497368, 945587124, 949382707, 366282432, 613919734, 589840291, 448881684, 800194301, 556634614, 330028859, 401982489, 411682499, 221062819, 919817980, 781624956, 491813524, 503434815, 8759396, 44031875, 20864087, 661420038, 441518512, 370031045, 146092060, 708630917, 526594381, 875883167, 799549479, 649041100, 270405497, 214632309, 512954334, 651999541, 241597439, 981291010, 5848525, 666523910, 123504938, 443285828, 634468868, 436414601, 510406000, 801551761, 531835613, 348954373, 585619485, 521498960, 679477350, 930221422, 799957751, 189755282, 1457352, 415701017, 724751331, 4222728, 397645388, 782331041, 870241151, 716445163, 165413954, 328116809, 940753698, 398122521, 157281967, 841068974, 369059355, 899260451, 600164635, 618898110, 132983072, 652704045, 597401296, 743971057, 378882954, 545752642, 144543907, 779751315, 902491077, 64784838, 361065245, 237387461, 972159779, 981493685, 772257605, 7872904, 173966631, 829401986, 217882632, 185883021, 385536532, 199384449, 77521529, 104413257, 504844988, 9386376, 136063584, 25580340, 800622837, 580449079, 197138693, 810700347, 763720982, 710241975, 415333057, 856117621, 440012626, 114874418, 883151394, 988916521, 803164096, 250309293, 17129655, 347825922, 110647442, 483309937, 637003058, 386259388, 802673236, 83851532, 386284368, 603113310, 287899051, 314487419, 357672055, 132138283, 153757680, 643352680, 620940764, 729354284, 120444471, 317296061, 244079872, 837361835, 328559334, 20753296, 607766336, 275380364, 474104964, 304815072, 554859931, 702578849, 299080134, 359335896, 273841164, 425700489, 391169404, 737455720, 174690882, 348945851, 539790326, 123939376, 91293241, 646955702, 910041041, 546962165, 698330961, 950246518, 491395984, 873356226, 525474239, 363683933, 797599340, 457775551, 655032397, 255530066, 387557965, 331626276, 174616901, 631235849, 301788375, 176275910, 471394126, 804523931, 188267973, 111549293, 762548196, 656012815, 773597299, 925800788, 742909561, 698169694, 284889618, 507442591, 535598797, 986885029, 956922608, 360737463, 181535042, 412633748, 415334195, 996174643, 123053682, 260358171, 581047315, 134878294, 838183063, 302086397, 504235848, 500593555, 286601363, 97145024, 374340006, 644823136, 942490885, 444650363, 975303189, 90817293, 815477264, 624435770, 655205631, 122735593, 974382955, 310837117, 888064814, 865550878, 912960868, 769355029, 291185785, 826544564, 174428626, 304974552, 95866444, 987313881, 820023723, 967368714, 74762275, 926055517, 383165581, 419141944, 977896516, 513039177, 337388264, 170779735, 716724714, 756025030, 408834521, 306287555, 743885292, 426085681, 909637787, 387178645, 280140144, 91051996, 982026219, 483325865, 20848431, 872255607, 840925747, 479195087, 227339302, 179221391, 218557659, 459990279, 582485153, 318270090, 814083344, 162040399, 914181390, 169539254, 727379327, 384270613, 733185434, 506372503, 372506400, 839079012, 502848401, 288666702, 307741746, 308806047, 113220437, 486000339, 359901345, 232543336, 452962805, 775755558, 494592194, 403968024, 299804084, 652727332, 712368182, 401426835, 22803499, 59321479, 828497152, 487330172, 851301692, 749979448, 570884023, 240776933, 680251868, 789206582, 928290712, 524972703, 984929998, 399739037, 105898794, 782263936, 705272165, 744183733, 263769041, 73042386, 305403469, 182852066, 898637099, 403636833, 577839025, 382244008, 700411289, 427050689, 299408758, 57799366, 540377616, 314427536, 335922353, 678469802, 416008735, 238007752, 803793488, 369580307, 233746272, 62634076, 907724679, 149464782, 682476550, 275541128, 530586550, 632813157, 400233055, 733622268, 40415373, 648246963, 526588515, 63744929, 392975655, 471355883, 482216171, 270893265, 259914148, 763215609, 280441023, 354647789, 303590337, 573200363, 514364054, 195579685, 122440561, 273551019, 829526533, 452504895, 122859094, 835608487, 421139542, 69814697, 658438382, 394112913, 944889133, 78509925, 992671430, 691182454, 695950249, 759893060, 405924113, 234170727, 773956275, 162153016, 287942660, 73294111, 566679839, 894485073, 289269385, 289244823, 320653827, 433078264, 919780754, 867145535, 996622318, 707182271, 718742226, 893027897, 236205907, 434486781, 814512281, 224605077, 955837111, 875209639, 190787491, 372003612, 52574486, 942782287, 969564442, 254820388, 916114610, 679392192, 64306857, 765030639, 417169671, 530084215, 343565573, 233487673, 780160623, 507440434, 197036761, 171241425, 863155419, 350747029, 296274814, 476582563, 243377294, 83771912, 84289201, 242627975, 434498222, 180509420, 88337802, 185962172, 617812012, 689597309, 163826560, 879974789, 418932665, 788363400, 649435529, 313121009, 441247062, 804318444, 359354768, 16826418, 173443669, 690525261, 762296764, 701860841, 524413693, 506157616, 198111318, 343513656, 867236064, 427051449, 272919536, 770516746, 956084158, 84357991, 362770002, 543111591, 6570065, 759336084, 83210205, 464997011, 419204961, 655827446, 822604194, 424985875, 500292197, 464214774, 668355495, 191803752, 26604015, 130184027, 989627202, 811824158, 715379195, 314529946, 467392798, 719861441, 781605620, 866657347, 911687487, 204736972, 442675495, 688044889, 39555227, 885934716, 891401652, 538033089, 74522073, 458231477, 553377229, 863054851, 857388030, 571332261, 747981575, 758683549, 519140828, 154459506, 194488988, 301982461, 604978022, 868006553, 724188988, 164119254, 195299280, 626396112, 670359125, 716573762, 817495378, 723227450, 294748272, 539658078, 432647463, 850138223, 281278771, 467448083, 276647092, 829422390, 774123976, 107540797, 450361185, 654203837, 921742552, 837815216, 645729845, 567468688, 327854146, 991014820, 278670012, 705473149, 82490442, 307224677, 326174317, 340256878, 388069071, 334141078, 182695636, 549986981, 199293461, 40613842, 901920648, 383466863, 988407925, 830700785, 746709104, 760238366, 93479607, 788611170, 782637518, 294902754, 176853359, 681818848, 292104163, 390786442, 217312947, 727921253, 222861294, 580816464, 264604036, 467493624, 76113899, 424199101, 560298496, 477306126, 605602552, 762949075, 449547410, 504834483, 829741001, 41108046, 997569313, 732403339, 844256007, 699010282, 603681822, 156479606, 743981007, 758352726, 205084796, 975860997, 475132554, 994227225, 571362817, 321557828, 156850919, 418589535, 295176407, 156253492, 530911542, 814793153, 416053097, 974803241, 600568189, 891672873, 540255959, 594091194, 54205458, 702587399, 574414878, 294014328, 198722730, 627471403, 156221301, 382378914, 847163951, 17890733, 792085531, 643856183, 793920644, 910551783, 105588522, 208099438, 595811946, 940982753, 5536712, 497075722, 520374060, 666516091, 792872826, 262574794, 142495788, 259182803, 713513118, 918485955, 894362175, 641330324, 642854117, 212883516, 337874956, 913610201, 519256267, 617189990, 979845590, 63258922, 803629268, 903376767, 741564646, 109689142, 928663428, 26304111, 464039784, 410381781, 458037366, 153065117, 229454854, 573531528, 22025851, 751323774, 172569541, 420485529, 662898764, 97952645, 682156554, 964219953, 164396834, 196608774, 550941761, 939096635, 5595671, 945819150, 601219060, 120895320, 220433737, 582245488, 373112511, 930899441, 796692406, 388050432, 468529597, 581321720, 970821313, 782364856, 504663116, 121797561, 738682416, 692912336, 100115111, 952427749, 971436316, 492916765, 32770663, 732855395, 686561832, 157073175, 589552039, 845092955, 715461328, 612053455, 470563790, 94230660, 609908077, 900831433, 481053795, 681448784, 276359455, 47099521, 528093896, 727568067, 396437597, 877656698, 140024573, 896926670, 88006388, 666298201, 151838532, 2033748, 973324745, 110800056, 556600124, 645760244, 267441251, 422538960, 537711253, 957675873, 349779706, 798698292, 584433957, 156465950, 738708536, 550165857, 873940927, 118694024, 973012534, 256205146, 427547417, 887471560, 341036540, 9208558, 288934787, 333404585, 98357914, 118442527, 727299405, 846528301, 630314507, 98050244, 760308536, 967371008, 317970053, 836470719, 394194162, 662605384, 243892023, 503884319, 134918108, 203217364, 809675514, 66601684, 97114772, 670707391, 851093923, 445306183, 157007255, 137706639, 51874766, 9809288, 836573986, 336147778, 909833791, 522625770, 838020734, 467934858, 377725922, 745883066, 131239622, 757752772, 922920780, 193307292, 517953129, 801318804, 226474747, 269116853, 736749125, 441583472, 712146988, 685049199, 78119779, 164730875, 36005626, 305438515, 526928065, 945133075, 546176363, 943268166, 265829440, 679987812, 967023789, 292593413, 609171096, 502200795, 665814214, 877986797, 589801753, 333795858, 223793822, 235448435, 775197237, 915495777, 723189118, 161171842, 284458039, 756369167, 244348660, 122961602, 77066766, 431018476, 751710128, 93539935, 449093294, 993242411, 257619570, 418869751, 254725444, 825550535, 951282500, 222153520, 627202437, 875136225, 484941958, 606180924, 541677836, 539919200, 144890482, 543473800, 872283146, 672339343, 741884423, 532207743, 205957539, 101238918, 206822200, 206632778, 37217643, 593170436, 930477122, 822987279, 296056734, 883517457, 894679798, 217587536, 418943025, 316432521, 197388955, 910994248, 35491135, 817526725, 616506906, 282153566, 282280791, 149859963, 920344477, 169520238, 392541959, 459318395, 165725395, 489155428, 824192995, 594134078, 621206309, 524794560, 458113747, 816858049, 693641553, 764559560, 9431971, 955789856, 235586888, 409390605, 593408282, 888938179, 199200181, 786567341, 16168104, 518033012, 654953780, 391266117, 73514264, 253014739, 869306528, 10510685, 698656125, 65052317, 145576308, 196278790, 682487181, 771434702, 189870854, 407975577, 560486089, 413436509, 450397455, 460244393, 337998650, 332755560, 168200870, 347410448, 575146860, 346155195, 498568497, 620525262, 654249163, 981733908, 715020440, 161822169, 266879256, 301822116, 963810867, 201446273, 746620437, 608509347, 112438487, 820848191, 342520165, 237476236, 54951198, 821673979, 91876169, 52474540, 156321410, 302102009, 401354676, 865493891, 200927574, 114156900, 885637563, 534388200, 929428249, 136876894, 138575823, 878638396, 662501500, 618481625, 409405863, 405671081, 999189126, 936786431, 870497169, 107619032, 816050077, 940488768, 658333857, 965928108, 919875319, 649693911, 557885370, 505364267, 337609574, 24054125, 427882916, 235671981, 753538156, 96897412, 403111963, 62648200, 307827137, 260416097, 359700360, 353915650, 403412080, 903996490, 190394454, 117016851, 416552970, 555384808, 981423960, 179648810, 900219112, 855489246, 438029458, 304423879, 819282344, 814153105, 806928920, 503320427, 962934195, 714169196, 971770969, 919932591, 901019470, 427236479, 725070563, 886136187, 100873028, 938076539, 378221931, 965294338, 676286922, 179460046, 809548938, 84116570, 571957521, 505328100, 575991326, 938761141, 739617991, 32116666, 339449102, 755562453, 536477136, 428955686, 285029089, 608820846, 601632137, 585123334, 734265820, 275686238, 599819255, 177423985, 570998061, 843022682, 46197596, 751938049, 558791334, 401257299, 732591099, 620431785, 422106706, 940569562, 907639482, 31918973, 684976168, 919769499, 906832728, 629706579, 5997595, 558421320, 354740192, 846629863, 279217733, 904927141, 721592106, 480642131, 864266943, 10363155, 92889442, 888533585, 132239001, 359963054, 936595993, 805479966, 558933530, 171439484, 328379250, 216351890, 262227900, 669060313, 760898455, 216656030, 199691858, 807478091, 829257860, 576112661, 581201850, 847703443, 542764930, 163633088, 886922893, 521650120, 559782044, 896631854, 653997783, 247697422, 441578618, 698773048, 655025152, 89209255, 762715264, 792242005, 461633275, 527815311, 903630576, 647806830, 580480762, 867917277, 248389159, 621043481, 10280582, 15205142, 171378898, 579730760, 808231349, 821974455, 285993711, 829643233, 550141721, 469875199, 282498818, 678635126, 409538803, 608697256, 761061975, 275920, 151529951, 835714924, 637341464, 941908749, 932741412, 874815790, 291156686, 823515369, 662740572, 642989393, 234643365, 771932630, 209507701, 95551246, 392531924, 378897692, 963870317, 771717701, 560572965, 539365844, 57495080, 424541204, 1387998, 757659636, 161022548, 135539696, 603921405, 321438152, 518033910, 407329945, 860449205, 548810091, 517350564, 348160599, 939355261, 568696443, 797090710, 86182254, 214652160, 155388732, 530768237, 780186328, 988131572, 240600933, 213993042, 649001169, 74006774, 163822237, 538446340, 172837764, 996299010, 219609558, 513383176, 207339863, 657566528, 821005453, 798157684, 492787788, 35910368, 673828729, 152397120, 809715620, 924249074, 895451593, 497922846, 601730919, 523493322, 981316619, 688187212, 297344226, 313504134, 642505665, 757240812, 246782730, 961185890, 377787235, 972116499, 323673564, 577160537, 691007405, 865987875, 126391307, 43578183, 152613914, 29904767, 196543498, 985184084, 79718155, 387601429, 659136098, 607955437, 623590482, 871824502, 433540188, 289370567, 758267797, 534176456, 469460523, 581379132, 218856341, 6014557, 715612596, 166356319, 207590615, 51010290, 876276788, 360195180, 493755702, 768620145, 526075515, 988212109, 142726848, 497074768, 645637277, 973752686, 812506307, 151225277, 23675143, 633391966, 517068035, 46441398, 485634209, 441194298, 18800507, 861260214, 828895960, 333128812, 994424408, 473955171, 820017131, 432481509, 901739721, 689324600, 842986424, 802190135, 41447207, 59573252, 478217273, 846052567, 761976075, 218942333, 511105652, 142407174, 774646236, 637614523, 567480767, 497466427, 750729873, 540603479, 530437559, 584988874, 660103741, 54402571, 666039128, 816876089, 776739440, 317934038, 740793766, 789212107, 214733437, 687019066, 558878137, 855190716, 939200870, 684194903, 890025384, 116443472, 413137034, 851155627, 470948631, 573641262, 678761998, 241440140, 656359724, 294333156, 830424185, 853120203, 298105605, 939921781, 265531098, 23261188, 589689140, 696819440, 805351308, 810115053, 571556129, 549052546, 131385622, 449344866, 142678118, 54874669, 640037201, 215237806, 687638983, 603448636, 849615256, 686651923, 362917935, 813083314, 696494932, 658447348, 602576869, 117130957, 403640422, 238515790, 388807260, 148608790, 520525435, 593176871, 75585276, 563471824, 935397756, 900252782, 385952433, 273199043, 576278613, 834030346, 761976397, 364271165, 233910377, 649887106, 242802337, 510365782, 567292527, 974802654, 645992901, 918698423, 554554102, 185921804, 875850432, 321758812, 845410025, 173081883, 290270340, 955087799, 915214995, 883653151, 541719090, 465931216, 677385356, 230394276, 691454722, 541976669, 498909634, 969729317, 439973921, 908645556, 502113407, 783538314, 837494078, 309298839, 682397433, 441549997, 657530622, 839152811, 220499618, 139132741, 303832054, 483475412, 421549441, 541456843, 32556178, 384615327, 878831984, 487451696, 475697578, 783738654, 29882584, 849888506, 503913852, 798176312, 460050124, 642040796, 741899064, 368924735, 462641121, 11618581, 924308383, 786162408, 916427386, 450615234, 263080252, 732241820, 817550435, 540271628, 855309529, 368197354, 554525522, 658529597, 42743878, 880381714, 709207460, 820503126, 952737217, 994504528, 631526188, 924178415, 603978253, 907182509, 742516580, 9029989, 273210494, 57439265, 805701560, 460993834, 351672013, 183726833, 112797993, 147801124, 762554217, 683347526, 884048629, 902257288, 973159532, 725663790, 251232490, 579136773, 516612720, 661113235, 244220398, 200272805, 975925524, 495914531, 340209729, 290956268, 320347736, 427677733, 371315730, 706073974, 545021887, 196056365, 474617462, 381639767, 96958229, 805088621, 807198576, 300812239, 712538117, 826406837, 895589803, 797330133, 757972312, 524591877, 683951452, 351620379, 24965350, 962598, 870415403, 683863210, 522549079, 647397798, 67007187, 41352218, 186646074, 748563677, 206726951, 523757764, 111074272, 65517548, 100158056, 643015822, 748193878, 633078752, 131081096, 464316264, 191117430, 136804573, 130986316, 971229855, 638702394, 43887481, 427718754, 394398226, 955302646, 387252441, 526448692, 391872952, 732410214, 316337474, 760952251, 645405845, 633272948, 792546167, 264213722, 756363182, 724187245, 885830931, 170113188, 53479349, 588648703, 805129454, 153508046, 828025794, 605384453, 654857809, 49417258, 236308173, 162955022, 304937522, 797076919, 102322468, 443616652, 380946515, 913833011, 969259147, 16708547, 290635451, 489509990, 398703227, 933914002, 841431430, 151748760, 880897105, 405406233, 556285632, 12267923, 970664465, 416344822, 898070938, 353715705, 945894982, 300153580, 694507988, 10453644, 315942391, 437787218, 742395886, 479478984, 527607013, 756909401, 198530290, 866816354, 582383588, 481742002, 684420702, 561734360, 119140816, 77017878, 499943245, 953742300, 351354811, 416038421, 616083789, 435977331, 504262974, 565992779, 885876351, 919226024, 648769794, 71299482, 727912800, 689154533, 398971303, 649659910, 264870556, 938525313, 195028568, 317334537, 129113273, 291781852, 982764086, 260387291, 605784385, 786185674, 389708391, 32672301, 656037190, 632554104, 543238401, 293213932, 439325180, 646925131, 556078501, 5561402, 128555892, 314305561, 723907023, 425300405, 974612848, 583643465, 521145312, 806009129, 749797261, 686679576, 234855367, 982125126, 975307757, 611932369, 300997373, 110764665, 728474870, 52336390, 444665417, 709248549, 446953566, 786778156, 970383052, 186462569, 558112723, 519416166, 166466801, 885155827, 932109855, 51487355, 888887016, 418734039, 169651166, 858593753, 111622765, 58959651, 931413005, 437758200, 629419307, 519756640, 28621617, 589407215, 599281480, 941776902, 680072433, 562932108, 314507313, 816412373, 220953021, 439274884, 921341336, 300685323, 733382228, 909225422, 396303245, 45839793, 632057455, 961034942, 156697552, 719679307, 510940913, 56766032, 934400480, 130648860, 106124743, 505831032, 451729348, 59126825, 545594718, 939934495, 586970702, 214153924, 20804755, 440685261, 17789113, 21131656, 556073805, 126662665, 459475290, 742884887, 378653964, 610907683, 405210829, 40502148, 597987047, 442510065, 815441256, 492634522, 506692099, 775029365, 352272950, 296706824, 92038611, 798222032, 133573095, 454851374, 385886384, 580962629, 701013246, 179767459, 737054025, 146695011, 951491595, 351042545, 659560312, 433197950, 18767192, 653919448, 327768093, 556803382, 851126809, 897678750, 908969532, 113499832, 626023122, 381399481, 501711159, 298748806, 138231317, 817172165, 268910549, 337474783, 296624989, 812730139, 516760569, 290601586, 543565835, 161895936, 908705814, 227639620, 713047521, 750203765, 787335531, 157002566, 6417999, 864138854, 361351847, 299946194, 911581860, 203452657, 30861727, 628305270, 292723356, 857300755, 39990453, 760661953, 330547842, 887412036, 259801924, 42621544, 491737166, 437507721, 507694245, 850492602, 933645722, 337472147, 698301554, 727056641, 902798440, 386608475, 931874766, 318914320, 760069997, 918031191, 966272422, 556513246, 360225478, 857683102, 788864254, 575263723, 741096649, 736897155, 659118931, 903898527, 787322936, 894071064, 647174057, 463869941, 298373311, 400670612, 637696221, 964245186, 566837456, 27088404, 537852709, 188322921, 862233868, 195870616, 411627685, 241122315, 847372820, 623928678, 632129777, 133254032, 987906617, 958080238, 745293008, 673136545, 284682397, 400816552, 510879933, 584465553, 740802605, 412547323, 226269308, 823725662, 838936354, 30537476, 521849380, 266364177, 12645448, 344034892, 545687669, 689719921, 75123494, 307792318, 308853401, 524695167, 565988455, 937061022, 504034063, 410644571, 667429533, 319315809, 996162584, 230463138, 464376606, 692963156, 44771726, 845711275, 725573233, 40181327, 78763771, 274306497, 86547752, 52399331, 345558444, 783826968, 210412844, 568202428, 158843826, 608005318, 997663917, 268468142, 93842257, 441069692, 772380500, 273343456, 115714082, 378615492, 158841606, 334636018, 124736971, 836744154, 441395996, 268162148, 285477457, 225648839, 505520480, 714189279, 467771909, 987156303, 984940270, 465803572, 217718522, 590166370, 236940417, 574615618, 341130858, 905979747, 905699524, 304792846, 627432587, 180590247, 451837849, 54025721, 546452878, 134763626, 127133785, 816292396, 392450706, 601823961, 669869849, 912759319, 297595465, 260998469, 992091816, 809283320, 957476781, 424430589, 225339918, 522894387, 360698913, 961802806, 514868961, 727904424, 689750967, 82444652, 156602344, 245182824, 279532925, 191484541, 21657008, 541236305, 345173802, 532158773, 484792280, 735202865, 916636267, 916888952, 570403162, 836299017, 347938925, 947077612, 971054767, 396527853, 596142044, 191078159, 601925918, 738903631, 195984375, 966252007, 205656381, 801230, 641691806, 723534631, 357542719, 745365190, 98257773, 34336460, 997925459, 778202911, 593251680, 763553724, 279037279, 245900534, 308631579, 911711768, 341547786, 676510334, 385789837, 918896711, 177833062, 273576076, 878904284, 659137, 262247959, 527620050, 469609053, 515225568, 419394002, 700231218, 307599147, 93274196, 287039819, 628863771, 265297540, 953684183, 572513505, 810487710, 332868508, 818436744, 738858700, 408624833, 509891763, 415006155, 79222974, 299881167, 546307136, 678885689, 883247179, 172047658, 794565242, 279755761, 579397063, 329339282, 609038628, 567637238, 726457460, 826262450, 586466331, 574326336, 485575947, 78586381, 762731324, 866201786, 911092087, 365654262, 915364905, 879507056, 974697768, 435200699, 292066445, 430776970, 442367424, 23886550, 192206354, 463268041, 622452650, 719562152, 693738179, 557824113, 964036575, 825791753, 886542257, 53229884, 988149998, 361891653, 646343269, 100664835, 81461975, 447083539, 288419881, 705696647, 79217207, 542609316, 345563502, 664120464, 3883985, 439104768, 108706417, 481011208, 823632994, 643666644, 649122244, 132639301, 746735840, 420044476, 705186385, 89440790, 550629950, 860139332, 389790568, 371498534, 366315200, 451746564, 753069279, 97506919, 674656864, 48226130, 850780428, 643955640, 293265066, 180724502, 902569099, 706253897, 455037993, 664299863, 840518315, 716091614, 201841450, 629802917, 198178038, 81322293, 33865085, 747340193, 285637992, 117139759, 503814148, 554278823, 658793038, 600544411, 993681669, 150418054, 410427823, 80786427, 766186401, 62507504, 341063294, 249905300, 201357604, 546432728, 386639577, 586456774, 916411440, 996134562, 703870039, 407293409, 399957252, 859703390, 123306609, 865204276, 903901318, 207589780, 519569110, 215283195, 768862021, 707076805, 169141721, 214623806, 395960458, 300992670, 155181373, 826279857, 507113183, 771992784, 189535929, 9916586, 644240470, 149284505, 118143064, 585174853, 105715351, 912023848, 301105600, 352183707, 378289793, 445575039, 500762058, 101266553, 846822969, 655878955, 773778827, 887026832, 565957794, 386225898, 2331083, 701859101, 35416175, 173186280, 410749885, 801648957, 597437582, 265732827, 525336491, 316989267, 895329874, 672564930, 716821399, 634931361, 625596251, 738557839, 778931380, 494533644, 804108209, 366332334, 898023129, 493158748, 412397924, 642124934, 840278414, 253537524, 858348810, 835644389, 54986449, 94246971, 152215539, 7663164, 540537794, 542203928, 956884846, 681179506, 415704609, 940400249, 54842343, 623978651, 563514227, 13612854, 731019300, 566469799, 70834831, 146360942, 694108326, 515503915, 44376329, 352734173, 999738545, 629625322, 923629931, 411588392, 11917090, 10752218, 183412159, 332040002, 610802199, 186111417, 990191318, 580568812, 182974997, 941114547, 415251128, 155066410, 958675559, 374381730, 578155119, 289445470, 774667044, 971907319, 436340818, 947079211, 536199987, 685193976, 874528104, 305872803, 682594289, 154656831, 265054863, 103804138, 469451427, 143457579, 474774706, 540328283, 366715792, 719638880, 816688517, 588322811, 299052291, 203321282, 376004399, 803899840, 854592047, 940919246, 17572884, 340415078, 292861903, 905200792, 513470363, 698475580, 48540262, 258510771, 658133119, 530961780, 948774796, 827674122, 404162277, 599899408, 949396266, 351910733, 762725197, 323872672, 223625686, 526998994, 562132608, 799229741, 204434863, 524485484, 817868374, 465647025, 6247875, 255761765, 300850179, 374914190, 382009576, 428212841, 650180164, 269480173, 304107449, 886090329, 245491912, 167885754, 575134235, 912916654, 811929733, 951185954, 945641399, 648631970, 320767003, 558761892, 15317359, 404167296, 389063028, 522516940, 704562206, 885210028, 57619261, 283859795, 285301829, 235529066, 998270992, 114142564, 188133814, 859621854, 138128007, 986850946, 748936945, 202000371, 476469096, 181899344, 176779129, 385255251, 47970810, 164643418, 617506619, 115002505, 439962620, 938600906, 866934835, 156319153, 234528332, 526203453, 45291204, 463922277, 389396289, 824332251, 329791786, 369675826, 360790897, 35575497, 219357774, 312988193, 392803407, 417930237, 890064119, 393382880, 651885356, 715113970, 538965312, 631775057, 59428495, 545411269, 880957865, 891209720, 810650441, 925665767, 540594601, 326975687, 619963617, 503339974, 38357883, 24079497, 426246154, 183378019, 342883939, 898000358, 131194239, 249284990, 893893112, 404510820, 993328312, 234102472, 67750954, 841523619, 104884926, 218908630, 120209741, 760630199, 226817304, 13645098, 134882215, 772551551, 278969047, 472286166, 250670733, 986660304, 753546876, 190733201, 129394933, 777423369, 645813843, 580812170, 410426737, 948972591, 976434012, 124370506, 456645911, 850321238, 979636435, 695266885, 202533350, 42884773, 308868456, 347524352, 653738223, 220974887, 897532349, 754795629, 424761866, 956469914, 561139949, 316694867, 964973308, 896418436, 720105265, 371982458, 924839957, 527546258, 275222901, 494648241, 302474041, 137454014, 378735962, 927803194, 437625025, 785726726, 461507491, 723275773, 43068606, 190267177, 555376908, 637621740, 965727382, 199887494, 236955737, 422993932, 766812134, 159378588, 375944953, 407159445, 22991471, 265142038, 453921242, 245686098, 41722911, 882236545, 824552627, 387438312, 679034344, 697476589, 105101381, 578114181, 949267357, 201816077, 944578484, 533484081, 465201769, 896690611, 981105102, 971353440, 609743020, 931656021, 289710352, 905818837, 449674955, 355035676, 421871456, 61224445, 303315013, 143615232, 672924056, 235435142, 398149415, 53245814, 422246160, 713857394, 870241258, 331183866, 754109162, 109105974, 148637582, 791197291, 542076813, 460410898, 294093918, 208172214, 717318022, 780723940, 493027452, 176761528, 848954727, 597029086, 253607102, 888168655, 300230384, 357267752, 779210006, 843552203, 283071296, 192719520, 514757860, 65289483, 836088077, 680455139, 565494088, 107780077, 817880538, 708918465, 990294312, 998873193, 404366797, 920235729, 378887906, 323400115, 345644993, 639797650, 741051613, 952385960, 326073757, 105031001, 500836356, 82200536, 650990931, 804921412, 231794670, 249325796, 264543292, 14388989, 278354703, 815307437, 869223550, 432427346, 325991754, 333466863, 37228004, 816843977, 12945244, 494577615, 143648789, 763966138, 19627283, 728899617, 557780186, 54304618, 452551707, 231223757, 967672154, 821392482, 97920516, 56090157, 717910228, 222022724, 211281631, 552477333, 207377171, 937913519, 251763729, 52366399, 673908293, 320487489, 216727732, 396418046, 426267969, 432640184, 2653271, 15622630, 317012899, 573292140, 640392901, 340158485, 646232214, 56169021, 191771318, 623948080, 123896681, 694340870, 527328212, 116436312, 338670524, 680085690, 809505663, 282525935, 166375412, 774462809, 305690822, 926420608, 441520060, 229045194, 974545382, 24754030, 5224758, 129569187, 653434184, 580338969, 235218380, 228109433, 549146922, 815909941, 39072646, 212108939, 305484362, 400498410, 893478847, 77331557, 917031080, 17861031, 437650913, 889283705, 242212157, 126865088, 394464363, 203959967, 996593148, 834751994, 961652965, 690185030, 176114979, 359647849, 372879915, 499899610, 394971580, 271247343, 589941048, 949344656, 388169748, 818940472, 667545311, 668387866, 362042505, 653052205, 571731369, 959216509, 703264043, 967115605, 801752219, 661219914, 788728790, 889471410, 805579621, 711600635, 112556637, 820730050, 6267835, 954441351, 45071213, 82600005, 905145879, 425438110, 711137835, 82256155, 863965498, 218752920, 912555617, 492663173, 871990329, 713454536, 88988358, 221811623, 99539997, 759327150, 841678612, 452055332, 821650753, 535433354, 15609773, 127046468, 795323792, 130903729, 615621437, 927510082, 239149592, 877156066, 908856644, 877647273, 677671370, 815568130, 251466715, 800103858, 46795987, 153700688, 973586120, 715210728, 597548553, 412893283, 516218263, 746419285, 456012880, 22656739, 590596557, 798004071, 414492704, 826578212, 186170190, 651664295, 628063901, 413073374, 231340400, 644416003, 265576400, 219588600, 876210301, 617295161, 768704927, 747429840, 730354735, 698173479, 906935605, 825792321, 331942397, 564838587, 806409661, 859766013, 672910281, 682938632, 602788765, 503452415, 789778494, 810352414, 978335243, 888112450, 335478283, 400354949, 645815400, 164952373, 2571968, 350598854, 59326517, 382974582, 396895910, 801000606, 155516904, 993368470, 239682451, 599795583, 707112273, 108139698, 492102311, 71724967, 364245053, 920447503, 464759298, 742529312, 247982024, 662700348, 977117305, 400024210, 240620387, 233315284, 882613941, 644081882, 264344307, 716359201, 103765765, 854966207, 549994102, 542455236, 315566580, 187125059, 985853595, 166207850, 231428570, 635652625, 616229356, 385631727, 256990283, 942380173, 122119949, 98623276, 320343404, 156301386, 317567265, 398580214, 963735281, 850082950, 332282160, 804217200, 569292813, 603922127, 347295105, 999538708, 945024747, 517852971, 157597507, 688598862, 315327193, 699111545, 574239651, 670975359, 29988105, 854618360, 787043605, 171045982, 929524721, 462479791, 672556829, 129251745, 90524612, 345799674, 239976186, 946962485, 161690469, 357337667, 881707641, 796067517, 260985324, 361024691, 950541493, 327787180, 550501995, 238705492, 244822756, 170310991, 859732864, 847826085, 715343470, 650399173, 904574277, 861392497, 882643173, 988214029, 783748386, 763013069, 605363053, 18967937, 384405007, 574882188, 8860347, 80499174, 345223928, 733229358, 904778779, 120532910, 952481426, 642332744, 966062019, 101142106, 108559951, 778813728, 57941180, 798431188, 474110326, 77622833, 129451783, 563886929, 808694598, 802643396, 806476964, 408572770, 39717027, 102484704, 995337279, 799901792, 3092692, 46545971, 766147289, 45417025, 277214187, 939866332, 374288109, 585739201, 232432658, 885463702, 356051247, 816457458, 233664219, 56689412, 856920195, 205447800, 783991597, 969668490, 261979113, 599510116, 101943354, 517711310, 973984718, 789923479, 454799856, 783786584, 62397238, 941697530, 648441467, 192004448, 301429793, 407386075, 181495950, 264286795, 686963820, 776017512, 476391572, 916554106, 188686516, 202385142, 821376867, 920477329, 427599182, 815365673, 268371039, 323371494, 720212651, 314083316, 996896832, 52626469, 721845785, 693639981, 613797579, 367528838, 741866779, 780134562, 226559816, 633635811, 339699753, 908718352, 160438962, 150608957, 215533449, 557260448, 664743480, 48018347, 814252170, 957683678, 574116074, 158671302, 170865757, 633424640, 512779982, 509267255, 364359804, 989071842, 800460097, 851606352, 112827609, 329445167, 157827272, 359478064, 725648047, 305209188, 396547342, 970847299, 996871439, 76638207, 500387434, 33923947, 287536042, 830556757, 823159140, 996968606, 558866830, 64311354, 707555301, 276565626, 434796575, 769449179, 641811708, 204163050, 119302994, 923012622, 512515490, 866948868, 687291924, 496262418, 975115316, 680502282, 475707894, 784478850, 412999801, 250774295, 850709128, 789363108, 816112923, 658711368, 444594349, 588539094, 860162463, 260573369, 91711942, 604200697, 594721932, 738875563, 100947810, 395270511, 78631999, 75451850, 326362590, 334525755, 764922430, 761549662, 925457720, 247208724, 507970946, 365156187, 265959220, 705180584, 27795404, 181582548, 17863210, 805091580, 138504137, 527123307, 733404215, 331430165, 472485462, 474389200, 10423622, 817378233, 476341743, 401877017, 73133871, 682221893, 62842211, 527932421, 79071841, 248442225, 934661340, 761555222, 394608623, 630807701, 641475931, 332836804, 444445179, 112287607, 244468199, 659380189, 467249972, 708287552, 793925919, 948948521, 743088537, 747277728, 93305465, 38043285, 640098260, 129103908, 55920126, 26389492, 114563377, 476824684, 741384233, 662101199, 239612311, 214222064, 135253043, 525170312, 123862203, 814575804, 582435000, 954101234, 52701603, 486049485, 11001233, 334563191, 872446331, 180290544, 103391935, 47748363, 761506310, 728338232, 165364139, 292675948, 670813918, 221265899, 961511229, 576788276, 590121062, 339024118, 61541115, 909007252, 827588583, 681543023, 68120380, 925169984, 859583599, 697561211, 915879384, 196153172, 671408779, 155677789, 498069886, 367237965, 239158505, 692983284, 255116178, 180310209, 528558814, 464310167, 903926430, 670102579, 864080485, 34873848, 913485056, 134225604, 96844918, 499895023, 639957410, 990277178, 998384442, 953368080, 849432453, 783512480, 532323231, 940408639, 68213667, 578688444, 694816398, 144828793, 795192202, 445140350, 701620092, 595620297, 541733034, 81504989, 458608696, 766796389, 483215342, 126851327, 120646329, 715464952, 441402650, 65528015, 147509525, 699937747, 853204687, 437275977, 280117981, 160327337, 529470387, 25329278, 75439052, 288183883, 302776284, 287285621, 103419506, 349527721, 774655525, 756453403, 307720117, 9888220, 223962457, 822022684, 972040796, 788025077, 498497933, 86141063, 212829098, 114978072, 746631830, 670947230, 743091193, 464393998, 666483577, 376269674, 9310072, 665288795, 387705442, 876096417, 311315291, 822389481, 918973584, 622972535, 160382364, 802388142, 694974229, 461681494, 792409633, 545547505, 271288272, 772465586, 879279785, 583607680, 945504156, 430245811, 128460867, 640027682, 727619104, 938958103, 470273780, 232700631, 139269472, 34768139, 44757395, 770560175, 657032322, 278088081, 799399765, 17935408, 967352203, 481644816, 909586473, 648534525, 700914668, 269107792, 101417720, 484126550, 124624771, 401205571, 501103821, 139012402, 352480046, 375294413, 77495817, 874225305, 238668546, 514629284, 842691237, 864058537, 831979388, 745611032, 778222789, 991292334, 773838258, 622541173, 67562755, 929105207, 354751176, 644521248, 706940094, 914249641, 506762456, 981360284, 868822515, 65207406, 443820808, 343234524, 720482144, 159224811, 215845299, 471128011, 651344093, 158501917, 406199307, 703452409, 282061084, 175914983, 561326571, 343890361, 656677094, 516764153, 414569026, 352329876, 715584331, 517742834, 464312039, 38607916, 243827233, 639465228, 984083317, 759043595, 5946183, 926814233, 725465495, 637855659, 903287880, 686097736, 796375449, 819815108, 604996598, 338188859, 621069803, 586911049, 478967110, 803668524, 767377777, 332992652, 390361677, 101568530, 113998580, 424136307, 821662924, 463398704, 717063511, 925018824, 434148133, 525590222, 424933256, 120972523, 666072751, 459475572, 522246252, 367641555, 791528949, 898640422, 768184380, 436987269, 451640885, 991405264, 489547808, 696298834, 586537371, 884409029, 106017153, 683460575, 34878000, 232326793, 876280554, 744861020, 3985791, 258290133, 556759814, 764985232, 58506583, 44372724, 618718367, 598223440, 685130146, 289526212, 987049197, 616107649, 29690263, 980815206, 649409812, 796515012, 124602251, 491919341, 793399028, 438929508, 42945574, 121671526, 624872110, 132477325, 775135746, 55092805, 504671452, 716066845, 439281340, 742485317, 897090697, 218382695, 562493582, 995009326, 480414093, 644788518, 174912391, 520439214, 759439499, 143624332, 774605795, 759242801, 100794661, 390240645, 393755211, 453545887, 938964280, 509277755, 58210391, 818115084, 680321081, 653901968, 143580477, 423851115, 235539669, 27850330, 679790133, 794043704, 83640223, 249363479, 278723681, 386093447, 742793870, 437968782, 770533571, 970896170, 255010090, 197469818, 255262296, 563116183, 592601057, 440110211, 845100221, 414546249, 301357122, 361489770, 330736944, 907485447, 461643609, 773648663, 240390158, 320343361, 505216086, 623472075, 213903487, 135576473, 40064991, 411788655, 1840920, 141988426, 239184305, 32171950, 877582261, 693569957, 574812381, 747702512, 162004029, 513801210, 281481536, 984163443, 376646581, 716292304, 830209373, 560190838, 60201774, 293996917, 939046840, 595429467, 609323560, 27889427, 687591204, 327332319, 213290287, 968566753, 766037849, 738180048, 346781069, 714937594, 537035054, 49190817, 60776400, 320484106, 671452356, 377600580, 712151507, 905379591, 492788347, 31573529, 119034970, 47416382, 499986805, 997092057, 883218518, 986707384, 20544527, 297214768, 377905509, 605798079, 330328375, 587761498, 855147112, 802527385, 866188078, 603342272, 261590046, 451189930, 920718896, 389941613, 47978595, 930365485, 278274609, 727367952, 362972705, 434532496, 975139096, 819440494, 851939091, 520902423, 740993011, 268447267, 16572673, 92568091, 523657350, 712628477, 343327702, 63763484, 526644663, 609642160, 623247421, 986505224, 44859868, 617748735, 543155181, 290540618, 158569856, 138097237, 983851632, 323254860, 800180817, 265306314, 654193962, 777340464, 525953159, 391292030, 132562161, 158724389, 766151825, 912593671, 596524675, 220560875, 457076674, 136839981, 587610652, 744121821, 610841916, 698847196, 688641873, 908167489, 232087827, 760766069, 692780101, 796199665, 389839498, 122994260, 64583394, 374287718, 474570840, 604062880, 915040253, 101737723, 507387950, 360394224, 698270905, 543050867, 819159047, 203147654, 493870317, 748913588, 599930227, 372712669, 522948573, 720506937, 730338447, 251188613, 571088941, 336083838, 997563751, 350012953, 102967365, 607677745, 772418688, 599355590, 747049199, 147254690, 23398461, 708085425, 39726296, 666981245, 916182700, 554978629, 589921092, 623043532, 701823916, 828669212, 298697593, 430564600, 804270238, 180549926, 339796670, 317333108, 727816220, 658214179, 704460522, 873274802, 573195641, 279685352, 228609784, 284540614, 24794261, 220871590, 318165848, 43923040, 131765909, 790692182, 119420782, 256259197, 176291728, 936750992, 275777831, 586153463, 177356492, 618480833, 496064602, 309159897, 712958258, 220447198, 815906771, 276485881, 201112005, 379984956, 964653969, 436953670, 573736887, 956698655, 515241013, 23598280, 974957640, 396585973, 245951847, 162885129, 119813119, 871832009, 848877978, 770089916, 412222790, 248759344, 260135954, 771341080, 65770711, 202333739, 818832646, 500934545, 865556165, 904574689, 566045979, 723961023, 697983691, 424231845, 522542529, 908799095, 388926147, 422767056, 420288606, 645543548, 529698396, 441934947, 188390918, 814388254, 571322036, 719072867, 532954014, 136178789, 316508755, 107025088, 206235333, 346187147, 721577569, 149384247, 746371584, 366990611, 634343881, 336777425, 806792587, 277637295, 445753852, 749130066, 542437897, 372775183, 588813946, 696425666, 712930085, 401006790, 849858720, 16741050, 159346677, 715804592, 459654301, 652721672, 866832161, 899987651, 994362497, 939296900, 614055810, 518436286, 562235685, 490644635, 425839736, 133165913, 269527754, 538656181, 153453535, 199257143, 904907592, 198076157, 325513885, 233634466, 838949124, 330433635, 401876385, 433476665, 485457076, 815449173, 294230227, 971868852, 881093963, 879257292, 906308177, 16868812, 583203212, 621878430, 919168097, 4171572, 278484289, 76005862, 598710051, 604738363, 467428534, 905420374, 138571148, 648426182, 565451868, 898042014, 900155151, 436258856, 733440131, 647360130, 516509261, 844041547, 964858698, 115966133, 723782806, 203219400, 324265305, 834193866, 3753234, 44567009, 591958194, 40855317, 140470340, 611674389, 547493519, 458966953, 863530455, 957239824, 166816802, 717833013, 695488197, 538519075, 939638212, 46985762, 217138490, 994426032, 573027255, 199240003, 219521587, 491404946, 795965051, 647739785, 593484406, 645774475, 998861399, 316603956, 334015970, 156199065, 277881785, 367343564, 322759866, 536888885, 484449998, 512859659, 449267770, 414937317, 572548284, 932492888, 119750936, 87402336, 460108315, 98358516, 329787285, 872810014, 39548256, 928455132, 669531029, 296563472, 388158807, 497357565, 247981374, 855784929, 124109759, 448979424, 92063689, 818576108, 726976171, 302380837, 587855237, 150338427, 494610526, 676629107, 116445892, 149880076, 941071333, 140138890, 660891586, 692993529, 855232946, 724205835, 228833801, 717426666, 625756850, 725235400, 761917260, 985087981, 832005982, 249626997, 404386898, 766900415, 695809069, 173072397, 238674466, 966300197, 74778372, 586824489, 52134791, 444683370, 68701770, 518987833, 442179004, 489260191, 295751636, 400186764, 436436748, 922116400, 279199037, 37350129, 476283466, 677019002, 840465529, 317710899, 364679938, 609561085, 934781644, 180927013, 478325528, 1518195, 354925266, 157804922, 967881002, 110404971, 978283605, 504583276, 788884194, 352409587, 439874432, 86108595, 894858182, 831555984, 633262196, 361608458, 603787844, 894401864, 67588347, 955282098, 321232596, 831961803, 811739214, 822291342, 235189709, 355571521, 774167165, 110554900, 634495756, 441048726, 683852900, 467536908, 757820551, 450364546, 359943670, 541292725, 616730170, 364215171, 194950245, 905539426, 32467052, 974753387, 173867455, 680770155, 538710134, 336165126, 691180968, 532497703, 851480805, 45552032, 660243735, 262173003, 852367623, 820411122, 247064282, 226022657, 468945962, 957224612, 911234628, 833445905, 583465831, 803315496, 933144749, 63963348, 482357191, 901245675, 142302739, 78936835, 10282609, 949064088, 697598818, 948059324, 447894080, 130103384, 190515121, 357342639, 796622031, 903531182, 263271238, 139605615, 8975606, 370197896, 214190428, 309856587, 739768377, 560994496, 840530545, 450318864, 403497898, 683678295, 500122575, 830513135, 16906061, 792583592, 282385304, 732124527, 790791423, 780286521, 67811702, 424617995, 41699355, 340241987, 549401840, 977558284, 140092780, 664009357, 649349092, 296244631, 980925766, 4507653, 325119630, 579717303, 16442617, 356659753, 678360892, 434144571, 869330975, 739834043, 15984418, 710733955, 965542634, 234127305, 978021652, 791785593, 323371510, 828211232, 239850107, 657997213, 999955106, 233794004, 362023631, 492544452, 92993003, 839241655, 159559090, 630738083, 657448605, 163147658, 612116259, 953518362, 505609295, 240673666, 917551, 156779495, 699301213, 557163852, 303347976, 609314130, 799264734, 535404560, 70436457, 104014611, 339085468, 834223318, 152417817, 515908724, 905142610, 157245258, 364290395, 113683839, 602228989, 47108946, 287901710, 260578798, 198370257, 36941070, 786264236, 125698838, 622882204, 918232106, 156631231, 288060772, 337527565, 130180166, 298889466, 15526979, 94608468, 914744510, 554422860, 667677542, 964945962, 794759785, 913242365, 148174576, 705412895, 7469369, 349004594, 503101429, 673630858, 271386839, 66634622, 760954883, 831793829, 399926876, 120005257, 41584947, 550115943, 780432201, 509670095, 682938837, 276156646, 123189029, 722304837, 258990834, 367334992, 7809574, 769182511, 802162627, 835323110, 963319302, 9536898, 963191189, 934708460, 66366999, 674289951, 43334554, 331249112, 791847234, 882819144, 407526595, 709617560, 682465646, 61906845, 533053742, 645217138, 940058194, 701580798, 116861062, 931802628, 548177941, 512037742, 447740029, 23120555, 656664651, 503212915, 80708922, 594503441, 753650372, 892828694, 78637642, 690532243, 315608658, 852051723, 790981844, 251796526, 44015398, 936785177, 737818343, 142810275, 599858505, 173834924, 865953771, 22860977, 743030618, 846066600, 205241179, 486878240, 765925414, 177020716, 97769569, 388644524, 172022383, 405411417, 172779253, 314674339, 988150960, 95342994, 601863105, 813551331, 563602503, 313915571, 971067927, 964474094, 703291048, 249803535, 471813462, 766968689, 189545469, 577903652, 792433140, 571398208, 757398464, 230016505, 181228708, 336750987, 383514763, 975664416, 731319303, 361210060, 623363688, 816329962, 312049955, 764936676, 440212440, 798866617, 876280366, 589528732, 49259251, 599395189, 388823444, 84937098, 331574513, 763715993, 341547656, 226998564, 636359056, 245482826, 567673362, 406168126, 611268057, 707476641, 152751992, 799798111, 153745931, 47931840, 665262714, 297991184, 451203387, 25739880, 967458497, 441282375, 817078939, 176602863, 61032732, 966123974, 643193415, 473346963, 663064272, 269356877, 16264986, 712721472, 189423555, 741395021, 345536170, 556341549, 213250633, 168887751, 625915700, 531098881, 597953140, 396592901, 114263738, 17603131, 125718555, 823387910, 879650370, 773644914, 301485393, 9255607, 267844422, 924540687, 758964745, 136745738, 460960341, 280907009, 364725039, 550542214, 300625915, 614786911, 21864651, 141138137, 199889826, 327036908, 946316711, 602837947, 612045339, 894883655, 430681861, 961056738, 176838223, 813208160, 568948954, 555118245, 367823104, 816901031, 151750003, 432291188, 996760941, 876712217, 170167389, 305787121, 484379667, 31203598, 389197464, 834246950, 635627380, 883768169, 176287609, 960208862, 836850880, 802307066, 318798308, 765181229, 694087892, 727581990, 436205868, 716519107, 811919628, 211009811, 994395838, 940320236, 900061348, 226062442, 135144726, 481425955, 500770664, 797581090, 624060705, 728925509, 293753323, 530564638, 460259890, 247801027, 468449272, 94555702, 670051292, 394570720, 627483323, 926972208, 537153924, 167938980, 356381102, 43020379, 212787393, 509625299, 88004907, 684819221, 125995679, 389294933, 659084922, 863185842, 311081699, 355530842, 571398790, 939225259, 102835229, 342198592, 211798715, 963926783, 486126396, 657612504, 974424231, 891219130, 132450478, 891889762, 229254918, 401064160, 927342323, 626089605, 33672693, 122795846, 123017501, 227343229, 746153554, 14691446, 614721354, 629619102, 73736575, 746881672, 540698963, 240739736, 361740480, 130496714, 896380772, 405951301, 497450401, 733900756, 916069404, 607541405, 135190654, 955258701, 988310199, 304200761, 561922221, 954205796, 14589448, 193982789, 316678428, 817157497, 113149294, 785778732, 63006515, 712975977, 129239741, 155378047, 136274311, 401595275, 877464406, 79188634, 417703405, 200962664, 429290488, 217431189, 599223542, 196357188, 824617184, 56016053, 735173634, 822378671, 363675394, 73943985, 982088714, 887477663, 793720830, 252910209, 351829095, 257583443, 432778492, 168047138, 516911784, 242643183, 322610230, 560830925, 286837463, 753895107, 601381501, 403315308, 575927677, 158808236, 959297723, 337469814, 584870237, 97375506, 871254657, 203099646, 229377847, 37503469, 248579459, 664934909, 76372313, 26266727, 554086901, 211050772, 874997163, 738982657, 528661525, 212409332, 683114083, 30075946, 922275571, 937389792, 304239250, 518009237, 486552091, 654790295, 139261818, 651194208, 946069977, 549874863, 791281080, 104539570, 493866648, 86886377, 631311987, 433480457, 78337724, 137913852, 770257433, 447216236, 528068994, 866287991, 946627154, 793872290, 911816135, 785613854, 548735092, 732204616, 257626418, 954284101, 660379743, 981753142, 291626088, 491361573, 137584635, 996874037, 562080907, 655509140, 765790272, 542990370, 752481068, 959427753, 71429333, 856484891, 697743668, 951641032, 923595919, 372191575, 61193218, 949450805, 349344555, 982358099, 233871679, 528214939, 278880838, 935615313, 866972277, 819626310, 824571952, 187060639, 323811002, 359304041, 962144767, 591619810, 525770940, 56782568, 562521658, 766010183, 945101001, 3105574, 448144283, 168205974, 671452312, 243617941, 91010033, 871622698, 961028825, 699310254, 117214327, 255112656, 338727512, 70939057, 982342803, 363773571, 826893518, 851029416, 812095542, 617915439, 343283119, 446557594, 239537801, 663605454, 937539164, 32386612, 40489029, 42359935, 783260727, 416378698, 439983523, 325651296, 897193724, 723241247, 340874773, 126683829, 990991720, 80575175, 369276313, 134838803, 875993561, 348205566, 789298596, 608944316, 75963077, 914472982, 990354423, 429164543, 995928990, 806552268, 886459879, 989765902, 519830138, 517914654, 401859944, 995122110, 192217950, 931601391, 766297398, 17415710, 544700302, 998939883, 307767652, 491752022, 46452668, 72130753, 419432348, 778682122, 402985843, 921668700, 610848334, 633693961, 724118613, 45128055, 141188815, 950906411, 434595489, 126462542, 242240845, 796306039, 191738063, 124158342, 654686099, 132117609, 503500865, 484236541, 690573439, 649362674, 664985262, 198900202, 410232902, 16602332, 61752711, 340826712, 538675354, 888598561, 949947703, 959626481, 355320143, 87882594, 51968756, 616953324, 671905395, 69664352, 918901303, 915892455, 779473729, 787640228, 517456106, 374062765, 3973408, 571611894, 355411599, 229663280, 474707955, 804569187, 281658393, 163479671, 486825489, 457435052, 108763306, 999081945, 905573109, 57304786, 783441733, 61119711, 206470905, 61069370, 276534535, 332936764, 701988125, 987468924, 292327689, 541819726, 291659987, 201967426, 591821046, 54882261, 741730089, 719505095, 442102332, 131677792, 302682221, 44393504, 846381341, 829048839, 91731486, 947652617, 400352444, 624135589, 497452928, 336611373, 472680380, 6684090, 743645320, 14733718, 817001123, 179771299, 315948267, 537244051, 350582584, 379135433, 789078578, 37934467, 156733318, 136687934, 535746813, 282532590, 460513783, 11476664, 142834166, 758776889, 94274345, 483321682, 527157344, 912625437, 852369692, 157756480, 710812809, 556900405, 403099718, 866247828, 580852893, 231393537, 86643448, 292669082, 2204641, 939341007, 78011798, 348279340, 966862695, 974363417, 39611459, 126881678, 483561187, 828232988, 353047694, 600004479, 839082077, 14089812, 330327702, 82748855, 523564242, 395905186, 475123222, 804046972, 618836125, 647394688, 640251357, 542373591, 300476409, 100209169, 541348340, 357127864, 517162573, 461135812, 72820014, 381051787, 984155377, 964956747, 490389744, 864379793, 171892821, 715112494, 484836022, 397525841, 995383445, 543822151, 651695076, 836473629, 680383703, 144024885, 538879337, 542453554, 218592807, 480364913, 204919736, 18259777, 694125666, 857197825, 457668159, 211971700, 69967338, 637134983, 124128403, 196908319, 841238014, 658857655, 205175343, 226198970, 162770913, 706672349, 413741800, 118221375, 653893549, 72262490, 695247839, 343686447, 105088779, 107570769, 89601816, 501111576, 314319100, 380203093, 952540620, 485119682, 345483428, 76486395, 542624915, 729832951, 627251279, 649812672, 184370589, 157053730, 709243610, 382090244, 696180866, 369477824, 382886148, 102492061, 684707506, 224913340, 602411116, 75992739, 849710585, 420698557, 652410285, 531858883, 261754753, 99495572, 133925223, 323837033, 391164673, 525930473, 777121047, 333823768, 511726624, 196385938, 784197560, 113853560, 998640600, 829992063, 199930036, 774425380, 444723793, 951526354, 776389321, 535659766, 412105722, 10524815, 402792253, 32285143, 794067740, 192615598, 661290154, 986010545, 106345723, 559998806, 529041703, 16153211, 991771996, 546224422, 183546967, 631989071, 76728391, 329752254, 190922075, 724278510, 825539964, 157868048, 968537778, 399460434, 316119901, 7589001, 705524500, 665617375, 312358276, 4167642, 581343980, 985559612, 251936668, 596547703, 391237975, 819270468, 715628313, 20182694, 180497846, 129038628, 364873380, 118786773, 909982801, 45181090, 243557936, 554794750, 101652853, 757743797, 136751408, 38267970, 732787105, 405970048, 889514555, 849105395, 270925089, 317452428, 89450415, 687042506, 233277425, 880223040, 569755351, 749486077, 933694476, 301382664, 454115458, 728346916, 451703011, 556172336, 19877651, 316093171, 587432460, 133324154, 657523655, 42688361, 360546394, 449393501, 613995171, 571196314, 901614861, 639573878, 77349289, 495337193, 969649037, 202513603, 672157887, 830099718, 380877704, 866906967, 331917420, 792346620, 587938437, 971813366, 464190622, 411836621, 661063597, 41664394, 396145135, 623571044, 360190628, 288298808, 788615365, 415987607, 991387253, 764089727, 870838261, 957499768, 458466670, 886243004, 23236655, 235070105, 993474782, 716608890, 332312335, 47651154, 627739550, 196630730, 34357483, 437090054, 920400352, 209916681, 83692890, 915373880, 155293625, 701717274, 791079666, 125958123, 678841659, 129260492, 614710260, 683132155, 272453037, 87009237, 161053234, 673997536, 115263950, 696899241, 229399978, 519110957, 354494851, 928401183, 574646716, 405928257, 197522126, 152280690, 422911488, 722556945, 978071399, 223153711, 734911760, 855317065, 850806494, 653450782, 703387385, 179859401, 218285815, 975935480, 51699246, 972643318, 448171217, 524737602, 187446572, 643095967, 822893444, 3244738, 788736682, 296195666, 433751741, 749621964, 36578255, 102009509, 102346075, 608365056, 462817120, 797361667, 385120949, 866249428, 996470158, 464128233, 488550741, 38139929, 775973454, 951007359, 526667395, 84936915, 228089589, 913522884, 164419458, 89998516, 757331758, 780496655, 726369225, 522542858, 929716216, 145233876, 97580852, 615651945, 759103745, 549058746, 521193922, 80474726, 461761898, 423577581, 924830988, 722505011, 617983077, 352012729, 931925399, 947491719, 810683705, 398087889, 284729079, 596565119, 822816347, 169477434, 261069012, 925081604, 812554257, 4614103, 212781604, 899416497, 692841837, 138502477, 367831317, 466585230, 146488177, 549418549, 414837974, 193506514, 264078270, 497821924, 284952964, 896458706, 240588129, 649012523, 908525619, 235193810, 662645371, 346671281, 386310029, 10333935, 92783829, 603793292, 612187174, 590585231, 691354870, 227682782, 727278232, 96404369, 23108196, 401442155, 924309554, 832107815, 695518370, 530760390, 558513341, 626752508, 497566921, 734338102, 391654633, 82025233, 443282496, 746351896, 927125511, 887621946, 7099976, 317388026, 534047917, 854907790, 242091601, 77518062, 484874570, 96650354, 728051850, 571023907, 137283793, 49894467, 307397289, 284784507, 843563931, 131308276, 480377644, 991765825, 858942207, 414143483, 236283915, 189656577, 469626924, 702210312, 769495460, 365246419, 687314635, 3919326, 184754913, 757548221, 974531310, 645913701, 166576380, 551539449, 280665093, 714501947, 959193732, 827033456, 349423638, 491470314, 695714582, 91682111, 761809699, 893074731, 732336626, 353244705, 447939405, 891427051, 653759919, 926311454, 165398748, 318839593, 295160414, 237473949, 334247876, 3368693, 537592643, 37290747, 178414447, 932380862, 356431196, 995307450, 187116104, 647215667, 896452907, 26634283, 137129499, 117646126, 501886784, 646217101, 336915030, 287664328, 434013680, 652480234, 432514153, 124735038, 411235136, 411602102, 84339813, 344963800, 618361110, 784957910, 456296136, 164846888, 408109854, 610709998, 824138484, 404395936, 505960314, 308662256, 178058161, 530381402, 782256076, 834051825, 70511527, 124993337, 201016071, 261978168, 127505817, 164207813, 930843312, 8864805, 610668302, 650768076, 826655106, 534240522, 413827035, 193505040, 791756432, 683244039, 633489186, 729781021, 73969679, 748475854, 134587847, 373792415, 203902324, 714402797, 162745388, 667972331, 57677526, 527205477, 962720077, 49910284, 547404260, 590063411, 601449358, 348392510, 283993933, 482340092, 644816747, 205307872, 620182667, 82612071, 484982344, 465315110, 698674786, 191001272, 172332872, 946119198, 719883941, 954679383, 914089206, 621924391, 987992178, 952114660, 592922360, 847896893, 485755689, 292189976, 884357307, 449996710, 686277904, 222445846, 544466060, 697154170, 485618885, 506673506, 349005510, 280475048, 907002449, 733685565, 598711818, 689703065, 992194908, 800946863, 478816066, 275228496, 444963614, 387971074, 874601363, 693564572, 643615233, 978734140, 968542187, 800341368, 814136933, 881565014, 478692964, 690699046, 806122553, 143508475, 679207852, 749650333, 304818034, 448882871, 777974081, 19579243, 264876486, 920578942, 950309754, 935341997, 676844542, 461225682, 41039166, 238261992, 597633564, 834674170, 358676548, 959055401, 732568276, 654542242, 20886576, 519496588, 117791267, 519724196, 874417221, 153153161, 393284013, 335225632, 566479586, 898443012, 206119413, 382629689, 62018018, 814637685, 40642256, 838745092, 757079974, 410594683, 127843591, 747528947, 501601498, 323842962, 202118376, 859901510, 995140075, 70878082, 569089244, 647497519, 709827653, 160841915, 380767638, 209585268, 426407437, 996960854, 293342964, 986859880, 388975931, 640288197, 558981273, 785279935, 663065809, 425242604, 795857052, 817885230, 292326438, 439421781, 858767853, 359024043, 563315405, 881886041, 301706441, 665668137, 940406452, 859341175, 610272442, 988650038, 467674564, 595733307, 224670151, 546273675, 26855759, 293117550, 755855066, 659210578, 677409260, 365752139, 809881287, 269353758, 286784911, 94065130, 493661609, 329558920, 349492429, 575328637, 813189738, 446960085, 745811114, 911348686, 304420614, 883891146, 459884635, 717520353, 157581584, 893771752, 251763802, 569248030, 64560590, 841536292, 744184394, 214586398, 546578262, 388198097, 587950015, 533409866, 832476678, 732092697, 345651724, 934405230, 700869871, 227490145, 351601293, 220154561, 355146024, 638611050, 332163544, 598086612, 805555069, 308733286, 151212896, 724226706, 332307750, 632979741, 842031676, 826395351, 503014816, 689491256, 427548429, 517796805, 626740601, 549773314, 657144462, 776728514, 764310372, 86473424, 537220599, 494007367, 952922867, 300207480, 769883832, 594495319, 165371850, 582182364, 50817791, 83306084, 262064341, 657041262, 403164028, 667547153, 296843495, 989872619, 195911261, 822427183, 966387374, 86068283, 685952323, 122923837, 722238175, 207943805, 289831281, 468111011, 934563545, 294361498, 540496994, 300966420, 56863071, 249927961, 942472782, 585938403, 7550201, 998829925, 358705423, 502385911, 106008357, 133251927, 836416589, 760120313, 206600065, 233229888, 671063507, 260482150, 560711250, 552127083, 575309032, 28873685, 993475875, 939597352, 848547442, 668233622, 790236833, 426699271, 214699599, 311868287, 974771997, 610414580, 983426633, 520768249, 295929332, 96489795, 781174831, 834902819, 127769013, 420478876, 515093905, 102108112, 747268945, 471146833, 501871135, 109054646, 229514168, 680680818, 53742012, 330075762, 458391294, 109300480, 136097253, 82363800, 596361267, 716975875, 792709599, 284220338, 876492052, 562320674, 375011490, 975550889, 445421180, 570337013, 447942541, 916875439, 623408060, 967009496, 125973745, 904021417, 101400346, 41086313, 47760826, 384081405, 668409662, 636733251, 824394392, 886393798, 598016813, 634779868, 312226553, 599717101, 701938853, 286039907, 255040303, 897272683, 523021538, 478540489, 143133073, 198588456, 136458618, 565492037, 950177248, 879068675, 846816074, 814365134, 759629505, 489661196, 935337346, 739541683, 217104154, 304422600, 330846519, 404897768, 124788629, 438335780, 372733946, 622362010, 395722696, 277100056, 908389256, 587561364, 9120751, 390929465, 385976108, 354010431, 944067176, 457015217, 855407385, 79851074, 881296732, 32616096, 629278910, 178662048, 576920680, 826079949, 470894116, 307504127, 893470540, 681329870, 907129424, 958307123, 425586214, 90016476, 287448101, 378762820, 103881578, 850744220, 414306572, 844415325, 993662674, 761368124, 426984726, 572143243, 549591193, 318531571, 732320949, 2550383, 604623267, 695921080, 272584175, 796846803, 167103546, 808785349, 272854035, 435066421, 273936919, 841230246, 380707346, 905040170, 68986745, 937094675, 696789447, 61670119, 729952644, 804280480, 151087797, 44834415, 314140645, 83933423, 871617204, 494749763, 484033978, 408035606, 645739075, 200185583, 878339273, 893449765, 943642483, 141808578, 550737281, 536644345, 495556184, 717343906, 626744374, 12873616, 133256100, 905167126, 584401550, 226617881, 403354227, 495162591, 202373221, 765960397, 646064048, 511682168, 813590852, 354720084, 502385164, 975681217, 36809955, 690333094, 775216187, 93976746, 440092607, 659446562, 409522990, 808426515, 711555858, 690028556, 301523309, 606509329, 880370827, 264064729, 638588496, 561106769, 539539705, 68273130, 561642729, 204204146, 342532754, 881873860, 45494865, 803713598, 824282473, 109062202, 48901013, 350413683, 519689542, 27230520, 885157499, 740267704, 440003074, 178568044, 649203155, 568132633, 776749234, 311489380, 988771246, 295944279, 881001290, 243548761, 961360298, 513082165, 463834896, 47343951, 947723658, 732081244, 410180203, 453750081, 207668803, 396718734, 186576408, 793940987, 545761893, 701746466, 422081927, 696284557, 919060774, 769676310, 203780016, 964554065, 303003429, 907651319, 386023160, 328757097, 258018694, 590624301, 986883448, 357939197, 108094554, 870218120, 950293969, 641049262, 319228397, 556217524, 452151101, 179377562, 624214720, 810736880, 557190247, 961863974, 291938490, 551923228, 959582628, 953015935, 881058724, 168471452, 34308296, 951451402, 240488108, 780874430, 672763304, 423475882, 815369973, 608616037, 434612635, 470469841, 559528420, 719190777, 569827245, 3093322, 138693159, 568075277, 333456204, 536005810, 666811610, 524145355, 723600196, 863088555, 809297265, 406650672, 533372275, 565168285, 143005290, 269012459, 326934265, 650641532, 948825463, 556401059, 792020380, 933092247, 117536478, 317599907, 741081791, 727165800, 839107842, 364438638, 829863287, 178330998, 675672730, 572780192, 232485594, 929274198, 456335362, 726893119, 648087573, 320322869, 681637551, 214349514, 472740291, 368217359, 845009454, 81824153, 44802543, 565280555, 895820097, 99224231, 444333746, 17019458, 268946923, 306356391, 36885376, 164839576, 422870420, 970738560, 289910913, 583938862, 31105828, 314499091, 448169787, 639773253, 655091467, 363430765, 508577760, 840370578, 200837514, 757601657, 905220815, 411142994, 817760242, 653318826, 589525873, 608418728, 351278933, 660987020, 201948623, 663565659, 636424702, 925676477, 107852100, 428590574, 103432586, 142886970, 975697402, 721371312, 306056268, 956463846, 973137093, 429260356, 400504401, 466788511, 449935707, 736416123, 937302262, 740939118, 351101897, 442814562, 871336807, 223454476, 522289154, 288575316, 491856821, 116716045, 690450781, 710265214, 805555057, 30695099, 327118577, 946790109, 23801545, 516939602, 289053761, 315952644, 579924388, 507451226, 485271375, 381160949, 125085623, 366845689, 367961032, 314286400, 710639442, 772332801, 156424426, 196563861, 217078283, 835411446, 305768609, 479720936, 910052636, 386955650, 578881846, 579975167, 447364654, 779181628, 564858733, 309766278, 485744376, 421078332, 521987945, 615156887, 781026289, 92429730, 138574141, 449658112, 447782815, 410325473, 449454747, 410542993, 721606781, 386286463, 138891979, 963589377, 67798348, 200785858, 450096149, 481571739, 997440884, 616763473, 605170678, 536271435, 364434420, 730277887, 423681603, 575760961, 316533524, 471777021, 819379953, 230399789, 602243365, 35168062, 857552405, 498741578, 849831630, 285094141, 453611263, 517662171, 104553693, 112848628, 763510840, 69700215, 796583614, 496401580, 738570522, 111281736, 666663244, 966107780, 529799487, 836614864, 991460244, 448160557, 673186247, 188117604, 579200066, 898988180, 182799197, 705021899, 374829172, 862397411, 508941550, 33057913, 379365272, 629300732, 214852830, 861531346, 234320376, 495332656, 908699004, 865425404, 487576686, 351557153, 975078062, 296833432, 317315575, 911334946, 381866544, 189994260, 225730768, 819815457, 538192089, 120165512, 906265237, 321498216, 543420486, 265800709, 425558313, 136248317, 510914129, 655789575, 960311333, 115842068, 146826991, 639007988, 682959798, 456704563, 534923945, 164467396, 888478019, 560263635, 185088361, 332296898, 907662766, 886416673, 369288158, 929574506, 813777697, 143197094, 952097362, 948794342, 901334215, 769180508, 185221305, 190282909, 315911023, 264706841, 399405196, 820887064, 463835797, 97957513, 994508459, 899349581, 164236578, 487480966, 368224623, 28195118, 710330739, 782320160, 950825070, 581524481, 373604699, 873274205, 933246634, 675540482, 260334961, 147118615, 654212760, 767466312, 809154662, 641838354, 595367271, 95043372, 49415084, 434090342, 326791678, 68888478, 802943805, 651114374, 971653756, 567166855, 287884429, 974974010, 251224807, 67113001, 396407606, 571146518, 361484193, 328539510, 839027653, 845177145, 8332719, 838894910, 932115662, 690130443, 434934833, 319468133, 14579893, 925892121, 387319695, 607300412, 433967443, 813974270, 434708273, 923666831, 582254836, 926459825, 109220202, 77279955, 59015171, 522417252, 600919074, 435881944, 808178255, 200613516, 871192494, 643897012, 740673518, 96925861, 703474867, 659939285, 471741859, 970469309, 838907402, 578462505, 148046674, 365406397, 186942896, 316067127, 995138640, 583710600, 91331578, 682346031, 764937409, 921964627, 999803777, 549901181, 598970434, 952477033, 846752769, 342865707, 227543503, 75104690, 516266858, 330043862, 200661826, 950026861, 254515287, 889662386, 131919565, 140252660, 793616894, 673318794, 830575032, 802585082, 89263333, 931150230, 716298391, 913299131, 672998708, 252121437, 720163236, 715365533, 134552863, 566747588, 465280837, 97160520, 286664879, 50885957, 93255921, 829652026, 922808483, 71762040, 771192630, 950485243, 620473233, 820488000, 410318915, 726910497, 171236219, 335735227, 369329752, 795083476, 233879096, 783926937, 787809538, 570394899, 35803497, 281661937, 393644357, 704641735, 899552446, 641603036, 329993282, 34395715, 302436143, 313785598, 900708697, 238214231, 341015835, 656634284, 272841938, 986527187, 679651864, 743802200, 522399802, 649526359, 778746782, 711901280, 358135339, 835216708, 595644307, 643972110, 256724220, 629755932, 439403386, 849244372, 935014405, 595362979, 681101458, 348032087, 412151156, 476197860, 941418198, 480527561, 732798488, 411596139, 569377035, 316526543, 430484122, 31458121, 982521790, 257979111, 650626085, 125631046, 45259174, 791819035, 688105733, 43186172, 879520579, 745437709, 49344707, 535310755, 128374497, 750165313, 989471934, 763655658, 963502965, 365239995, 659668974, 432744401, 219004256, 43236286, 256031574, 81825185, 965878819, 953914867, 919192735, 307812706, 270374152, 836693242, 273132579, 476428619, 161527230, 884745904, 216548943, 301671825, 313454843, 865239510, 529421372, 585951615, 293698417, 930256360, 851314588, 863413307, 286404893, 2195353, 406707616, 438492860, 241408057, 673194214, 477470020, 97492770, 53160464, 105741053, 286728737, 209400637, 650587391, 493200524, 310904043, 738031373, 648494613, 292539673, 879949298, 803609009, 647990295, 874918943, 425921595, 828327756, 905057456, 888898003, 118638112, 386843617, 13560673, 369022955, 194597462, 413863356, 339987505, 506063175, 869674636, 563703689, 467989264, 648664898, 389494728, 184216693, 74673977, 247886161, 391154808, 800354188, 516700975, 538857298, 97633066, 248701197, 289601955, 35251393, 974685921, 207159971, 501582870, 61807787, 566157909, 432800064, 448307408, 139361647, 752172671, 260454641, 702127328, 181766908, 344793957, 406440404, 524778184, 807160011, 487815169, 360173465, 316750904, 246989913, 543431742, 437548979, 152239743, 142456595, 200081211, 147156887, 716577358, 543820724, 543995554, 628148362, 446477120, 893161310, 908942070, 411620182, 43379379, 588034715, 477681310, 579464194, 854716748, 385113602, 409362063, 923031946, 218933921, 469735073, 670024505, 816737592, 326193181, 190524165, 863149, 117144540, 111901126, 557720020, 617224125, 271355123, 984505640, 801074305, 428333343, 996365498, 163736019, 895202464, 606872499, 937100559, 817006480, 168105221, 137539855, 249072398, 876760488, 868254596, 220377526, 301538193, 696807489, 466351245, 88966740, 789894853, 113510571, 304534003, 659538364, 189074911, 828161504, 275137812, 158894257, 14870659, 516670153, 494237227, 548735363, 804981085, 751808980, 700022914, 194823141, 481679169, 580229680, 609577186, 93390946, 753139005, 483368685, 456310706, 967857121, 990786111, 947189681, 173608133, 920043537, 596128894, 339457160, 385426189, 812705344, 56821674, 584027226, 48672937, 751117248, 378031097, 275978775, 548607537, 710101458, 807517477, 433576063, 515380877, 401507827, 460679472, 516482149, 481994007, 676503591, 573678202, 12833184, 515325902, 243665496, 770918772, 273502283, 907047066, 872170911, 997988283, 218847474, 549585759, 241992357, 394586036, 437115919, 298060111, 952332026, 772648171, 755049140, 470031581, 400064459, 485462874, 820936561, 441247717, 331877710, 8600657, 429446960, 921527735, 953879151, 598622070, 436810402, 497814807, 193307898, 6960779, 398875528, 194976754, 375487213, 851622051, 527781725, 925175918, 73188435, 264346529, 905885440, 514638895, 655842709, 385602498, 713956651, 687527141, 766167365, 100342716, 817571941, 284508702, 452855414, 267739299, 562938360, 370791624, 982965789, 517477936, 455461382, 668890931, 731815597, 653744437, 103174471, 207483581, 223785494, 620512886, 883714826, 607533706, 458598890, 447153731, 578770851, 991082816, 409825844, 947313072, 611863680, 641619051, 915527944, 219868687, 884844371, 320282756, 935910090, 723334054, 866420765, 432661210, 858640720, 399012870, 274594490, 619427457, 287114183, 526113103, 117079936, 953176940, 348204958, 330039038, 96649300, 964255651, 76396483, 560049300, 171742833, 753359230, 955409568, 701138205, 106394086, 283109605, 659966034, 203469473, 322067923, 705270679, 527955533, 644508649, 453243061, 334781304, 67161693, 740239736, 845276576, 606254028, 968633413, 270153230, 15609874, 556896113, 473048001, 952026023, 155024247, 8998372, 808878561, 90299280, 256184723, 528969810, 135127449, 294752131, 519091287, 597347636, 484178318, 983115861, 986523245, 982391115, 211087471, 718673428, 280193826, 961685921, 478746454, 622959905, 488452369, 215431500, 475298644, 672808055, 812220649, 129881590, 938263230, 225324862, 551452162, 642621178, 252563814, 343155482, 718791305, 150998375, 522990841, 987476746, 973450520, 13780350, 536636163, 566202945, 469358025, 269010485, 590742601, 490368447, 398268500, 754484287, 680270667, 738144905, 546979769, 891441127, 839618226, 676486701, 534327077, 18410771, 712745100, 439665032, 973998715, 251758473, 107240016, 369514425, 898227701, 913356569, 49993499, 863673055, 102964880, 500497333, 932180724, 739260615, 851220709, 516718684, 884688895, 881837804, 864898721, 898198439, 157092668, 149569962, 84749678, 299212506, 628166833, 347804602, 77971286, 947183907, 954511938, 705491353, 702275009, 245800435, 131769945, 843468954, 286112306, 474536317, 759420360, 506838542, 904281379, 36147631, 48374304, 590613169, 4567540, 846581514, 4218417, 866975656, 227946538, 285289124, 802272596, 569796677, 599551926, 551648808, 401867835, 123877689, 437131181, 756819363, 978030744, 680406928, 439707356, 256161616, 933029007, 460897678, 302662979, 993174909, 752302344, 892740959, 140295730, 259872679, 372022669, 294737191, 379296980, 914479296, 699616799, 678879908, 735798660, 282637198, 892675904, 586857450, 159511658, 259683720, 828864364, 836588071, 915672883, 916968245, 989264680, 383917973, 97063267, 284314145, 777674784, 158017025, 835459049, 377613286, 639961404, 455844893, 367144039, 196173019, 237302493, 797545388, 250759510, 743579771, 686599720, 667024929, 981399332, 60613076, 508281481, 87331087, 322048384, 388881812, 150142705, 903371857, 483270733, 350856070, 276655865, 884448113, 118717917, 556313968, 31167998, 537573530, 181298663, 632802073, 864915106, 67724929, 596666269, 475598371, 623835548, 44787751, 157746260, 223777373, 164632886, 609599525, 341031194, 85033113, 580474066, 13208933, 965498017, 130163801, 647994691, 292203283, 925434943, 102702379, 946728937, 39826707, 574698030, 658433269, 397800637, 704419188, 931450316, 411767838, 366351065, 646336687, 176344362, 191679281, 75556938, 58973368, 3218152, 618316253, 250821515, 313406860, 532623839, 841011772, 223309583, 556155174, 870059877, 243933433, 175211890, 934707688, 780761246, 11359400, 371564365, 673150414, 351175999, 291115749, 38891848, 301962843, 411486232, 516877756, 723851104, 73965722, 974497020, 492180986, 342706112, 753093367, 158220204, 979586405, 577233074, 194508705, 806173734, 748368, 520958330, 244197405, 330882986, 298730479, 661182063, 888944717, 143437490, 967367041, 364803711, 455190360, 690696999, 737051690, 573843117, 358260951, 142176931, 559743527, 318271254, 237800975, 215724646, 857838583, 746012189, 137791770, 458472384, 649699269, 622531836, 406789211, 201621307, 253319713, 275520458, 279276021, 271704284, 125048181, 609944319, 953334436, 195441216, 793939906, 772366633, 28840526, 829116352, 510321088, 64670846, 879689322, 987774, 433238720, 774260444, 425137601, 339840412, 189797030, 729406428, 270570642, 592171879, 804379631, 52413932, 165881688, 617957463, 646944415, 568341675, 108071671, 611919703, 93147523, 451987707, 1607942, 992413706, 655301052, 453804636, 213026408, 118394261, 567118201, 457240833, 222928598, 238578817, 93228069, 421164362, 237482704, 878961040, 41261614, 600236901, 992672382, 611345648, 242618495, 307349352, 597451722, 91873110, 878404944, 615331857, 252748995, 658530937, 412382651, 335465809, 158197678, 877133891, 419957196, 264480433, 529121317, 532657139, 757662623, 658296384, 130633535, 620318965, 758820720, 543594273, 910068187, 133603693, 689223716, 47935942, 103805811, 364895168, 7562600, 326456562, 307799389, 762806623, 101400368, 401428519, 33138792, 295226394, 905759641, 718353656, 976602785, 442118145, 196667033, 873226571, 317904901, 375909392, 893472771, 480996636, 321989373, 531861785, 875300465, 426070983, 547884832, 877846695, 176508789, 865774296, 865649775, 322445565, 648870647, 367921534, 612629197, 589614120, 345054597, 422925088, 651649273, 330361455, 64133505, 174957910, 685448984, 693065435, 80483864, 976471519, 887069055, 994721324, 863001281, 447365519, 771713149, 711921631, 877279512, 22100553, 314695277, 251097133, 169331996, 364409454, 764751124, 250763534, 516226905, 143962397, 624828994, 822801528, 693915417, 478568026, 928241645, 610057491, 141124962, 264059137, 256758089, 101794811, 579419161, 539358054, 345440035, 477733296, 821100707, 638936437, 253148016, 601578049, 394307354, 151651720, 582916995, 393777146, 13646419, 432700597, 993428107, 875316212, 806514254, 936213550, 905679371, 940320401, 829245842, 932730924, 362980932, 618279821, 82340475, 561171162, 22141237, 830173107, 392075026, 941214025, 440381232, 52377502, 119904829, 157354681, 689822577, 849699016, 661567741, 257137000, 923981802, 454285513, 38927215, 181680345, 454437758, 87713768, 280150329, 970107625, 831695693, 484159362, 463304544, 496944089, 123472960, 831604000, 71739042, 153229273, 106297005, 37142690, 963662759, 247071638, 632700227, 966905844, 457127990, 485852764, 113476979, 318276105, 355236508, 76451547, 704898948, 575087092, 163128955, 107548452, 234744201, 243555040, 903182697, 846150516, 483788672, 662660595, 397736851, 49347019, 470250498, 75727487, 182554961, 806928334, 943238213, 285518270, 481445966, 318078051, 950980460, 718422139, 140108202, 794006176, 245252443, 465136378, 680181836, 477929664, 316579067, 854371076, 321414839, 17700762, 16408800, 691948880, 412827872, 224778154, 474907217, 271227144, 839429554, 166326684, 318904342, 607894826, 128918784, 504844822, 263628223, 798306374, 982777833, 544934058, 109100343, 308419483, 65305083, 747110157, 241876360, 138328203, 64527473, 996606751, 466036867, 105341835, 607336865, 610397061, 536506380, 916148715, 712623038, 317971675, 66178585, 975227262, 971884423, 260482022, 929041781, 172666494, 128979462, 952743659, 546369495, 968666262, 190772628, 592305700, 36608007, 252862205, 403710188, 830991188, 247670400, 540238133, 478799614, 121339973, 487504370, 853917198, 33756563, 361211150, 955317848, 982057642, 929985389, 719821202, 966852668, 854518984, 44072911, 113099323, 489122972, 564888685, 782228354, 316941843, 967587793, 176094958, 972061015, 286448925, 878827714, 601165015, 79012603, 608884782, 568444368, 370316526, 403886558, 47473938, 233041528, 290603434, 884774420, 190565495, 891557315, 18294026, 324295655, 717088952, 145845242, 184190531, 258272085, 518258612, 665321656, 505198860, 789908896, 725918546, 831706171, 49662920, 332359094, 399589219, 995901752, 400797353, 279087721, 736899154, 242414293, 188850743, 967181857, 3566564, 869418591, 385828372, 559465968, 384074028, 217187641, 754213738, 301996045, 901926994, 368159305, 86644611, 481383651, 545833600, 634039019, 165021260, 680472418, 823426663, 804756391, 483951822, 883605273, 671903498, 406103228, 340279543, 291165199, 328358375, 730959671, 981669752, 783065460, 835459869, 625918879, 451260650, 560399166, 978114792, 96547748, 397797194, 336190163, 692959665, 432027731, 135333392, 369624994, 219280228, 781754273, 300980847, 327819310, 386250264, 349925829, 397786077, 23595725, 214821763, 930579782, 961827542, 417158549, 757115662, 475619185, 66143066, 223493609, 820039299, 229484430, 863784690, 280923827, 162130527, 905033864, 422369748, 644068477, 785057358, 885379637, 646477182, 418656779, 505056782, 727053873, 259226312, 972453671, 117645710, 382508016, 771973663, 968666011, 847467700, 913904976, 183329339, 450162823, 46566130, 699623814, 332717611, 429775125, 534492651, 962391879, 443231580, 258986803, 381592242, 425043963, 380220176, 767203673, 538467676, 586131243, 697520864, 7568165, 229823841, 902381948, 101302039, 685515168, 473475665, 201713009, 254193721, 123586217, 41439893, 965066407, 899403604, 996800382, 109383056, 158585220, 813868937, 65000896, 764458233, 197973089, 893565574, 370933566, 644033819, 853856107, 204819348, 676506848, 811855744, 194554913, 446421233, 842016569, 568974301, 72574602, 853763096, 785951003, 145650361, 128736890, 929902038, 957090421, 558068622, 606498352, 56944947, 16347504, 641463994, 623693696, 764936442, 206148511, 712168923, 57965818, 51072578, 30702425, 576003802, 889902327, 604780073, 662487020, 983447369, 743171873, 759313901, 50280522, 801558525, 947491471, 981984837, 241357782, 963287805, 435647602, 458131266, 373349702, 610583246, 699352491, 491475352, 417383272, 804799465, 236137423, 452141692, 969126621, 502606981, 584458011, 694353581, 329123065, 413968878, 370580720, 266740800, 688378977, 290283256, 901799705, 861701845, 609179885, 312462770, 150499657, 41495472, 681706504, 998810702, 960418947, 630022640, 204907115, 262648082, 959257353, 613662887, 272117135, 415292654, 41904193, 822169368, 273788879, 723468938, 756079640, 681147777, 909467445, 55303267, 566432645, 301657081, 890620444, 852725669, 272074481, 898442665, 358730533, 632984774, 669655580, 437799276, 442864874, 724657594, 81642203, 295212280, 704714265, 528250379, 468658748, 319485637, 289109633, 420826795, 802571131, 333089160, 9105168, 121804180, 277349377, 809611190, 637825551, 810155749, 781244279, 708121069, 74844781, 85845403, 174947523, 813995491, 554729, 487724406, 969261886, 910070813, 315810447, 575859816, 259540544, 339189421, 794153639, 725332850, 741959802, 874531680, 625018533, 807923706, 1016939, 814599856, 662249010, 422331290, 388845287, 45597134, 318055390, 520227459, 375860611, 279796235, 148019281, 954531613, 186203250, 154620612, 731086901, 331526642, 40212927, 517139381, 313868984, 622852872, 301699838, 959898776, 81775147, 716305797, 91445233, 231891111, 437569795, 650094342, 25865053, 252697830, 279844433, 865882161, 305677417, 972107840, 839714624, 756774902, 663867140, 236186007, 513125379, 813287956, 909221992, 996396975, 458162908, 478669916, 944980147, 229426540, 338406906, 116339799, 932287331, 598131187, 739367745, 998051224, 159257502, 197887194, 930433391, 250109854, 300534137, 387781246, 172780670, 995506495, 194850789, 13966488, 653151101, 529299935, 785822554, 376967092, 983891666, 910987948, 37473641, 750585466, 719968498, 952315449, 30248919, 915945047, 79331976, 6918658, 524430326, 307608427, 40322164, 828284607, 410477063, 491469487, 575433063, 901918558, 866377867, 694128078, 398492071, 662052770, 61475445, 13518324, 234815923, 936267218, 383138505, 472898789, 345311002, 474441895, 299912571, 298349142, 459152484, 798739868, 74894701, 601682776, 48847280, 262229010, 626968119, 280091036, 888899825, 848751558, 947289800, 493773485, 103011530, 193019276, 273733572, 211990864, 152009458, 895425003, 629915013, 848564795, 41479083, 595616871, 75526163, 127211841, 991549626, 136486090, 783914822, 19212538, 334961074, 389126353, 739634777, 286679433, 221771713, 353811064, 538694278, 349012859, 601934822, 319401303, 872350995, 948077345, 780690008, 63767061, 687514777, 262571454, 540191404, 427269317, 407805, 521770570, 238985751, 632981337, 191894833, 954183090, 626556382, 612561129, 486447371, 325705168, 211887440, 161272634, 863360122, 925808813, 907724102, 664364632, 621258355, 689738325, 970390749, 289107741, 968907607, 386664108, 324407786, 189214202, 94612769, 593540865, 818396722, 254777408, 66691030, 834792830, 966296331, 173098037, 303149574, 561165641, 661186855, 841073977, 667171481, 781289985, 299363357, 51022632, 202052501, 26016979, 578175746, 145430618, 652713007, 471261297, 772450324, 784999729, 577988244, 67890273, 741389201, 118465541, 6050095, 342625702, 919884813, 253709131, 406017492, 845663064, 642741056, 657956728, 163205371, 959937828, 700319548, 851518414, 600022558, 59707662, 900916714, 304155974, 186408548, 447687211, 38917455, 667434628, 827202270, 394995313, 887970090, 496729829, 913606802, 774537916, 243516441, 288139983, 648316709, 874569150, 12359921, 258576758, 10470075, 142644236, 751349131, 789374808, 583619371, 28855486, 755680848, 482495919, 858044358, 965621204, 463665465, 160139927, 254576513, 3137613, 682370755, 863651484, 254083707, 606659902, 124617064, 526697937, 415206917, 927615905, 345783120, 406155363, 88667915, 564652937, 452668074, 178281423, 648198353, 43755348, 619453515, 52059752, 597836585, 769189848, 612453815, 598885316, 225595299, 432050619, 86706456, 156089499, 780935774, 735331951, 464717825, 235545049, 904783686, 712028198, 260692842, 98425338, 708548297, 539306974, 183093098, 876238134, 273623239, 268052704, 402230585, 295585367, 136393737, 159430223, 838742875, 66136179, 865967320, 128902827, 393184743, 271261920, 847771598, 422915902, 309622271, 823500218, 750431417, 555225771, 535173550, 187718294, 540873787, 36188775, 627630638, 698226492, 771685991, 180591225, 253185367, 663333008, 934005090, 989720905, 397568532, 332281166, 323438160, 590369488, 701385518, 125043879, 100763482, 740685005, 174968061, 193406147, 782576920, 425146376, 57774011, 801434431, 259065302, 998444973, 531249774, 79513070, 460945026, 386023741, 308675594, 624033198, 288844530, 223862878, 767285952, 775848095, 760544423, 149206424, 653926693, 806088, 973654478, 356310954, 310683711, 552031652, 657320302, 502172167, 317078379, 912043267, 426454236, 1525211, 972505356, 123243739, 305733203, 302837337, 112216714, 478046820, 811350688, 346440555, 880333732, 88600295, 214354380, 752630263, 476239915, 369268847, 109018340, 937609199, 216510085, 70779970, 912585285, 555923233, 244378232, 580137846, 428237395, 131250989, 542770151, 528765499, 257549549, 279480697, 361350456, 569874965, 778742353, 131198130, 220391377, 890988791, 266179110, 757366602, 894525444, 632264883, 976996481, 34168160, 770666346, 14913825, 699198648, 145539675, 347831319, 387549936, 360171497, 704466824, 369032493, 525472286, 655311528, 13831945, 477525173, 72688342, 430823182, 399852477, 151427728, 90651225, 237114877, 738051275, 339214329, 882866547, 260578702, 52265072, 438937738, 465177540, 476887776, 685094257, 209749737, 597179396, 588413973, 151115073, 571344897, 193458025, 740492759, 982231666, 598757068, 335058294, 875262949, 972568489, 357178756, 909058372, 998165642, 95450196, 954093196, 507210548, 826485751, 507555160, 882023761, 946059965, 335671275, 57747441, 679491626, 260964931, 619028054, 765488126, 793672520, 265282067, 211080148, 228306876, 855969708, 97210537, 628871705, 458519333, 446815272, 940666410, 530840423, 275928775, 861687702, 516814285, 532619015, 176372071, 31622202, 69014999, 494778071, 518374110, 818922717, 335125010, 324754357, 249928610, 397269981, 957760055, 59590883, 980538640, 169766809, 478549851, 742793553, 272172360, 817652701, 378450331, 314452383, 212632586, 370032194, 862925085, 839775596, 401038312, 765882590, 25165547, 409081185, 758717854, 29323144, 802113406, 619335348, 670187597, 432992764, 842300893, 451190819, 543777190, 955899663, 167468838, 911305454, 943898810, 429047069, 870305674, 108945073, 375917020, 157236084, 269449257, 509246236, 623982958, 152174729, 214323077, 326196592, 160257757, 347196106, 427685579, 101980047, 148361038, 162482083, 397455571, 656528552, 337869993, 332644833, 951987822, 159756238, 911309883, 445389380, 53561727, 389885080, 892891025, 615089903, 397677586, 826739378, 597832725, 820872628, 92304719, 974260177, 188145987, 496908853, 652170816, 442522275, 135927893, 78123716, 184120078, 184137826, 933891864, 154815712, 976529142, 996029324, 364254469, 439608844, 813275602, 402508956, 93046189, 398679305, 185801436, 212295926, 439035545, 347505648, 983238079, 531951038, 891923807, 374326942, 15383427, 269669111, 253280873, 743917086, 24854336, 937583156, 413136149, 605154802, 676774715, 234441052, 377327301, 116490810, 324311745, 274836385, 459002617, 642516882, 551396111, 999882622, 68450921, 1175391, 993786840, 466454106, 632627337, 677853710, 46385419, 766606653, 554175716, 195409438, 800676227, 998397981, 603943619, 455388781, 796053487, 74531244, 750692148, 527969567, 15571312, 675420846, 547105516, 614303552, 867181126, 118961158, 254387999, 997958504, 141355567, 792788923, 195849658, 139015753, 186702814, 917327862, 657267424, 957504120, 791970733, 391916529, 104634974, 21408071, 882177415, 639306152, 85771927, 145946594, 502658797, 84541966, 6037049, 607214057, 892819474, 381942649, 567045503, 982239196, 536589177, 413343240, 646834247, 952516105, 815609737, 73110969, 32844520, 690559674, 485839152, 270935012, 837605968, 930228322, 648048461, 262494, 59563011, 155651427, 602871424, 271981151, 341302491, 393093646, 347279617, 780965491, 407384524, 371554884, 98929662, 461255312, 978259876, 480744698, 224461704, 435067194, 887615803, 567271624, 803306762, 665097394, 673323885, 836951559, 680647204, 682723396, 558406523, 947807862, 950256734, 674056879, 279729097, 839146595, 98739001, 556215231, 481665717, 693320682, 756390517, 243299690, 657060868, 884378811, 524717438, 452407484, 58830953, 300892817, 237906350, 195229497, 803119766, 655150059, 941488260, 358730238, 371764031, 832355827, 23839303, 207738227, 16373697, 182385232, 380362034, 512306434, 894095701, 567218130, 192638973, 197385856, 242273426, 422060930, 927336265, 882999313, 85163850, 90610765, 33516238, 776923674, 671945613, 767518373, 860734720, 513009892, 472622396, 819011033, 211774526, 855935661, 421296735, 54833051, 1416094, 509163150, 50750086, 339376333, 365461760, 591744996, 442439639, 587598543, 160213172, 34913210, 249568549, 914294680, 894468449, 837470852, 494512780, 560807828, 276349974, 260858355, 544586482, 624530253, 849676050, 35894795, 427983737, 634172670, 273198955, 461621948, 113624766, 205576139, 782246301, 757272230, 842899237, 905693435, 700009439, 591057257, 189436606, 641184817, 587002957, 463527400, 403404023, 402230310, 38604363, 262577276, 405489435, 357904488, 993262554, 865360593, 491408058, 876957195, 311669384, 136847160, 574403364, 180979520, 987273841, 222568585, 699944150, 21794238, 895981287, 680683489, 488202442, 136390356, 536222139, 65700491, 78705970, 554264708, 800700778, 877949733, 936619470, 591954633, 79930816, 232205499, 37931336, 179217025, 305784357, 196364163, 935032428, 552372894, 509841874, 711591431, 996630040, 642916, 198447071, 915387142, 385230643, 426677354, 179661606, 666228106, 281381972, 21429528, 2191402, 295070217, 607871566, 521848641, 275787847, 653311201, 648284498, 967871972, 903775523, 105354847, 569100761, 822251904, 275538852, 817375763, 572291096, 118333166, 608263793, 498534249, 919601492, 471522834, 259782980, 334129544, 456851834, 516704059, 471048481, 126884638, 30081818, 558935040, 583999555, 61163733, 951959983, 878291251, 499057382, 343314917, 994473755, 764749508, 83074152, 255800380, 838086053, 778110962, 998662202, 417771902, 827436248, 445301100, 271108584, 958805228, 913987415, 249598684, 555368814, 126805845, 311277480, 73260345, 925419810, 165617237, 667438706, 773770039, 337277232, 831108292, 454416114, 874855177, 441074449, 906486196, 782284609, 295082215, 190072540, 121569484, 496608056, 642677391, 512247467, 873809389, 786633911, 102873144, 741263564, 769060751, 627628656, 139637891, 741475920, 426381493, 762813552, 394760846, 593805238, 691291458, 513182619, 327390967, 816275818, 462583724, 421047168, 4215878, 21775094, 532928014, 349426192, 970410167, 188617352, 817169677, 688570103, 718024792, 282214936, 317892068, 114773345, 583410508, 739470781, 94259673, 222912358, 738351720, 539132037, 39110660, 313825975, 111631432, 930240694, 799716896, 37829409, 90700055, 765040251, 202940178, 31774394, 843145447, 53574577, 613865045, 170916701, 740673169, 66242574, 447994721, 154332620, 241825115, 221628267, 42426927, 295021729, 187970787, 199337830, 511017251, 609990874, 187911787, 584799814, 306857594, 18098904, 642531198, 779530001, 122663809, 945498313, 358155409, 388933963, 280750065, 453524674, 361745865, 311474775, 21450966, 400540171, 945495115, 466756739, 334373940, 12551322, 831392833, 766253952, 69538398, 858018825, 449528783, 947166417, 49062715, 957112193, 428920544, 723426839, 505318870, 836263110, 861684657, 34751022, 548529387, 108983646, 251654221, 497438877, 378555567, 599603889, 686154590, 201411534, 273011910, 38224192, 778627463, 782893383, 661223512, 246845715, 621158987, 120250031, 38693343, 418418530, 265971666, 734449581, 465850256, 429076292, 552575684, 747114073, 655379359, 978748955, 344425978, 641850087, 878812392, 460399252, 504818791, 939041896, 530873458, 571966528, 947544044, 397643361, 889040140, 827855632, 107802721, 137555469, 375116253, 226267054, 361691180, 630946265, 295389486, 875708036, 321513361, 616054935, 161133240, 61648419, 725988549, 813232915, 652535669, 365046239, 897259434, 959336119, 328361321, 396973885, 71397766, 581117480, 489869662, 460992716, 917971209, 51184201, 690159198, 940767627, 973124740, 265477103, 56609201, 469731120, 967549345, 977409499, 30294318, 796423675, 70708268, 104452036, 121343816, 940465673, 625350932, 797652177, 109187462, 746373726, 705459831, 80487522, 855767497, 942139863, 568910441, 895048574, 700590502, 415404273, 252217289, 94055450, 874235040, 122183486, 968016460, 968614878, 828691592, 254812248, 523490646, 130727131, 459286199, 309967067, 833390190, 220402695, 511094645, 220300093, 268174725, 215845968, 488623676, 389256368, 138136913, 836426446, 275077522, 264633042, 858862295, 915566835, 214320683, 349513725, 86088675, 526247205, 1700558, 893993001, 841981939, 715256704, 140563385, 631019443, 698068815, 231899014, 111686518, 199655514, 540424465, 531214798, 267882778, 784866455, 799347117, 353588410, 971786551, 156430187, 565553809, 881876002, 331880225, 874832854, 511205301, 562763196, 923845265, 330271805, 60322815, 62502709, 122414205, 632820266, 405262634, 425725055, 896024188, 348400951, 470749323, 976671021, 824936190, 939001425, 701367300, 112163366, 933483820, 971535286, 283400354, 233196847, 403610942, 219204911, 71500414, 848345305, 352782827, 898523232, 91443117, 889609617, 565883503, 448977602, 118249615, 808569208, 625833554, 127672920, 784729794, 644993716, 810757642, 512950813, 519619492, 8568259, 887384931, 231353434, 922985111, 747386311, 809094756, 911512113, 759298643, 46077263, 929973819, 499857545, 691351502, 678348757, 536348909, 491359820, 351274326, 789957387, 409753268, 844615730, 91931982, 838875162, 257831421, 386366850, 494492965, 883904471, 388612395, 828568935, 521117244, 434355759, 78218608, 98904475, 91001285, 163101649, 774830410, 825536780, 473268970, 886616187, 44585408, 672761234, 531154845, 971312894, 42201937, 374104877, 217729653, 130610711, 781051513, 637073473, 164601516, 976702498, 79686152, 296832558, 510366757, 927991689, 385958478, 371563135, 786213492, 711428392, 210238491, 13745017, 217103950, 820921427, 217787485, 380017179, 347828973, 439541232, 503462259, 456307830, 416940005, 426211136, 326200475, 177568034, 967198783, 114296696, 957169224, 293349105, 747394558, 154211810, 62410548, 806143565, 52332520, 377130911, 977261652, 435871599, 407508034, 73674120, 139382365, 148706460, 879606220, 797879289, 156369444, 339462214, 523028992, 324632342, 464689503, 197567132, 58905185, 421193436, 796330951, 982358570, 310473646, 265066471, 287988234, 291864971, 315960951, 366067801, 506497255, 547385666, 971493023, 338560962, 122370536, 959160777, 357941253, 9434272, 830153306, 859341283, 937973251, 49370531, 521893201, 903786626, 790399646, 894276400, 903222513, 685799357, 358065184, 181291136, 774917506, 885888507, 224879640, 627205562, 825355570, 293006912, 360617824, 423386310, 722949994, 474239002, 587027227, 73018378, 527152439, 2364845, 300887166, 763586731, 539088422, 915295637, 778943620, 211892412, 261581172, 780254877, 73258932, 833103048, 807528799, 788659340, 745015038, 175249943, 567118538, 848857792, 15861337, 872461336, 554173529, 60780917, 903022017, 730173290, 911355463, 369478815, 135315569, 913642887, 561167237, 414861934, 838117083, 558130852, 888336283, 964857226, 670688658, 603097383, 822444638, 730055488, 890136457, 321344697, 594520233, 614676708, 684584794, 450172507, 759647440, 795300852, 496345923, 23434402, 171265437, 696471192, 484926459, 130474058, 886921116, 978962903, 75304233, 83144210, 632235419, 91052314, 750626304, 305613920, 552055828, 844058303, 638360532, 844024437, 725493496, 152620754, 388529120, 379227534, 537023216, 881387373, 51382411, 179635836, 213610630, 544049700, 986548874, 373327268, 740298135, 487360185, 356946053, 973810594, 575704981, 372815408, 837954179, 888163710, 859437700, 439957356, 379186882, 425572734, 17151186, 471190295, 807741660, 878693668, 530412915, 321590759, 568236824, 250190458, 955609897, 611008215, 92361195, 164029717, 73685446, 66523665, 506137498, 402586347, 818453749, 513730788, 425844930, 581093945, 186626107, 881906527, 572206979, 953820917, 218623244, 667593159, 730230499, 82022003, 276863138, 259288238, 871562639, 309774004, 901574227, 272803967, 986094813, 313719478, 563782200, 550321319, 974926430, 51565918, 680528207, 598928758, 954879289, 454367651, 89217175, 426272620, 528609468, 356339537, 882946011, 541155220, 910403347, 679182531, 789987651, 769268709, 545586281, 260932373, 953901399, 614243501, 265665124, 522158120, 93508886, 217809415, 373690731, 59394985, 322524431, 218070480, 348413551, 190872799, 795741345, 18304232, 30981280, 161186209, 93764158, 742293354, 231016397, 660996306, 879905982, 295603817, 803417050, 800257962, 645705994, 51662926, 489770883, 348800998, 162219632, 306283154, 993959005, 458172277, 292681888, 621100450, 55953959, 277770324, 768080358, 388918303, 508635529, 147204371, 653757323, 608212216, 488155246, 905442431, 269819737, 348135643, 802721705, 727538620, 838869694, 768846325, 72705567, 2917271, 156586064, 558767351, 46099501, 73129814, 201208153, 319867050, 668413395, 149807342, 167762847, 580923731, 51579738, 483011118, 729358604, 878049390, 35995329, 633140146, 961892000, 557871030, 178741044, 700471875, 679023190, 484157946, 698010337, 900991985, 109342881, 874920003, 238435832, 851197205, 315562463, 618815599, 107603440, 916956036, 740141927, 114643909, 568596525, 134475127, 449056364, 382120449, 979201285, 150289259, 170928417, 459364641, 385272422, 176618349, 901332432, 251464096, 606114608, 78948602, 675737703, 586291298, 318184509, 201557694, 627171010, 981175079, 942875884, 79112814, 11126652, 220746187, 860661751, 535105527, 285652218, 924014055, 886913577, 651521984, 487467879, 860854605, 208189453, 514330753, 282248253, 346498262, 899115750, 964797665, 80112349, 56718332, 241434680, 390615064, 15992928, 768775700, 771453997, 730314942, 187806076, 127859046, 579982129, 999035537, 284408078, 486947377, 265189729, 245302679, 582234386, 152215567, 93626834, 20140945, 253066060, 781417035, 722912618, 510676540, 700434291, 265335267, 80019467, 138137745, 786921628, 855442313, 545371378, 966986296, 43926316, 965220069, 834131258, 694586307, 955270213, 64571830, 428858967, 714250637, 875937365, 721103773, 743266500, 410974686, 841738982, 721718392, 192532226, 281722487, 980628386, 308122101, 346455837, 974901010, 871585719, 403486615, 288011484, 602675127, 502159124, 428156069, 161132354, 281841246, 108137019, 799048156, 181804317, 56058428, 760466481, 863672379, 570422177, 535651742, 940764013, 73742745, 46691152, 767431245, 75782565, 580992610, 235798661, 528362502, 361433951, 810916148, 503718636, 147124920, 784609103, 250773233, 358579612, 136893555, 290762904, 539894506, 356827242, 468478938, 234308605, 764451582, 414990687, 359103975, 607817419, 828868724, 625332183, 746125268, 847896215, 249649446, 738693481, 307223826, 900080935, 371915368, 19934399, 459081657, 122924506, 981916796, 779833178, 972858689, 666949399, 358396149, 985306500, 642696770, 702670415, 159745706, 907509139, 773432631, 38103458, 239809570, 851530440, 405843614, 251018626, 661928953, 926050372, 957056330, 959840395, 323285397, 924207971, 992726456, 138495836, 452156222, 67332393, 765743835, 111967099, 342543530, 40394068, 441185389, 838389071, 818485865, 627680886, 30537274, 955600892, 916053492, 27102407, 823045200, 826881383, 774023529, 250054422, 494135371, 695497413, 275728531, 222546046, 423641123, 422697817, 870331817, 129090800, 710165049, 314261885, 85657099, 278457417, 631018571, 527536213, 167710262, 297061627, 595658186, 906356203, 996739817, 774718967, 569092555, 917124190, 985872029, 37854163, 597885816, 76105975, 425232593, 114620617, 496361983, 845543834, 213834730, 772362164, 940157357, 457095306, 875201413, 949362426, 619157958, 983650259, 918155649, 414114875, 446099734, 229926358, 618805821, 681785499, 680434040, 303063948, 518379601, 23957944, 935436813, 400803950, 727262787, 855642325, 426244346, 244149962, 899581461, 416922029, 15130327, 954137168, 196215227, 216069713, 285011004, 716815089, 759246963, 141993273, 603497766, 689237214, 198417373, 630592492, 709464828, 387786543, 373690973, 388099666, 601225061, 242444525, 79697603, 850145602, 919992347, 473272416, 129208382, 669091583, 199905613, 165914039, 950787160, 456444556, 298768092, 891239943, 871414129, 873923941, 217453204, 934666286, 730565127, 748390764, 904593166, 671477325, 751173496, 31455102, 913359282, 563702548, 763312441, 636497600, 443242973, 407868989, 801959305, 357268029, 785182063, 776929735, 245163613, 53463168, 729059770, 844784893, 982897964, 916042548, 684234056, 750295903, 454213989, 958557996, 704123155, 124773408, 747789678, 624361752, 203383649, 266160873, 532074552, 866449339, 196304148, 695132716, 877603942, 125601734, 349087002, 164475724, 738651033, 673671540, 146685989, 336102161, 817918988, 759423881, 898490938, 267782873, 349207092, 409959242, 174903716, 875233705, 644587668, 107258446, 807970494, 575098468, 567864876, 814860164, 812145023, 73361276, 128302090, 582760503, 64362997, 293161538, 420446532, 753739370, 749024856, 440921868, 695372138, 530355028, 137157144, 299698708, 304762186, 266852379, 259997081, 335960596, 295651483, 75748580, 813995633, 624583780, 458780768, 704058007, 967918318, 976948501, 345235104, 580762717, 887268490, 621596015, 910128015, 501969879, 334591172, 56951730, 486417821, 879739185, 228912463, 507461977, 268337507, 822948650, 88344354, 292151959, 579711582, 645640875, 522205658, 69453717, 842341659, 839432720, 858159750, 962943188, 658785855, 791738287, 460820562, 442121645, 833144297, 915682199, 157243110, 698488400, 757297069, 969228484, 634692983, 662470068, 766095008, 99762503, 568209873, 873156079, 966679164, 274972511, 999935604, 421388279, 284330122, 364007550, 148652805, 690492643, 84045000, 393911307, 147335081, 55893709, 779866591, 513227205, 802840675, 345469386, 849948576, 67455147, 793223988, 440569200, 414141978, 192138225, 694196607, 809634686, 226721255, 6937929, 477953755, 320585254, 584216582, 381489894, 504128766, 142182045, 293374683, 75852730, 765165325, 173790671, 24148504, 381907510, 738301828, 77301592, 263544094, 600167459, 441423330, 472756510, 438669301, 700297566, 332243535, 838404631, 605435919, 297760252, 871143030, 760575336, 749352903, 283154789, 530354052, 597474318, 768482466, 457816017, 785962416, 512252352, 739598308, 761673790, 211464485, 364803929, 659785789, 216530272, 308039663, 72328488, 656539167, 515927222, 275505151, 476315414, 438508579, 262836591, 889507418, 21718498, 170484470, 422706660, 234801896, 252382185, 509700794, 56092078, 783411558, 471942916, 488673025, 306752017, 495392329, 933541945, 995722700, 81166867, 94300972, 416010790, 491799027, 486566568, 333195311, 788569734, 213384988, 628689339, 362965631, 209614483, 736342462, 61918932, 42407847, 387070428, 684670516, 708537529, 691427860, 972576235, 460882302, 135671169, 678579303, 526400524, 82332336, 228285408, 421089488, 530519348, 35126611, 799392197, 385903608, 165481988, 347953446, 923532436, 433558842, 37265955, 945262965, 587945162, 543777200, 384142225, 214670210, 234138698, 260372135, 11357265, 675280704, 888239589, 146709428, 727397867, 356139670, 296787824, 432853592, 214221713, 581773141, 689508395, 882785628, 897365028, 965669867, 618288713, 784103326, 987054639, 691301706, 280974678, 467670, 567202589, 657835403, 225668959, 231794114, 470934033, 463418767, 892930146, 488101996, 113206014, 532335697, 330093615, 833839900, 117267457, 140035313, 680525048, 668786912, 357856772, 713191217, 889032634, 715732963, 646389460, 776160849, 169670459, 991672330, 700603581, 608333509, 233284725, 322146922, 983995544, 856789200, 227702190, 170691724, 470785192, 56302081, 956479399, 695575446, 523382368, 161377338, 78306686, 384039744, 76977749, 876297715, 11932850, 643114007, 702849735, 260061758, 573509928, 283021639, 369423428, 153846276, 882015393, 109476902, 700993311, 428018306, 874542293, 945778675, 912017653, 471026903, 28636787, 711856860, 488240871, 303220911, 251221550, 819756752, 236214049, 326478346, 281787335, 203751404, 18215784, 778628237, 181827839, 833223129, 686511336, 889260557, 729991206, 594757393, 442206721, 273864083, 384515331, 498547703, 43893904, 369354027, 276435734, 638831430, 925423903, 169244447, 713571854, 299793714, 983123116, 6137572, 309244051, 947922421, 524362359, 937839278, 575359983, 232557369, 549173814, 605540478, 717738697, 573000968, 278461952, 779167530, 908713614, 254373222, 69042323, 446070331, 152604039, 211148618, 756713835, 225057605, 805558514, 384757371, 144290779, 130318371, 265027278, 455143480, 45266602, 775642009, 963732204, 654266367, 970497697, 115382794, 696780322, 398234479, 717278431, 39511188, 605472602, 383930491, 251295223, 953190711, 224443665, 129139683, 789728038, 34551920, 181054167, 440385937, 504523438, 110423967, 70296556, 560697036, 153648088, 63465732, 276720061, 561743072, 783292620, 433499438, 813231545, 217668702, 222015669, 799037663, 532469458, 67418169, 112908703, 979712956, 498170560, 889325879, 586355132, 545873908, 923848961, 41556268, 16719790, 765934070, 481138422, 302165970, 907445460, 433241265, 361828344, 848113380, 10725932, 135348035, 300143467, 977403649, 211486864, 996581724, 857308411, 30799664, 592384025, 118291046, 862606361, 813197625, 154198508, 521000208, 63418145, 316042241, 905265785, 615144761, 399982377, 221692047, 146591014, 996230327, 140733252, 669617502, 436236718, 85439385, 264640272, 294214873, 473522066, 349159543, 978310929, 587017871, 157116111, 244805985, 713087973, 604138936, 917408935, 767545133, 735962944, 501309183, 869698117, 374047213, 284729114, 274950670, 184467706, 632518228, 921051614, 908329701, 127291830, 744000609, 783609542, 317289750, 563583281, 247110221, 506899775, 91856877, 968426730, 254507513, 874871206, 575635127, 57435169, 746994297, 270199279, 586078303, 534321245, 89231316, 243409389, 984872695, 602875687, 967193641, 504410790, 324320432, 304800220, 10521796, 884694599, 676495875, 586838365, 509790815, 157561197, 774167141, 491513562, 792482408, 394148935, 48076889, 275628373, 379638863, 135909169, 872322060, 56542370, 793881914, 479648044, 882974572, 936470318, 698841280, 679338441, 280697003, 242669991, 51860054, 19311647, 544563396, 645639294, 817836345, 291739587, 137774091, 664759485, 207205472, 785646140, 472371166, 814061619, 738607318, 798721454, 562874834, 90637655, 482896215, 180230722, 670725360, 825790750, 750162303, 76458241, 212563156, 81578370, 730833567, 154525275, 710887944, 783760398, 135609983, 822847829, 959137681, 896091487, 285429755, 878941490, 991946966, 939828831, 675059043, 240827909, 797730460, 491094367, 484390208, 586788685, 519797221, 803029456, 120049921, 331729630, 397300202, 468600471, 828310349, 638126999, 512407676, 735815049, 127262936, 360343240, 7214375, 473778287, 235353321, 701002453, 715479638, 498559607, 269250768, 17435562, 251019353, 426105364, 347104312, 240219577, 628274267, 757358261, 597600425, 296858682, 666252098, 695389094, 293106674, 415656122, 665800058, 743289643, 382080907, 184920043, 232781552, 28659416, 279425793, 751073673, 272752149, 113606357, 464422580, 332790942, 769105564, 66227382, 655754767, 653635143, 883077510, 279612181, 332563529, 347448883, 297285810, 726023510, 843570161, 298154159, 470796295, 327308944, 113299238, 420094140, 621563499, 732594414, 527424672, 189955811, 88601537, 626969880, 269283967, 740152930, 353906394, 57253165, 944317805, 620598263, 683428048, 36852308, 871862030, 678348288, 310407690, 953562020, 227682529, 572993318, 82430002, 969777815, 554836885, 4873418, 683126130, 194441563, 745216479, 960711940, 693571409, 64208011, 945689679, 299701949, 697680525, 213296897, 893596671, 400586138, 41173684, 922268205, 958418171, 488821749, 36529135, 540106555, 163305597, 888193507, 72802106, 40085557, 257306459, 965204803, 18789935, 39650900, 818242382, 206953651, 505422039, 828151969, 938142662, 290115927, 673156181, 41602560, 470608759, 826550194, 478289274, 231916019, 375935944, 464624252, 203862981, 654765651, 475202611, 357143587, 703460680, 922164684, 797317963, 798629850, 657656608, 216063806, 953940252, 785202388, 609890670, 6070761, 590037797, 261732383, 728031156, 241277287, 320810213, 46201245, 182836601, 754966506, 912477679, 712052485, 718347636, 402664349, 280061965, 390476070, 112291771, 409647473, 681680536, 571240716, 488320887, 330501527, 423725809, 307436782, 667885754, 875599826, 868342507, 739163591, 867478879, 377571395, 462261459, 910035125, 340881623, 821972217, 973002933, 587897458, 95223618, 213731211, 625519532, 702748071, 763165112, 117498976, 280741451, 911555769, 291782621, 678441732, 78414036, 218754310, 503291170, 181903682, 527431509, 341541936, 824366369, 24087331, 403096850, 835643270, 356380095, 137038296, 379940473, 641028920, 267463118, 159922152, 580147292, 245576907, 985289324, 825503700, 75333101, 324344277, 107539347, 735471268, 983095077, 633527988, 459403618, 681886098, 119994641, 442437245, 39091298, 953624636, 422982958, 708465168, 78935680, 314924579, 277911085, 923660822, 22714294, 611620744, 963727647, 476973023, 330324835, 478335574, 72355991, 544175411, 964656943, 716739422, 552686247, 592826379, 808023158, 259666800, 347002052, 984521898, 814791516, 344934666, 719828517, 469381415, 884908741, 200180287, 423779896, 41633238, 339758222, 560420792, 859462956, 336479717, 433063522, 442090958, 204755917, 822941177, 840693411, 978598224, 639366865, 977983683, 925515878, 678739322, 75207901, 309177706, 830157283, 92747617, 246131952, 451185842, 670662922, 285923176, 947753495, 654538696, 40335675, 159488505, 523544064, 977203358, 192587577, 265007352, 779596339, 320103439, 961678983, 541360377, 597394538, 54730152, 591734791, 217078181, 996935610, 814574403, 924288531, 298744802, 711774921, 28039273, 280372620, 820034597, 980882203, 773310834, 136014992, 171449411, 41741132, 730813893, 481589193, 570447133, 991236757, 692966948, 65460580, 184658084, 171501287, 815773176, 825117500, 931547129, 387941744, 908458727, 487557708, 76385657, 827276764, 205478515, 414272069, 645950877, 876208898, 569961692, 757503587, 877666335, 884968386, 245737184, 323677992, 317195208, 889574872, 384145786, 930587285, 530919159, 813408878, 927773635, 895141725, 277900575, 264735404, 933186467, 57780251, 80114404, 659834834, 13855452, 794169414, 123524600, 105237100, 497059383, 119462424, 141899200, 96046910, 677566679, 482489122, 917795144, 55577609, 558261741, 942262253, 669596670, 5533979, 231193661, 938720988, 125715452, 330012465, 561431792, 602849400, 29398540, 88364399, 916987529, 988017263, 595622798, 663106284, 717020886, 946344088, 401886877, 91464655, 491778803, 585268694, 767167093, 352231945, 793528015, 700821486, 168737843, 728863788, 351355858, 642892016, 934782279, 780056996, 189398410, 640479396, 275680174, 44959867, 402603064, 939592466, 484707834, 720999673, 484138750, 311007072, 650497665, 477425697, 279917251, 793053232, 347000982, 459462237, 624383496, 840732695, 829981890, 812798015, 834549047, 904859071, 861079068, 349014573, 728195373, 940381353, 161509916, 98629444, 65919379, 931746946, 860873110, 51745688, 392710988, 767153449, 376345771, 780480140, 341017321, 631497010, 426799303, 316555344, 935706066, 740367913, 878456862, 290369023, 341149647, 108018899, 704391065, 946613030, 888698675, 625735641, 705230057, 682993926, 917724882, 267857696, 533789043, 854033932, 902228283, 961793006, 388168134, 408216414, 320802404, 624710290, 625665173, 115125988, 86937866, 422682070, 133614559, 108947940, 59509483, 672451663, 846420237, 68051314, 494655172, 524261551, 371199610, 819169902, 947108113, 313958922, 604803634, 471389148, 427535663, 895367576, 320165536, 78619523, 699553733, 523981013, 468048896, 806425190, 178042814, 820486486, 655703874, 511308259, 267289904, 530097822, 4752455, 633073694, 893995653, 255335811, 23733245, 234557039])," 1 (minimumArrayLength [880134581, 772576344, 399895356, 285967908, 867328643, 442745784, 424034268, 345772360, 916019994, 542598802, 933956188, 790793630, 683928860, 739568265, 956222957, 333512601, 626919162, 553949110, 627736799, 918401986, 613953728, 387419984, 458262981, 817382805, 248018453, 688854223, 838755468, 470061499, 869401840, 303790130, 838894964, 165822129, 594444959, 243189521, 669050758, 737400510, 231655911, 30326960, 235299222, 649728743, 671186820, 286886018, 436529751, 185275958, 547596220, 600755891, 209994949, 961919305, 375781259, 759825101, 626503060, 25211291, 934281965, 321043477, 542621448, 689843640, 219739535, 411035537, 449771194, 226860314, 896492991, 996264811, 215102042, 756270916, 178304891, 261744798, 558714022, 706782684, 956959014, 490566913, 542120187, 719256649, 416303989, 61347588, 153604934, 762771462, 603882321, 427415285, 765590810, 150127576, 154080204, 615974251, 14547133, 593013610, 676690296, 667964848, 886562719, 918748935, 986729577, 62084349, 924807360, 626914636, 218372326, 166342871, 420648285, 955220235, 891435030, 565138979, 521600366, 338037871, 754271599, 107000763, 888415279, 351965887, 701171583, 473187119, 448322308, 683063263, 621336856, 441295215, 451921142, 675330910, 627256387, 818825062, 44897016, 582385043, 393380812, 340108689, 233337944, 392598383, 130523171, 482971695, 852799954, 106048655, 369166645, 522158820, 499886164, 611754363, 216567126, 415808131, 14652524, 258245719, 924670087, 192796564, 317461463, 753866154, 890410282, 980006795, 352341946, 490438905, 169688110, 37675331, 394193105, 631912887, 669203877, 65544428, 970631344, 706011143, 8176764, 501677981, 339117111, 176773217, 791368146, 587962126, 627740643, 733236899, 611860782, 562305253, 766521040, 312178013, 47761851, 98432974, 588162107, 444674798, 571338681, 114611482, 583158315, 926899872, 897431605, 836739450, 768186063, 310965058, 139757743, 778356561, 367377726, 710071529, 865143542, 116307916, 867012046, 356666333, 921026908, 54450768, 134760156, 285246220, 388482510, 630448736, 528156768, 176528757, 931414016, 307551907, 99316255, 266686125, 313456830, 793419672, 266440651, 533941226, 886515287, 72275303, 306917683, 124564538, 377120763, 430900101, 485708981, 979664933, 657691604, 90500814, 207190418, 967831406, 179496476, 431639293, 461749564, 612003348, 491543465, 143042116, 966639695, 794974882, 867504308, 535412914, 997445736, 485066855, 255377770, 400095408, 774358859, 603140676, 468099733, 255363971, 473944888, 197176342, 973530146, 172853722, 199954001, 978998390, 830249155, 171041494, 120249799, 579789336, 107296359, 438775113, 865549448, 562505285, 231622051, 714284255, 416414838, 269725703, 813564951, 944196270, 35646766, 968437086, 546502886, 546422956, 875177829, 326017648, 683369044, 63654388, 914744887, 494446264, 832996181, 566016927, 233133088, 444528299, 204444062, 250989857, 118983280, 119662544, 320619678, 613517678, 646513731, 519700369, 622410353, 711144761, 266942622, 520873743, 104955789, 129013154, 554852411, 725295921, 899119983, 32574354, 205539784, 900472700, 608023236, 102802351, 811913593, 867657831, 425237762, 489011961, 34960631, 778647993, 48441060, 113001319, 880043047, 404956576, 873335266, 931093557, 354633711, 908299247, 424017231, 702019415, 682808317, 448773159, 272677484, 998023769, 275324422, 181769605, 135097231, 374001181, 550506573, 281125676, 574620620, 289257907, 733000269, 726248148, 900258599, 216092838, 240121451, 708935526, 506559984, 963363142, 253694543, 777066885, 419847752, 2652071, 627294638, 171007737, 907616306, 519545295, 661559856, 565333487, 898602413, 13958534, 711190046, 173167041, 758537373, 237579306, 670774187, 819935884, 433063890, 915907577, 920122143, 261554375, 289850613, 806720049, 90279520, 669013334, 722036381, 729756124, 575351689, 192568727, 859312670, 128539214, 762993428, 241916328, 486223592, 481582130, 615943868, 351001380, 594050060, 94773984, 693430750, 533892524, 449685957, 334808432, 987874779, 888479582, 370668495, 811783463, 93478705, 69267479, 872783381, 190302820, 667739790, 145636316, 63906558, 548643453, 985463619, 387166978, 330385720, 125101087, 213821867, 651438543, 834569065, 730846149, 932085945, 929269685, 661825104, 861763088, 296522335, 150480786, 559100677, 710561705, 773008032, 669361091, 40518632, 676061939, 843546521, 565118836, 825528783, 398193933, 984187516, 589127548, 813097488, 95508608, 153585091, 548697798, 132398524, 269756492, 932618409, 736498963, 626086192, 780365242, 486370081, 871224782, 677702319, 732835810, 715527718, 496235293, 156585614, 612477670, 811854968, 608070165, 127260843, 993953090, 884552894, 13981110, 658916984, 395298925, 418582978, 749389445, 208198562, 484086863, 842428799, 475951277, 104882693, 385918757, 73796067, 166532765, 132510202, 537121325, 673264417, 165438708, 913594804, 326855874, 784445863, 896610721, 667820898, 882894177, 909420690, 49880421, 16788138, 566527517, 404188221, 407323260, 732317301, 743768712, 614759288, 816320839, 315273597, 835026277, 293575911, 206271346, 90936162, 668736539, 302389864, 459844314, 162515010, 862326889, 177225784, 528516817, 823703198, 229755259, 957042756, 517440603, 45020469, 309685972, 571201613, 888817946, 339605797, 268092512, 350297303, 286439307, 892585975, 563766413, 513505346, 872215479, 854012212, 218379954, 157282502, 470437082, 761379652, 276970771, 493873962, 58666708, 781357424, 151773969, 153870990, 348396378, 697076565, 343494124, 39075594, 37153310, 747327376, 122061654, 230235985, 221466327, 883883323, 732694798, 817210114, 325957917, 18766305, 517066355, 959470517, 421080533, 435913042, 705598828, 5348100, 285893444, 78046703, 488054923, 572627920, 432743852, 948900250, 736573135, 738344964, 988861227, 398334267, 277995509, 498754434, 510417446, 475048505, 481959671, 151876203, 700786392, 417931322, 508328046, 218383798, 81050850, 4313417, 473279813, 673133917, 651855879, 381360874, 160050498, 170551997, 476899325, 738621887, 351042132, 543581701, 861974785, 355566841, 826549942, 237117440, 543117197, 483543531, 745213607, 452335783, 621175847, 111318154, 935765313, 909331452, 951966961, 512011656, 833880599, 597741088, 872274903, 560446748, 744208922, 218081788, 142263085, 573883519, 508791472, 362161935, 279607720, 384278637, 965625191, 297709186, 462405913, 592725170, 413244218, 582331867, 664571626, 985169835, 916123874, 524935945, 484435373, 137106007, 649542576, 326401842, 244266171, 489351182, 297897611, 889704034, 155945450, 174442632, 26784993, 744683236, 986668727, 90041339, 495527940, 689047218, 762033464, 155512913, 60674792, 742149376, 596709359, 163780172, 646548398, 366898016, 320965012, 995240516, 723505963, 210166510, 798029805, 478153548, 56881214, 888721357, 542004888, 775626756, 809451122, 272418222, 173639111, 286098594, 611114581, 641980247, 701500272, 611823172, 939271211, 71699397, 910264860, 262532802, 64658012, 177893373, 662385997, 132751936, 98329502, 579500005, 740419958, 794639957, 142057103, 665985676, 914527982, 861261245, 428488057, 56775855, 910959663, 68015485, 360503160, 874976061, 190543094, 987695376, 558939973, 414401767, 247235645, 304530811, 493345265, 606075312, 479464367, 997036831, 737833138, 77451196, 869699626, 324606997, 813256583, 744407651, 955824666, 754177258, 740449609, 534833485, 379245616, 573202702, 380701824, 827132959, 377627300, 189601742, 558175455, 401128069, 463201588, 560587369, 731579902, 767139271, 579312239, 81695574, 801099849, 538042779, 407492156, 636329167, 25890949, 292048859, 151982005, 634079655, 754850072, 260757988, 468748736, 561942506, 697499773, 786723516, 371086704, 876426870, 717046791, 175042717, 882575342, 645212179, 546168724, 470672062, 166754854, 274065461, 569537741, 934786224, 865097934, 847170782, 800668609, 242817177, 489067315, 466647660, 664841831, 616484459, 423313670, 217250759, 767812248, 797333026, 749631803, 570555538, 379426258, 392460932, 954688478, 999734125, 495397031, 759678331, 649160808, 563505130, 898832468, 15339902, 283184511, 544660738, 85248101, 222703515, 160211141, 878631619, 648286438, 352828235, 838019019, 512509076, 600878809, 938338531, 41425638, 211520661, 599034085, 718208994, 828142874, 458943629, 759078031, 260160591, 134766086, 527382561, 781315434, 467586385, 435971510, 805718715, 283227731, 73074346, 472269190, 596254440, 694634299, 438716978, 777087297, 483236731, 156053414, 766189998, 532906092, 185416814, 84218400, 575273728, 529965932, 809119906, 85322015, 526122603, 401655498, 780076639, 442660256, 630077768, 36342618, 542794984, 199822166, 936772901, 77180605, 818811635, 201206097, 645087205, 979075212, 529223113, 42853898, 257526141, 853670132, 1720867, 236863356, 694651676, 512028949, 187912206, 385718107, 900644686, 50834120, 690257769, 601236484, 732283314, 110237559, 77011139, 289987174, 17427166, 324629539, 192776784, 544978481, 306967470, 920161449, 908974656, 916583129, 2248877, 805749663, 237375731, 669110904, 8963267, 342045943, 111357842, 470333536, 917153092, 659765236, 532679838, 398986864, 685861428, 96358107, 180004551, 590781972, 955957460, 771681539, 543948536, 392746777, 401956067, 710398302, 106514925, 347856221, 599578170, 116437387, 154764380, 715615838, 579277010, 845671657, 494033278, 780901733, 139390024, 277952692, 179821844, 998953360, 563279363, 688607075, 789711207, 671569314, 819485210, 981261276, 461562095, 427689991, 602816934, 692361233, 93224972, 143566458, 587418818, 892790495, 467671907, 241249859, 673915634, 453065593, 958982220, 581218739, 909532277, 826566853, 32422828, 479989188, 616245339, 367747558, 865774050, 80895272, 854099804, 940735465, 713823710, 357997900, 908651039, 431558662, 511202840, 912915540, 348524445, 211561092, 662037418, 416614013, 583743789, 759661735, 191792744, 835703055, 94302797, 565989672, 407178331, 93793489, 797953111, 669445167, 517768701, 984130624, 922044946, 809419816, 240115778, 278337927, 532041230, 661214810, 535945003, 898362132, 302496266, 921440348, 927427908, 594629097, 215105436, 496506064, 538979114, 475379294, 502812442, 235637363, 432616979, 603336447, 76950014, 686533318, 70537644, 734543399, 424946745, 175372282, 844018573, 761543055, 35205055, 628687645, 950267177, 549983511, 198485422, 187359376, 176747298, 859964012, 376627453, 657128300, 183569546, 886172616, 256221030, 300621767, 31234219, 751394526, 593680602, 553840813, 22071677, 97957834, 261117661, 184885080, 831609621, 263373030, 325013264, 743131724, 363682873, 328548105, 537817330, 125466955, 975776780, 24702259, 65316095, 216264569, 158011448, 882818224, 349215164, 420639521, 452781685, 191103336, 622343398, 878372588, 907975301, 758066951, 975328122, 62985578, 61909456, 386874032, 713724838, 890473535, 185195713, 11065797, 314089135, 795360450, 706327741, 527825810, 920672612, 174968481, 981349202, 534311286, 37732071, 631176666, 841586215, 927795421, 120036032, 320628049, 782545674, 749094841, 740887370, 270207196, 67485636, 902423647, 51879070, 66981155, 523366167, 419607420, 672979049, 791043663, 530046309, 416682213, 812732392, 59711099, 120523508, 545936022, 611587157, 535590655, 285963266, 8145664, 599957583, 428105620, 174340714, 310558245, 70447271, 940842957, 570508289, 925456263, 98443414, 643220660, 277755316, 850283835, 540825140, 788939941, 998154476, 325098342, 380250563, 850094965, 859131515, 998188075, 418435195, 834469150, 387752591, 365563465, 451960681, 134334846, 891956447, 353489891, 337029105, 267027321, 89371550, 169408345, 778259043, 779660290, 42067294, 903738791, 977290722, 327805349, 153628554, 67370584, 223050152, 216192237, 422626883, 723733818, 701794979, 766535550, 736867524, 850994919, 858194214, 837536082, 112330226, 940167120, 945766578, 166409496, 812378888, 555885426, 929659699, 421668388, 601088615, 621827512, 14859556, 366179882, 280106429, 869154158, 183493139, 692369111, 171396178, 897359245, 941617762, 363206494, 78936329, 862799901, 892769282, 61190226, 795640030, 425614094, 904416199, 299516809, 116911811, 275966376, 459508017, 900447237, 941954168, 996501730, 588394149, 436021075, 645997381, 756179844, 503848726, 566747041, 209474506, 979152914, 68140211, 470617450, 617381764, 176938785, 847368396, 141207456, 305173944, 737893686, 222174823, 161525396, 504857329, 401814031, 212645175, 528881497, 651687005, 108938678, 555698488, 596216009, 58281356, 875618559, 293658280, 184101557, 259458365, 991563909, 589089716, 666700585, 599546523, 856012064, 444852982, 54340573, 218873795, 263926502, 892015658, 133745280, 699845646, 96771102, 523544304, 570136135, 51721450, 172387488, 479090931, 786819469, 171460363, 591513922, 862728817, 752485090, 526487159, 696592596, 24678964, 962421987, 769000589, 48852146, 661017008, 302618527, 680947335, 740857756, 563600952, 183924161, 452180034, 693831759, 101967127, 31054786, 91737730, 651514973, 64883071, 609927629, 357201698, 939343995, 509341846, 651440103, 57979123, 945232207, 686351205, 711889560, 875313201, 677832830, 898234859, 510122457, 265197318, 773297210, 648845235, 709706177, 657632913, 148241707, 571881428, 839670173, 988238577, 646014857, 615165986, 541727120, 73485003, 443930949, 449762269, 979604289, 383926461, 227276678, 162037204, 495227167, 433029221, 424448698, 964862201, 829425930, 102024962, 562401930, 329558494, 7311074, 419358016, 494307195, 797314957, 424710001, 602063242, 173556290, 125967227, 188150945, 756824129, 713111706, 814169505, 197166219, 712966411, 879461144, 406442641, 510256168, 347928793, 368754833, 890191749, 682372365, 138240790, 747721640, 219309338, 524181514, 370760113, 436301661, 860516073, 691836876, 692611666, 394307541, 291055171, 742487977, 670666604, 752328679, 367522778, 426769960, 567519212, 873066011, 219728513, 121789517, 81472970, 709711604, 525944912, 876902987, 42521265, 114998371, 270989922, 50771903, 779680368, 57052960, 903587836, 943165240, 152928669, 321759514, 325023225, 343090394, 879846901, 153627120, 112113062, 281766978, 214000481, 221281563, 393210444, 333557984, 769202502, 44183180, 123977758, 607898661, 163389256, 625546306, 665003068, 695035568, 270652424, 945461310, 864562928, 461380245, 481649749, 852837953, 476267006, 206786506, 209312089, 185441970, 373448724, 929552897, 200210500, 103459553, 144584992, 491412477, 184851199, 479789037, 91741401, 488779870, 964247927, 552844256, 468009547, 239812109, 609852086, 818950291, 102327732, 863709170, 813045574, 678415650, 986123934, 710239254, 210831962, 505162691, 420461693, 545438476, 7797730, 568810553, 931345382, 906217549, 430456515, 173628963, 292494095, 107219426, 549508067, 963564693, 849151182, 534795215, 480840604, 646518941, 604736001, 959477896, 467692514, 421180748, 421787878, 721141457, 581020237, 740191213, 288716393, 85717855, 619401017, 811949627, 656967405, 592961859, 9411446, 29759375, 559454848, 551489736, 502164197, 770093946, 669643578, 344958550, 541577042, 779195339, 684602386, 913457927, 200132908, 450227575, 733159299, 828704931, 393186364, 799931151, 989534405, 218836627, 160081407, 47949021, 985620554, 439767022, 600714, 495495185, 60199641, 268790512, 196435175, 113966723, 302799307, 60534034, 606501938, 457288995, 167775528, 964982527, 689021281, 226628045, 780137520, 264998706, 437816417, 728808339, 867920937, 880621703, 601897238, 609684610, 763433141, 587260378, 60814402, 827278057, 237049497, 690916996, 482725843, 654099597, 18528212, 430960501, 473937225, 482783971, 208103646, 770778613, 512019572, 880733956, 490928234, 618524844, 803238729, 665597934, 616789008, 600587092, 643721641, 158496757, 134282568, 319200580, 28258385, 743498717, 396052512, 103573165, 36531067, 223986369, 254329795, 947187062, 940789394, 164377888, 776672798, 464676212, 301994891, 75651122, 903905978, 986104978, 106547723, 268020873, 219739741, 487257993, 735791232, 989211030, 378452656, 134419170, 455535464, 705992556, 780465696, 441150358, 447708575, 728959143, 515254405, 841302849, 699058320, 334771242, 635985965, 800545078, 316446845, 526451793, 655597577, 962426078, 993821776, 416489243, 516026856, 868204626, 217210986, 859142864, 936553674, 515610154, 886003773, 698797796, 992996010, 743396685, 380582672, 528882456, 976415193, 557079670, 586004974, 16205129, 149273514, 205225407, 984103384, 482325608, 46915971, 112526002, 698204581, 985735014, 769870509, 23587066, 331246758, 816497241, 417735063, 755506684, 384056946, 287854193, 651352498, 316285895, 734301170, 438300577, 813685254, 466187095, 744997108, 132352140, 336389235, 604950873, 517850562, 449840557, 923138843, 247753537, 304262871, 936434074, 150583455, 172885342, 73138219, 514111262, 154051255, 447694590, 189667118, 836505073, 493201418, 741756469, 203092472, 31690956, 981778826, 73767046, 568051413, 429089611, 977403653, 952200436, 14455362, 573251540, 191730834, 276579102, 70853738, 171808054, 208442406, 851465524, 532989525, 653667313, 752657273, 58946045, 272740085, 886739804, 112852903, 499398597, 864446296, 730620154, 81106425, 299526731, 900727649, 100505327, 299352481, 991008226, 723257126, 563137055, 878157515, 158782475, 588053481, 502838215, 408446454, 781625212, 21127776, 896622836, 918759002, 935425080, 61888471, 612182673, 177366247, 690155543, 115011574, 748249537, 655721797, 659690898, 228417059, 537151795, 842722133, 993917243, 730423320, 449628813, 6364244, 100039232, 117368215, 259066785, 645933208, 609097517, 405748786, 551432159, 600907654, 468230450, 950926704, 387420380, 688027441, 64837348, 983246898, 721375778, 330290051, 358806879, 934728758, 469044479, 493285999, 197978023, 615097485, 651161792, 504194903, 69153659, 648684407, 349740669, 131591369, 278256733, 453913684, 662163947, 617552739, 261153686, 723600336, 396672550, 995128794, 254881104, 437279852, 48798391, 213660407, 617865204, 147315456, 585408779, 56923662, 728651466, 584396128, 919784043, 680357374, 305368272, 11529393, 167379580, 116812010, 814682781, 329090073, 941329056, 66669214, 420872178, 811550443, 837222041, 567492099, 783575592, 710768922, 137575014, 710342549, 82981288, 987943564, 258456475, 468771019, 255983643, 362200413, 47502277, 289159318, 399635479, 442212665, 111649090, 872160154, 367896929, 913241122, 104593010, 742256538, 99382518, 721327260, 730778209, 11111220, 693491268, 77197842, 986255623, 817697531, 82676340, 170633033, 724107908, 139906038, 578055297, 379030386, 365378502, 681448528, 238487398, 970659682, 178645656, 219647130, 640016793, 193327590, 842854339, 469888791, 602792684, 896367446, 895790618, 736489903, 993802620, 431518449, 771225963, 424566083, 665618103, 393455369, 297188008, 902745447, 795308555, 122243562, 302527475, 401265707, 124186401, 655007361, 452165170, 996297717, 249240501, 327468149, 704503438, 885391687, 68148599, 786724826, 545753051, 853072026, 426870106, 89241862, 520261417, 83933253, 259308983, 164457204, 763768506, 441763015, 264510823, 838686598, 67631513, 916142290, 483325405, 579048898, 498085083, 476232898, 150605306, 867076467, 972788442, 85301124, 120540672, 617160931, 149817747, 632261526, 848427828, 688408611, 978732678, 849819215, 768518709, 611630648, 638240344, 135657907, 92299879, 332481787, 511810191, 28021996, 141540783, 65787126, 586562957, 269445371, 59233012, 599170217, 39434403, 623399301, 173620216, 917426988, 611925862, 269604200, 135145280, 478531362, 373128932, 364449381, 727537493, 578711396, 378809101, 78883507, 735615072, 751887574, 225407373, 92672921, 153629933, 181387715, 379259787, 758209495, 178626801, 251235767, 533765874, 855945630, 403543512, 561320502, 905203378, 851629389, 951733071, 404594014, 751693488, 139595787, 922915032, 789803680, 151577066, 719385155, 535058971, 375930054, 414477870, 687269879, 456160510, 580337833, 24528308, 90762728, 246767754, 621541402, 794846439, 141426772, 447790020, 164921437, 731591452, 578469376, 395298172, 569038719, 864626212, 339785938, 69146035, 771499393, 70689027, 59291569, 741811434, 961303996, 508605250, 548333580, 755747157, 633038155, 148848049, 668313240, 104373766, 350354552, 162936130, 296087603, 760609343, 862695741, 951721561, 995208806, 300108028, 392859482, 984989099, 750297115, 297797683, 631804731, 981318307, 574610714, 549598639, 140394307, 503830565, 259101642, 705520360, 820390021, 859915830, 846788934, 229133577, 767976744, 331844732, 69798730, 641436386, 247177850, 596697633, 697053935, 580017933, 214227730, 953002617, 618032872, 812231634, 402774115, 177987237, 636706626, 666118197, 24460186, 792776090, 563113284, 190520849, 622985094, 728732889, 583369663, 329377401, 871472336, 641861133, 293626715, 373799186, 35695867, 479155415, 254490628, 300750322, 692446168, 694321056, 846338356, 212582822, 157416787, 919545078, 842930596, 120076839, 313133540, 904954772, 609252495, 770173639, 859608129, 969925755, 16360958, 955212592, 44157707, 190278628, 426555992, 460422723, 452244153, 419159704, 387954827, 706823702, 78285174, 438956589, 63328254, 463394999, 296821640, 769584373, 498213425, 68803662, 986819385, 80218182, 167618716, 865524752, 72735552, 316623758, 974033857, 105271371, 758583434, 9717387, 70773112, 993343705, 347679241, 481037028, 185612719, 872345821, 431825976, 812570634, 395056075, 802189373, 290366213, 875480868, 633330130, 369201188, 405095154, 572545798, 833505626, 947939598, 359122225, 433202667, 80286651, 658519099, 952492304, 714907217, 32973500, 568352327, 279790242, 19065587, 962868116, 217880562, 837383273, 621240372, 759916378, 442049269, 253180365, 90834231, 307579845, 88943641, 747922868, 438782671, 258850955, 194207089, 281747763, 774629962, 433039410, 611661669, 481490435, 333595310, 900179970, 655185148, 135789128, 980194675, 960851715, 239709283, 246534646, 960461130, 421521249, 796831313, 111278653, 674136070, 749467478, 698566870, 695240956, 157281280, 619420093, 543026019, 578052070, 577949874, 534745180, 238719521, 704613616, 100786738, 422622127, 227634021, 891045564, 22568487, 134377904, 707191161, 134738821, 260834729, 106127363, 425578281, 276730987, 114500982, 708262188, 849744077, 8695985, 952519759, 426410880, 263097653, 748578107, 985301557, 227742037, 378878077, 659929914, 795359723, 526922511, 559456295, 552487088, 111622971, 39837625, 338800241, 129607375, 111359509, 247604166, 752502743, 620086098, 863923357, 493961085, 156780742, 467995463, 700596055, 365893473, 805388765, 414743121, 462166346, 755138510, 352275527, 863297149, 897246513, 533560236, 611620748, 344047092, 511548960, 538166882, 326774152, 790792184, 969759827, 14228468, 790569648, 656749223, 901574409, 121474565, 465703526, 299275550, 204709903, 418016999, 940698960, 991006749, 859119046, 443194910, 137070530, 222897214, 54183866, 312380392, 780630321, 369682894, 2480034, 532864381, 32284294, 353630520, 585544937, 143995076, 876190582, 725301183, 418823086, 254447506, 929511656, 10249536, 965878678, 333852087, 859476766, 847392027, 548091454, 494615494, 951679252, 21496311, 91776224, 657743618, 303969631, 588258572, 746531310, 720042308, 456893573, 201306991, 857560630, 897488572, 657456847, 312885102, 604607510, 176237782, 760909188, 917764102, 538901744, 709228448, 163580968, 347078808, 280789372, 561588265, 949745639, 321879801, 481349233, 129357682, 287456062, 790099015, 503389519, 798310544, 647352229, 309257212, 234797849, 39635800, 474306494, 154174829, 521924648, 918597576, 464102856, 769510331, 724065379, 322714373, 360702606, 327708720, 272620202, 492824845, 291686464, 35709477, 521848201, 12818220, 665496599, 415225050, 734114117, 992139588, 547331410, 316797623, 703351064, 929752390, 787824152, 757360642, 256458546, 681361391, 450699039, 319461551, 44352269, 474536512, 46868709, 152686036, 386573958, 204094073, 825579934, 197151252, 560877903, 528503712, 364689940, 70620046, 659869127, 724771240, 832810343, 754116596, 49426883, 267241002, 747138124, 273144391, 478277993, 453790794, 890766060, 847152275, 262720034, 458974246, 679028981, 520702921, 483367399, 981746812, 14028504, 176728008, 658791441, 875735224, 467407109, 468214839, 269472309, 268261275, 73363443, 297967191, 54907598, 974938344, 17806392, 292662532, 895947619, 840555959, 884385441, 841708894, 257746916, 489857544, 232996929, 190619201, 423022793, 743083091, 438058220, 554408149, 111880559, 965219302, 668017885, 823259574, 472428536, 813910760, 986702605, 556845780, 433579323, 927368928, 473608965, 166680194, 283332311, 355720431, 128215598, 173709844, 163856707, 779657383, 780228060, 553135678, 694035129, 492397970, 350727737, 517127464, 878483215, 219748709, 207253745, 514304549, 431027779, 387991334, 461610399, 818427897, 847103398, 978515377, 652539219, 982444559, 993615212, 850571612, 960687715, 48944000, 742202851, 455882946, 21496059, 875233018, 596427840, 888015296, 846792885, 745388990, 118447504, 191973880, 64382136, 703577285, 103252524, 690054196, 308189091, 897929584, 872710586, 112274640, 767463251, 767290138, 952724760, 291311206, 352014967, 632984407, 501905941, 255121980, 593074290, 550734819, 553622678, 319300726, 682151721, 491122144, 795700186, 36869078, 303956606, 325317411, 327520520, 183506678, 964994271, 441377748, 932875058, 382431616, 511306776, 991732249, 967211389, 335690295, 395306130, 379167293, 481793903, 90409646, 114086824, 621442278, 241472451, 90190810, 968244321, 659585256, 296379969, 209416969, 384473440, 844575369, 468856345, 101260546, 811652275, 462950044, 93861448, 901433789, 223030023, 628211323, 881718298, 379607418, 331955406, 243841695, 124533777, 49155087, 296264050, 710571806, 58593104, 463893355, 730268310, 457565437, 16552135, 651497092, 93997826, 95881278, 959670066, 513667873, 966289241, 336946518, 863090289, 316675647, 369905251, 240966169, 562203917, 254819235, 954523195, 406261168, 989704716, 811617148, 805942349, 669298573, 922333436, 495766959, 768022814, 346283329, 80665061, 527444685, 515437651, 56817497, 174867389, 510709873, 983555850, 768574475, 506938762, 915760168, 715766339, 480193700, 207145374, 691764815, 892287236, 396738393, 150987107, 814119155, 736722811, 113129493, 135182635, 546307251, 127435873, 830569372, 291188992, 736971886, 960467793, 791057203, 911460590, 69528754, 433324528, 907867001, 780090987, 139382960, 801165571, 651259270, 521507548, 436751795, 153808064, 509878617, 567196036, 537556510, 776338834, 849023999, 340222502, 415929831, 736333387, 241422204, 219298991, 986199650, 289741199, 648777652, 516108253, 444615167, 783980859, 793363357, 676120389, 570184159, 819033135, 75535488, 300066219, 773278827, 451014167, 185068744, 164200345, 805605623, 77006993, 937996921, 843320920, 367229113, 42840142, 610608164, 10972894, 964124946, 558898715, 226164289, 348070882, 561992089, 610678903, 363948351, 294505764, 111587811, 80006759, 229403605, 909993966, 929850367, 732102768, 17040263, 728766037, 321227193, 767600099, 207661541, 464910357, 232668355, 450946302, 966684884, 782808877, 897993721, 465118310, 124561280, 527900867, 725610669, 194090322, 179788987, 707062152, 160728261, 973048993, 921184038, 423853397, 870466952, 742677869, 864580595, 201523670, 235766777, 704388351, 45917948, 193774480, 905296432, 176894635, 236912686, 614488260, 962052167, 674555229, 922119958, 701485511, 904012554, 355469519, 142567181, 102625984, 83532121, 317432383, 535893663, 713108608, 255708417, 826352987, 617926694, 652586716, 801788709, 268511627, 381245261, 478063929, 726875318, 850366219, 54454013, 835225928, 6166094, 55866645, 551548516, 698483712, 770704894, 870096613, 308675252, 553047494, 922311472, 944040560, 180288397, 646407218, 188125223, 72463609, 415461677, 803015332, 993367544, 827036484, 793395299, 327229055, 911109358, 440305471, 30153036, 650239477, 441164598, 205119301, 244069022, 972503849, 762679101, 909836228, 463363925, 596615288, 393459699, 973990140, 661772404, 983770394, 222644062, 260850523, 699712164, 834288108, 896053421, 804953673, 361108198, 764260449, 387786231, 876055102, 733912460, 496327412, 28906063, 742522280, 835899426, 167001884, 721601621, 93917791, 17744687, 704978276, 630176563, 138389261, 673890514, 956990842, 657980310, 632674839, 658423364, 346887378, 96958369, 792655726, 354000256, 434244671, 612020773, 792019673, 145949764, 350556720, 88502093, 816843348, 235552278, 754323284, 497443103, 55318948, 867055699, 773683539, 788552042, 351513256, 605329669, 985896236, 796044510, 18318804, 361584718, 568236444, 993887814, 629974510, 14056167, 216664654, 986971943, 781163539, 534481592, 418460557, 570205087, 742816843, 836692632, 666841808, 933401201, 622046792, 971313156, 796600480, 13794002, 419957322, 158449101, 997450624, 414974852, 919851708, 672868381, 174892855, 280972602, 272482210, 927609504, 573587730, 676339321, 332036593, 153071535, 511270624, 432031659, 569789161, 621456789, 737839181, 336933984, 330416480, 455615059, 133752696, 931141544, 477683891, 924840141, 274965781, 870826416, 561586854, 409846459, 756537093, 267311638, 90623554, 26533151, 330369024, 587476827, 460760665, 977740816, 343299788, 295053106, 791378913, 720355053, 280472762, 806856571, 211491855, 884357770, 902008889, 557880149, 124419528, 680573207, 199985189, 599242259, 459787465, 893252389, 775922515, 889571665, 815978086, 999775890, 546735512, 693730544, 884889311, 504429606, 570431720, 301654576, 109074769, 620793591, 106852855, 950285865, 636998811, 948330806, 434854123, 76336199, 87037364, 126875410, 257404116, 415957109, 450901735, 982811168, 652813311, 96789243, 479394058, 402027280, 804418577, 256750393, 310122095, 550095414, 213343238, 436112674, 970157153, 347627411, 924751075, 263324922, 405989909, 953672635, 395130854, 220216423, 598098972, 390486101, 570305912, 147127222, 135162789, 910814514, 392825345, 199228979, 904056378, 706822341, 796348124, 195651094, 55090466, 51404839, 831242045, 71053383, 706793573, 365404648, 910864736, 615848151, 14040903, 533191573, 256059452, 272224994, 650044067, 955263900, 463962933, 288567186, 1059290, 362518991, 238664170, 215464522, 578581578, 410088224, 331716891, 598103799, 797007738, 542060965, 890139565, 409733946, 489382288, 888577990, 932370496, 827881207, 914382843, 858649374, 591942253, 333184193, 200447622, 785482464, 293449843, 873016338, 817529732, 876038335, 642151293, 553193932, 733840042, 137977518, 918846105, 521015156, 49644976, 93574011, 561348823, 141279894, 194024133, 584145723, 710897726, 857903368, 870621594, 747637295, 203142752, 306547309, 479038854, 73282208, 524282220, 580600766, 722359618, 204874237, 570956293, 533566142, 142645675, 519885631, 197606526, 814260815, 318093659, 800481754, 440490494, 192718433, 179352440, 344864854, 506132428, 304563239, 438505945, 489082912, 107544023, 478909596, 562705626, 736609117, 216374588, 995382803, 255321652, 132167848, 298973257, 866391899, 540479898, 227036188, 630809582, 817532550, 332810716, 146894316, 507054191, 444362786, 667965827, 923634961, 877880578, 249989192, 14898486, 539826443, 547889572, 806756175, 532262933, 813127498, 720254853, 205195315, 862492372, 810737066, 584878575, 384203520, 119141621, 683663171, 195928392, 453003032, 304067196, 476836096, 848749725, 835881380, 585873030, 727565936, 285477434, 757326406, 568507555, 682082937, 527848281, 213205650, 221152408, 911706457, 70694944, 815684282, 303822894, 198651827, 609528639, 757159847, 119402432, 332766224, 70520799, 183107082, 6015025, 269223199, 975666668, 671034337, 608343774, 7733205, 842929343, 399400795, 347397681, 924393384, 387948451, 343177287, 511796746, 635489005, 478992215, 914824459, 720655351, 463371696, 442116776, 563952720, 349628288, 238306824, 145787247, 397392068, 736871573, 609284354, 261778891, 837621769, 972229118, 316662297, 446242402, 620364484, 285759421, 102391441, 49821084, 529376411, 301346556, 792725271, 752847219, 19606588, 68322406, 926562896, 875313624, 940141258, 805233937, 866335231, 464119828, 774249769, 542626114, 260300869, 160131392, 297259556, 682626302, 380514599, 368496145, 767287077, 51033754, 808085364, 720254435, 585838696, 164936849, 86668194, 539292703, 296739006, 382410329, 666651647, 164146624, 727629670, 371562736, 791755799, 219879086, 944776441, 65733122, 879686581, 783187187, 535438748, 266398843, 346960927, 958854889, 887821383, 48848797, 375664882, 6601841, 264275589, 729837000, 25363950, 3498445, 770362583, 644998548, 375989318, 606002411, 835883550, 201580326, 317441248, 794211481, 7210717, 398879694, 716682770, 368251954, 695270297, 333999755, 141600013, 737554884, 293484900, 837672634, 129245889, 867573931, 580119374, 913999056, 764820265, 336516332, 859998647, 943239384, 96192992, 63360356, 381230045, 588792549, 132859371, 270814525, 512659945, 188237960, 889468382, 655075210, 207168250, 887929270, 609854032, 957974249, 674655543, 87508141, 143729067, 843607804, 174479291, 941145656, 495220403, 329140743, 240060384, 551948939, 61941507, 339744783, 98641702, 588902916, 214292932, 757280471, 556616858, 72817925, 518624794, 775535762, 101996668, 176516478, 971544746, 547494665, 463165568, 321972433, 701479274, 874886829, 555966677, 544814220, 813284662, 588066396, 370057978, 736083696, 667295787, 809087215, 965708412, 730246651, 281855061, 139316966, 299372089, 395904154, 683438244, 694566403, 105505448, 348098169, 397986618, 924094929, 642083120, 73421702, 297964295, 841897137, 478519716, 911628904, 967770471, 28973035, 395502229, 724202687, 905462666, 651720743, 628622317, 122192207, 203924878, 793303119, 810760931, 172610033, 359557007, 617360680, 869123641, 284859831, 144335523, 776337900, 910500686, 401805191, 636162023, 352156631, 855188794, 223033767, 567501411, 229791377, 19511173, 277302825, 233289092, 37791261, 225142993, 874685244, 187126225, 285846969, 885664904, 902428605, 266335161, 838086798, 262776164, 238701940, 288447789, 458647171, 481152043, 961482773, 928311384, 580161094, 869304570, 300777512, 556127642, 473857967, 930483027, 970645309, 707434368, 170131100, 549346706, 272578009, 509565345, 613173892, 751359362, 725817754, 659510236, 864752856, 746221644, 421993953, 190999588, 188287770, 142430024, 351920374, 863812543, 400969501, 246038929, 962933934, 53744872, 121665871, 79737161, 136023059, 626507177, 90281498, 688596628, 58943141, 755285157, 293290127, 292342583, 883364655, 850394396, 491632557, 899684436, 395748263, 790468351, 414579929, 856719364, 882938687, 794211192, 206940108, 776736, 436575138, 484895259, 773283766, 8809984, 216748895, 295492106, 14140123, 373993964, 561753250, 171520731, 755408422, 203087322, 79068990, 779361578, 701978894, 555537656, 54771459, 757119820, 88715750, 770162915, 810108319, 342135890, 255582108, 184074599, 496315337, 104908941, 261996669, 385084151, 23601665, 323424138, 523690595, 108513093, 916676162, 564261066, 538450577, 451984897, 642241231, 504349044, 496645380, 716090839, 588371860, 647878070, 563635501, 807122538, 981303916, 398496651, 126180417, 275298989, 266693423, 56712929, 789285936, 376628847, 350133807, 942731597, 497500127, 99103108, 727154939, 170009926, 788945464, 60662061, 820865279, 464411818, 341126122, 483255514, 766219160, 180027434, 438228633, 10098450, 942084823, 175765207, 844732696, 632544411, 903236096, 353992117, 528050515, 579129079, 370208810, 753424167, 39569493, 555857383, 259808505, 715905470, 298445642, 909354154, 266350409, 520368776, 915685683, 458575255, 800979378, 75292975, 641367096, 834155316, 816108094, 654351668, 235559309, 635033025, 312306814, 175956998, 796688802, 630046553, 798923836, 433801005, 464146382, 160117272, 182340545, 566891216, 308334382, 26295098, 581610815, 942746090, 342711479, 572575106, 653104220, 359339345, 845599134, 342903346, 865015279, 436986773, 686093031, 618478741, 191845648, 650935906, 268928361, 594754478, 360666637, 706535463, 813415878, 156192596, 565892602, 848411844, 783422241, 105077991, 156041502, 636858751, 636331427, 700346479, 248281495, 385890794, 33781830, 588304430, 925195974, 815650634, 506272131, 92660242, 380973580, 790562096, 920622579, 849722836, 132468869, 92935171, 163324983, 701790704, 689308168, 605351924, 193882497, 367335732, 864985638, 233641662, 524703629, 246369392, 457228461, 881721385, 444014121, 925581040, 457923535, 995187887, 737543077, 843686909, 216597861, 138643448, 565917668, 969636024, 842805996, 840971129, 828288937, 761149897, 348271281, 695879940, 667216424, 903078258, 397525531, 934141886, 993730584, 4735899, 494938308, 800083351, 765941201, 637401606, 900966734, 259622531, 509520865, 266745640, 372963788, 82126517, 952387819, 500370389, 268041591, 547069513, 104089501, 616935628, 403831475, 629897579, 884044426, 746762132, 556187222, 107407339, 294866649, 896349578, 710370968, 760426145, 58412972, 251911809, 76989223, 756885335, 685195342, 477546730, 50980413, 686045585, 840529210, 46135819, 332345562, 377098078, 745226509, 5322720, 50705096, 690854733, 570300016, 151279462, 732648774, 580042267, 695880737, 686789789, 586312017, 955153493, 627818876, 531479331, 226568966, 759247414, 133215932, 66225957, 334332781, 531015000, 807190510, 950382481, 757014042, 553926409, 218062721, 644950002, 336314663, 577558395, 883442078, 889175168, 807044813, 506442050, 464418522, 327653887, 213474144, 326829266, 836547073, 295916132, 853832486, 315986389, 218437138, 542721607, 476637614, 506837195, 502480932, 576360738, 912684430, 574035845, 187837674, 18796986, 521066136, 626115837, 267716830, 365875508, 946134001, 327778673, 42723681, 610404364, 589200680, 13113228, 248531608, 904965550, 926571901, 157924153, 852625222, 253068432, 942970458, 770971644, 841600990, 913283778, 431835096, 127701545, 478115772, 774894189, 43908397, 617756480, 274266143, 777205639, 48436117, 307443798, 306538936, 510728881, 317678196, 795395664, 621593057, 688247337, 976029814, 327993277, 948440397, 480378356, 966690718, 665809615, 100432262, 976857390, 886332098, 873476823, 564751098, 922164883, 89557981, 714268503, 579357314, 719971399, 623545657, 201893267, 133982505, 958366251, 188136455, 111128181, 331798975, 691408490, 28831126, 6775001, 389199668, 146065215, 388435881, 170763116, 942650367, 784902834, 859018783, 40091388, 408170389, 537755027, 91705508, 897836136, 804538818, 751857422, 150722947, 252292879, 906764829, 876861903, 572827041, 774231497, 966883782, 600669538, 60727346, 594849838, 137369791, 60151235, 279548987, 740482972, 365022610, 437421257, 472472776, 325693648, 462659347, 901939347, 329549203, 690609580, 432205164, 9157621, 742222914, 867716465, 391176607, 142824827, 919797755, 29422219, 858212791, 113243081, 515206347, 123352417, 124310355, 581902871, 692955514, 193179223, 120947612, 780667084, 195845686, 282668929, 773399011, 902370267, 72743490, 447927540, 539970413, 202279126, 618179301, 757727971, 805236810, 587926366, 913086970, 719864351, 253084109, 21846546, 148016384, 177864964, 813811611, 177037415, 778026288, 905864225, 879014793, 319163686, 685948883, 816665283, 339084004, 899249783, 819146688, 527436856, 513870628, 788931159, 568653060, 34991929, 996765027, 920518752, 806700487, 959821437, 267997479, 181919380, 139427519, 322837696, 971247558, 898793783, 141034000, 47064671, 651861915, 35086504, 166109558, 528392704, 149618522, 262414755, 614472139, 486647147, 494254189, 245691628, 225397917, 771234796, 493281498, 429754018, 369102842, 284504182, 14066854, 922998025, 387087423, 401124734, 813784588, 523552982, 888063375, 2780235, 60383251, 184399857, 908693674, 629022306, 809614407, 909270088, 251625985, 430745056, 720630766, 246860881, 198878428, 757951061, 733440638, 736131215, 699313932, 337243294, 570704448, 364204858, 456525009, 954981464, 404334987, 705495032, 686919890, 216412449, 390528199, 383451243, 132400905, 261934898, 341733037, 985840218, 974034486, 114271227, 857894643, 534596624, 931659514, 595085799, 32830291, 39647797, 654163924, 528855273, 4163342, 290230882, 408652105, 536093775, 667250961, 389917672, 629092315, 999450648, 971476784, 480046574, 862846223, 520726960, 711900, 551892082, 927149816, 445714364, 920633995, 916583065, 768716360, 496190617, 891421291, 76197819, 714388753, 638722831, 933063722, 695983506, 213229474, 343888563, 302442438, 544403001, 131198613, 745325242, 100701469, 591768667, 400415060, 507407809, 865193032, 116359748, 899145702, 944023234, 207155618, 799655861, 345263167, 418005088, 411897764, 672510429, 22600415, 118787049, 998737128, 234312040, 781997429, 769722754, 831316579, 712871081, 733698423, 598778664, 220907032, 271960907, 957611509, 208440159, 861577264, 967238881, 411625980, 586601042, 31719116, 272335531, 600581978, 470750673, 987950526, 261726094, 467273992, 901983038, 538611613, 225652353, 793254257, 204180096, 378716572, 664448740, 693881871, 839899577, 764475526, 266600222, 929501041, 507376520, 250116696, 224669799, 457017903, 133196122, 924703312, 26239488, 405843737, 661202830, 220200731, 299764280, 639979754, 679137159, 485513356, 63525400, 660861265, 723051326, 194234073, 6189175, 4940641, 904873142, 493982596, 411368875, 745562888, 331404346, 509906787, 954521422, 32640292, 404850513, 701854898, 291710210, 690721043, 760483851, 637314822, 525861163, 593861334, 731510714, 111100769, 148725503, 951950588, 268641578, 655813636, 286432518, 728031645, 653033289, 154437464, 678105744, 990468424, 978122233, 925627685, 720559438, 802092890, 776725803, 973222759, 179535230, 433444836, 621585749, 683431896, 891600330, 153075488, 716239588, 363697568, 549660085, 734964305, 669861153, 337284999, 93266559, 279733320, 980731461, 809775392, 683093364, 113578100, 364170401, 826625648, 616117392, 601229389, 844131111, 996589078, 72602323, 871903812, 682176966, 571741668, 777999223, 244639293, 999577531, 704164217, 850885214, 561120263, 150580631, 110025599, 474258865, 479464651, 665203750, 983236011, 466079958, 460144500, 389127370, 746427865, 81175346, 141635259, 772278259, 522949561, 999375162, 440820155, 716541506, 693346353, 640408470, 630615834, 163022026, 393668813, 616828456, 229131703, 2412587, 12294336, 513863155, 140876111, 431352122, 34883960, 448972095, 140755480, 939015544, 734235693, 551521290, 396033048, 4149768, 727955208, 414964435, 947438184, 876884060, 326702095, 626269364, 527686663, 405861532, 657023516, 728828355, 258733585, 876808207, 243000351, 866023334, 412330504, 530377894, 785068463, 355837179, 653576374, 222767463, 570908155, 640734930, 949208833, 38831890, 731920276, 848804754, 695126396, 455630591, 498936699, 519308347, 82109727, 238067085, 218182478, 139574790, 180429266, 522210421, 77527403, 613613492, 590838697, 11926175, 502335492, 308404094, 616437276, 761371914, 184977032, 782059846, 280001309, 11927892, 524208726, 686121466, 858651710, 547028887, 624696561, 774823572, 472480839, 124316134, 326106526, 210819929, 644884489, 1343671, 245403188, 334936991, 262543185, 321538591, 716393651, 917848660, 764160243, 169767408, 609768419, 900707996, 998511126, 983039154, 450174782, 55504538, 547114589, 537939590, 103579505, 89764400, 499060390, 637576283, 922462861, 623051201, 270377986, 890402635, 262701236, 467001171, 159044112, 709162711, 815222942, 151003562, 818775764, 488131936, 848624275, 71450854, 745112634, 262682477, 37924678, 534928391, 665564801, 102683437, 846203906, 291332406, 68849837, 415595672, 553769204, 845982950, 21588256, 813561246, 240195245, 989724376, 535437375, 600102086, 451751172, 674976834, 313770734, 822853548, 600821898, 650905106, 641246955, 218427387, 224391087, 754727151, 681521127, 667766811, 244880664, 362950515, 733244051, 343444408, 967469830, 149423327, 719201383, 182089659, 986203540, 29011796, 870498989, 171732664, 514743605, 375666054, 333608574, 138562039, 862404750, 719025887, 56009660, 682539953, 746036723, 785011749, 665312701, 102991323, 109988203, 433332181, 449569210, 543381559, 78360608, 229422931, 316273687, 653128913, 291118305, 367033528, 354710556, 500897961, 219233984, 226576592, 838930779, 417459117, 292845441, 84602220, 675175188, 945473021, 517845033, 648078998, 160207906, 648649914, 375160597, 606199996, 471183966, 954393555, 689794053, 431031433, 150102334, 916610517, 905777587, 360890199, 850899138, 240630736, 443669701, 48433269, 824372388, 425664823, 285703100, 305334223, 361709041, 717817130, 179000360, 22945206, 346908812, 649624837, 20170505, 712450518, 363814046, 923670183, 638830024, 61696735, 535131671, 642997116, 149404229, 404135851, 825685775, 941723964, 489770264, 491059513, 225953857, 560213359, 37381747, 478195287, 62289684, 43088982, 511633201, 13573168, 590983808, 861413758, 212187091, 28766105, 88573500, 542767436, 814761843, 106149206, 109265322, 168139134, 39588156, 888956027, 963977908, 876801940, 808538325, 796205940, 98901023, 553111699, 251371369, 925993364, 275332774, 353717302, 929306911, 149942386, 458059983, 958895709, 296560809, 978477384, 300483889, 37755941, 752542151, 217790131, 498041350, 937603851, 145536104, 418403807, 523162280, 79565821, 185879672, 278844397, 285640054, 804754853, 112479171, 2861596, 462200381, 636694272, 513904413, 157177342, 836280404, 184367370, 39289255, 403856351, 610344408, 833280427, 181347066, 335687503, 462679806, 676084168, 62480982, 318662902, 201889070, 116884043, 680246875, 553070118, 671074635, 267975454, 957648018, 421946304, 857712873, 273649091, 529741171, 415926534, 528974234, 802612655, 399987876, 846844985, 309698160, 775507669, 903684035, 165577354, 839728227, 23314109, 580507739, 518326716, 339349883, 322917474, 403780146, 101248936, 183351208, 485183992, 899287009, 230216388, 476153534, 476180881, 126872321, 461482354, 209826151, 202199348, 861283539, 443326814, 140107613, 865756176, 766226341, 424330470, 717028809, 498299923, 608087393, 780066013, 998012147, 277589888, 636892530, 915263301, 960275975, 742789189, 869125153, 828401347, 67305991, 401508942, 266211210, 391178858, 999604450, 99821455, 669502030, 671713539, 43271555, 258296097, 246353842, 430770486, 60303, 223469743, 159450586, 27998647, 338201520, 795043157, 247235419, 268633373, 612391187, 181564339, 52570901, 236386178, 863242103, 7678825, 473458473, 318010217, 906646618, 879691340, 966178235, 75780991, 370824841, 116624861, 576549259, 944040769, 986195432, 824554420, 679196196, 799126052, 587662237, 561795735, 42355331, 108984884, 407828316, 465197912, 966481559, 893227525, 6795154, 746807368, 956601637, 842362556, 788793565, 825282315, 294503251, 66141413, 501306726, 554349921, 378508021, 67255273, 409932925, 132510741, 839067377, 544698248, 425052546, 454631494, 253882207, 282033677, 473613276, 409123796, 212259467, 219507552, 432051513, 134552237, 782589502, 104587457, 805099852, 621686092, 307677090, 149127423, 738555759, 37091998, 326275650, 383234334, 806427721, 751437504, 438843618, 520928746, 911631242, 202301160, 861926799, 326322946, 499263980, 828409281, 599841411, 867420740, 925785656, 28711916, 906146755, 649130256, 874456776, 617574247, 516321250, 971095261, 103859731, 197436243, 690601790, 777983924, 831308642, 499837113, 342843208, 866153407, 32770461, 215641641, 71436856, 581312876, 146890445, 383187688, 273693177, 724837601, 551716450, 494345814, 39520618, 680201151, 762771021, 956022376, 929320618, 509370460, 498283605, 160713860, 191768148, 586313956, 654163874, 79916786, 772788632, 422138495, 907028585, 733815728, 920722380, 914763921, 868362416, 148485132, 903114571, 798150975, 67457889, 646387851, 99708242, 632239330, 278591696, 179592392, 184729438, 287806359, 407219041, 784718253, 69721491, 930354925, 895201432, 687908854, 836338718, 589228052, 300509746, 494516678, 206697133, 378463131, 490352449, 693472309, 409918506, 220644021, 828277036, 173914740, 204896122, 606243202, 40301597, 153552096, 974330964, 660023490, 716079297, 815684250, 103558465, 982664142, 258809696, 152641969, 202591601, 163899103, 994906817, 585093459, 683591612, 201003775, 497576039, 262522396, 37828791, 277369834, 900994408, 506017878, 844237799, 723699604, 233804001, 899089482, 466561118, 528040275, 288406710, 836203606, 785980489, 628655494, 43261734, 207115046, 696365649, 705056529, 683643403, 641462721, 371512969, 834555095, 201393204, 879007237, 618142198, 549712120, 458219540, 717288811, 34860271, 822273050, 227705657, 525039836, 859952718, 254644020, 947105971, 142810503, 446633396, 780695772, 731581263, 623257091, 312551899, 233721043, 93523055, 437469135, 378941459, 160391489, 196704840, 77006501, 709463535, 419702806, 437283271, 295170512, 614120860, 936408982, 347034594, 93382315, 695423766, 270139380, 252725, 803344799, 85225899, 427296361, 555323618, 233133837, 918619780, 797357979, 352315640, 403758121, 699335142, 233637578, 344511428, 950881430, 758192197, 789669696, 205468194, 285105309, 197163772, 312368791, 621913299, 697228543, 875245373, 433117553, 284384640, 470179353, 8444376, 208744058, 372707189, 156194697, 406743001, 434400566, 364687364, 594968395, 695397211, 55948840, 683344559, 979069432, 534293505, 309084727, 187051626, 816628362, 978579426, 265658374, 600880858, 296245550, 542424593, 110739241, 10276331, 91621325, 388370316, 492914032, 276802354, 604366877, 623452743, 806858505, 449146410, 313894710, 886503824, 573383623, 855827797, 193668767, 386068605, 876146368, 675023967, 15696195, 24256176, 660023795, 30181978, 17584916, 691445663, 874281186, 767821870, 569342509, 935431676, 150373153, 563667042, 638663738, 902389347, 952013547, 898338050, 764972961, 260241056, 258424481, 174044528, 454714853, 142911426, 189317039, 486892826, 451274134, 967532401, 469461175, 226186167, 873568232, 24899818, 965102317, 642284849, 515462306, 508830842, 560504650, 758749914, 526600173, 413889574, 679064381, 219209453, 796923916, 111804355, 282087985, 236881997, 800834230, 525042374, 228058331, 893366181, 371136683, 909719192, 641056845, 97410286, 302853331, 810993527, 763514029, 306961333, 699679877, 257896013, 806565650, 537709563, 876754489, 748334113, 81995219, 157881863, 140842264, 670282077, 547985458, 64513214, 405928609, 994525577, 376947787, 304233154, 915511490, 863968649, 873667084, 122461715, 797712349, 375774139, 897830234, 971416937, 186664125, 107717316, 887630980, 378935547, 552317867, 823875799, 271799030, 549100442, 750932927, 181122136, 683205237, 953835599, 799411681, 161647711, 518973034, 458722690, 29111485, 726813390, 711840987, 758857822, 573611555, 90038192, 345107778, 299452619, 194944513, 4666924, 782941744, 54925165, 305996020, 469147598, 887746949, 348483533, 985127971, 508548865, 151477073, 868536934, 80821492, 933206658, 179469716, 425829410, 893897979, 34667461, 720672741, 160143784, 319860638, 198799829, 785290106, 145639426, 764012831, 540715677, 410956625, 391885080, 466611052, 874019715, 484318287, 50294484, 997290875, 399313346, 852020155, 105152784, 204170844, 219260526, 158512409, 707395269, 153696777, 287569801, 620145605, 482753765, 266302509, 215680523, 199117104, 743997999, 899779784, 950991754, 622097178, 420341233, 463516342, 501647306, 745975833, 113018382, 960022410, 291602574, 263962459, 188116449, 954094284, 382849089, 46590717, 348069866, 485389647, 508458554, 89525595, 233652481, 696516926, 24321184, 163872200, 735951302, 300226949, 248741928, 632317909, 136282234, 143719374, 975195597, 55208784, 564752192, 981124424, 223828321, 538830707, 711313649, 66974071, 437098027, 336175281, 590238409, 167356767, 526276073, 514768947, 868519304, 221412521, 816670724, 18801863, 379524911, 883331803, 242017101, 893190695, 82237653, 934864756, 852672273, 416459172, 246374481, 741868360, 280981989, 43715295, 405549333, 415067929, 820035538, 544928107, 866603690, 503156359, 547226788, 97248285, 22159204, 959837922, 403646071, 488036984, 345874502, 653887929, 189576369, 233490135, 478231519, 508179005, 25340513, 26478687, 810417562, 730620894, 607298558, 560947072, 235915960, 398674805, 565106168, 662628926, 312399783, 754856819, 585232429, 597194457, 305675515, 74459999, 377900109, 522643437, 228637621, 861375469, 336670545, 448349245, 829531542, 13531289, 358909926, 11563703, 538337238, 929960995, 192173963, 939460069, 8389419, 890620625, 531532432, 258499297, 694712933, 264653999, 386159160, 448095995, 67838328, 981277457, 348170804, 515999819, 262238375, 381082040, 572959823, 294562831, 87770856, 271361957, 591427066, 563210504, 70251544, 318825048, 530836914, 574371096, 396777387, 320126943, 497018950, 598846491, 438541602, 756191772, 853387698, 411348887, 908007414, 671603185, 269756636, 697390505, 369766151, 756858016, 956197792, 561950482, 404392790, 716221604, 43246742, 624350133, 526883941, 818821270, 365755519, 258826429, 898101016, 664534882, 259303149, 368628354, 37404244, 848104107, 745110804, 381716125, 339951589, 586708010, 454065748, 71316035, 515206090, 237836906, 968014943, 565825718, 890667493, 31226507, 508594272, 50955851, 503890031, 564294466, 197712730, 274175372, 593339530, 305436426, 51776934, 417045366, 690567719, 722347073, 121887735, 636846, 512102589, 718907937, 160650633, 414966735, 574292294, 260747385, 191997848, 470374250, 946488980, 641494831, 56205254, 932319973, 887660777, 958753808, 442171022, 589483473, 725592812, 244616412, 117573291, 647070249, 565860621, 858831203, 553639809, 56040835, 118411056, 164407534, 322194030, 419610972, 666942108, 25802237, 221901613, 39840244, 786745379, 676336474, 939300035, 334930840, 121542381, 690663717, 191409310, 283016110, 795501849, 282921733, 362047173, 377572928, 378480347, 316194427, 633424204, 249498490, 249628144, 895488240, 141289038, 272388798, 39463673, 45049505, 376528305, 210179894, 4017612, 765645235, 204981814, 135735651, 571614673, 113738763, 990547483, 157829164, 118386828, 341141042, 354510356, 394922004, 449842189, 871555953, 699194617, 670042312, 447279936, 582317882, 1940768, 98273502, 776115414, 78997919, 190916599, 802764879, 553454346, 103954446, 835339133, 878234966, 854172638, 310481275, 566555306, 4827650, 254452092, 829095682, 858395929, 998156182, 414121733, 576247307, 981597730, 865373827, 490714776, 496762144, 491743134, 177607724, 630245385, 893315060, 732826454, 488915486, 533315707, 135071200, 136067571, 919534489, 542487929, 706386933, 590939102, 237893857, 132938132, 107694361, 328898991, 121484995, 277681880, 107860831, 336585002, 586712386, 273320974, 162940780, 159093931, 210861603, 390443515, 174031772, 947755415, 528380380, 600438489, 470851073, 22642529, 584317181, 77828744, 992573789, 501604831, 626911249, 794697508, 525999330, 422097790, 7017574, 449625986, 100410684, 416624579, 545678797, 1265032, 903335123, 249187808, 68331025, 385538065, 831521089, 93135389, 687373064, 806324465, 890752633, 63069127, 999375199, 222994774, 703575047, 866218339, 511820586, 183420397, 158491556, 272519360, 224179399, 537460989, 159633697, 747610142, 392291181, 499851857, 800942699, 94209326, 538402059, 86791634, 199726542, 496071039, 952316915, 911925699, 180388437, 561989133, 389876895, 754982287, 554988352, 561502683, 404442959, 185498990, 902861475, 235682024, 875047597, 353320622, 276889634, 753322412, 686129529, 817945105, 428840147, 469791041, 71218325, 329787101, 875838129, 824133780, 831832514, 379067057, 526981431, 226292434, 809213613, 222768309, 431381502, 400524577, 202870433, 845394727, 259955145, 187763726, 465121830, 346314649, 320618507, 665618727, 599905082, 754461801, 405389186, 857018504, 889477477, 651978919, 209143232, 569193395, 98921660, 361997820, 616528367, 855802305, 153283187, 237567371, 751406283, 593844100, 345130588, 599285003, 129063650, 113855211, 72587103, 590815347, 640765707, 421089207, 164922934, 385109240, 287810894, 168528536, 404808336, 486590084, 696469943, 608464094, 74467210, 838232319, 539089408, 396068999, 915599626, 362636577, 841602591, 580097173, 280703823, 278101088, 404871083, 914361822, 137309648, 268742932, 884288832, 43911715, 789872596, 892665295, 250479643, 577329952, 576315413, 506158942, 108852218, 504392083, 405531695, 534883148, 392198980, 882945432, 509397114, 471617656, 790704890, 411370532, 114382991, 372416505, 368471305, 226578505, 27875610, 53774096, 494946819, 50415946, 75099234, 269109491, 846265466, 861701084, 116827553, 346374561, 361055818, 895645402, 934792876, 850250270, 694812370, 787423986, 433399809, 245666961, 766188603, 23049881, 955543901, 905728306, 462235474, 82672144, 480670745, 741215897, 199563051, 385482569, 298635756, 851373061, 829327678, 189727707, 128912617, 963425809, 110802210, 990682153, 474363121, 871990026, 340329925, 482431799, 399925325, 255205448, 342079157, 715711859, 39847254, 904088100, 982786021, 478186541, 587438430, 330764922, 505339093, 860935445, 135183198, 769135979, 290394826, 389008135, 43429799, 982628510, 318762927, 500314578, 937054149, 487902775, 121372993, 13709225, 392449771, 162464475, 566184074, 531267749, 301477215, 624785468, 389341419, 385435134, 227322135, 801781926, 188104232, 283196615, 160365113, 581056190, 317857363, 865785190, 937913028, 126940639, 560715083, 826826858, 696527655, 228660818, 341330262, 490264674, 99035217, 956769417, 43415017, 626974220, 484739338, 398044696, 629066880, 511035683, 917652682, 816666236, 738289452, 562023190, 763721953, 811347185, 872413421, 298962947, 683302008, 806492002, 311288274, 758878112, 781642740, 546929653, 86838099, 347954160, 410800277, 708019071, 428796195, 240381087, 111249697, 470521723, 878004287, 749893101, 926115153, 766918872, 313384902, 282514125, 693559512, 410619175, 550574002, 407264197, 842111779, 659304626, 408802622, 365498663, 789707351, 889638136, 334285344, 494976651, 968668286, 954846953, 368720128, 760936126, 831181971, 552170313, 412087386, 572626412, 143030824, 786996318, 749700913, 762341634, 114337125, 628008929, 929185922, 934028724, 491686710, 771401120, 325826225, 202348777, 615107456, 273284693, 600543652, 50752360, 126805969, 614737460, 636765451, 647109158, 94437640, 788397681, 284207207, 382573419, 929742652, 175298806, 716723880, 108141843, 166305017, 616313653, 74722255, 555618663, 518007720, 586481551, 651507213, 488005339, 620294443, 717100095, 9717322, 357740149, 671767197, 910916252, 424069911, 599048828, 869717096, 529228725, 469225815, 515460374, 594338267, 520333183, 541090644, 912264580, 904337760, 231987686, 862786820, 802363828, 537763354, 858161862, 792479596, 852123267, 859618453, 578460562, 215256569, 985573552, 967853472, 646617428, 91309097, 862662274, 110458276, 662116844, 693710585, 168520340, 432655071, 932398443, 976468558, 68592319, 721838937, 730171891, 248385497, 708534510, 163710167, 292095449, 650717376, 384781381, 743704575, 967799158, 323357458, 682193918, 274946255, 995632778, 269137745, 690331831, 359002061, 938163282, 700167185, 441672117, 106606811, 599862772, 634798515, 994372954, 663848195, 594144281, 927632734, 551702665, 329759823, 490147282, 859850790, 760227946, 453739783, 543959965, 579362595, 823994490, 722053778, 677036864, 449909459, 495166545, 730780537, 155549731, 335369447, 570066131, 704098367, 285469967, 987132026, 559732429, 540410959, 159228312, 565909814, 895746125, 770040567, 197382773, 78676379, 953438936, 603004260, 500936672, 218021666, 108803126, 962280751, 493199984, 275799633, 655325422, 117544957, 67882297, 832840614, 895904863, 161439503, 193914677, 999811802, 271184450, 223965536, 321557566, 604804816, 464713825, 416286916, 717398357, 708059032, 592207029, 140214521, 941799187, 319151700, 15291444, 847182472, 417155278, 863201543, 587064960, 238506183, 836526635, 249795870, 81061827, 272359471, 545600756, 371697085, 763755565, 232618784, 426640390, 402728803, 226944363, 70831802, 82494286, 47171629, 763751272, 877549282, 305117867, 138828288, 755795023, 289702146, 678986457, 871810178, 67193163, 120052191, 954786038, 747466406, 370056051, 316177627, 678620700, 479497118, 251778792, 151857509, 7077282, 804770544, 12116986, 303816762, 783125253, 350517603, 46967405, 724105147, 547380804, 666863832, 807569095, 40346021, 800106796, 661559140, 665173898, 280463093, 31074576, 322138290, 599321817, 725887140, 243145555, 760727039, 915643557, 747028016, 361042556, 894809813, 577086541, 989451413, 84956926, 38888761, 665232001, 904241394, 931570960, 258546120, 53961456, 635979889, 345007332, 797931551, 918889723, 728512363, 27100800, 303917354, 62805133, 654051042, 655533258, 645278238, 724238932, 589514164, 805328818, 158784661, 125486099, 219091020, 304643090, 420468971, 757453148, 560259634, 727239974, 903087849, 699986947, 675949719, 935997518, 582924635, 336469611, 614097112, 942252990, 199221366, 831072648, 587643128, 385735445, 168142593, 556922810, 417405662, 329065738, 163026156, 840396234, 607539188, 374843690, 669697568, 316305352, 605653073, 472444499, 799289649, 5532541, 650266281, 908555849, 933138546, 860990846, 623466296, 109796920, 584498060, 350025516, 838413983, 56579103, 434796545, 696928870, 174463777, 102883399, 641519407, 344379012, 227243608, 885650530, 984889845, 872409764, 122494110, 181658728, 589283123, 35057101, 47380874, 721999086, 457605499, 124243585, 41419963, 59663770, 874399262, 367747447, 928452355, 842944276, 508718153, 121126902, 46827602, 515091845, 221428344, 481888470, 567414921, 473194436, 209389437, 228873364, 321061797, 841760778, 985486962, 405734041, 315771199, 451485835, 314407439, 379378607, 389414735, 287736463, 449313374, 140468628, 388856224, 956381493, 718303417, 58484561, 602398830, 664838024, 686643003, 613603750, 416297718, 281437202, 283723289, 993700708, 446290658, 177070294, 465380303, 20893500, 263180947, 586100343, 641350356, 568064335, 430067240, 814200544, 3567442, 678205760, 963812405, 5454662, 882118012, 989033018, 232020473, 802258265, 616794291, 75840527, 446564186, 60370171, 377084395, 45837857, 254027712, 863258937, 633787774, 843307359, 901566376, 458479242, 908727799, 111114474, 79109951, 937722111, 489669138, 457376752, 355603028, 739521490, 458955330, 810060311, 257754372, 283208811, 932651230, 969919994, 659432050, 227733030, 374222468, 460275823, 969601145, 462016313, 503905488, 206081523, 783051750, 972220761, 384399402, 709208064, 882127022, 539417312, 660275008, 843606073, 753053480, 613537001, 635216179, 160997453, 131114301, 471532844, 20051654, 632054216, 119474483, 739361674, 387434727, 388506446, 720667059, 542357321, 30562057, 254434164, 507337002, 293416315, 113940441, 333855272, 838517635, 236620935, 986007058, 438968291, 537442288, 639470852, 871837629, 316479540, 46933564, 35774178, 129419506, 201279556, 821381798, 778839415, 886105382, 344307782, 873550367, 588711921, 776177207, 573848830, 282660687, 580938295, 581281942, 667751962, 690934143, 346412941, 101867075, 372732157, 699646389, 323269763, 314915448, 466933915, 284770712, 671865971, 955139052, 760113685, 884388647, 100895882, 915695156, 468675065, 540590271, 290183982, 815685406, 160613378, 355143423, 313432517, 857543316, 462823962, 734821719, 497243277, 29162460, 825376784, 782906448, 406882721, 908727777, 407875032, 60288004, 232623240, 734861264, 663842988, 470879842, 507767374, 775478191, 75193663, 155859958, 915445869, 707415831, 261309633, 622736095, 893809054, 576939527, 351804799, 648225574, 501509789, 815979444, 766622992, 153700874, 395358500, 713865332, 581210797, 481445631, 549835015, 301304300, 291888950, 747924108, 410371589, 985582887, 571929626, 551675702, 956029061, 82402804, 104893878, 66460170, 145996633, 653756537, 76854097, 522675148, 857601709, 315350935, 609872790, 743056100, 10290668, 850978662, 646002570, 942132543, 457137174, 953034925, 626565588, 956796768, 168671130, 618518818, 482762276, 756169102, 773830852, 564770931, 156236886, 913541838, 198264906, 261270788, 700151910, 982850738, 807514705, 642484888, 268814421, 973890390, 332393578, 256226335, 548032193, 746276232, 14965220, 449203065, 475591467, 450927734, 402836993, 966379948, 487886229, 565109301, 109377857, 330244610, 483285356, 675611747, 149415529, 587796778, 558422809, 460546550, 482836461, 692763117, 368508689, 388202470, 60954542, 808758825, 562888743, 572765398, 733029857, 861904455, 239842326, 667100302, 193139094, 842664278, 496588707, 442737485, 865708308, 240037998, 339091539, 644030248, 217276417, 547790371, 777551319, 871591325, 699568382, 256522539, 363115456, 578090236, 20691150, 54493771, 509875932, 832788116, 83775256, 95923646, 581934307, 137616677, 231504737, 957746752, 29436027, 59584405, 451413067, 54874763, 816668805, 671229567, 930790237, 159583389, 251518215, 25264721, 196288042, 852221960, 119796398, 784199117, 157766725, 376689328, 63975925, 653565846, 275071181, 320602829, 724419619, 242348220, 942058090, 234941555, 699563922, 722092216, 389102861, 996276086, 651949173, 939328987, 266073259, 929687564, 337930201, 321325573, 559323711, 686055839, 768403546, 743141393, 453550650, 394859039, 379778228, 738944807, 748783687, 980799175, 652027468, 659289120, 137657, 216327066, 64573497, 480953810, 24610623, 75075422, 423231718, 429223716, 102480287, 623920276, 50111737, 188594822, 60370349, 278101133, 263020853, 305671423, 470437590, 862999123, 208103445, 810865801, 708568586, 191082083, 391324720, 478227104, 723267228, 684975202, 125713971, 904206207, 192777025, 966349701, 72157773, 660603727, 777805510, 408625874, 663706244, 817508868, 34901011, 398931444, 218679528, 658381318, 366280942, 858991986, 936707950, 558481535, 985562464, 549532782, 385267796, 293846877, 457953406, 938874690, 437185270, 797469272, 887022183, 252894543, 88926513, 170406627, 735104856, 512459895, 208178933, 871797316, 473165858, 301399145, 209816870, 598145315, 309718012, 796305091, 498066683, 17825754, 550528081, 621451166, 649476299, 355783481, 741641622, 759341721, 433099985, 501565184, 88932769, 649961467, 974813613, 675047827, 116031492, 32019323, 767376963, 86999109, 19121768, 474828967, 358541041, 943322613, 982108093, 708909189, 835302523, 726689511, 999142504, 534362710, 316045480, 34619127, 575619520, 76263275, 969949501, 114708174, 540281884, 622786878, 957492434, 350849804, 179298647, 313241771, 162586442, 142158064, 514242080, 868230450, 820659724, 857540468, 785191701, 362891153, 486150784, 777170000, 492026078, 798039520, 185769037, 753102021, 853606422, 427625100, 639257235, 535604816, 995321504, 262393481, 815388674, 422697295, 48147555, 676761599, 154286519, 48577932, 815833710, 884125321, 632970074, 894235738, 362576464, 159328838, 35430185, 729499639, 436266769, 776649271, 120118498, 570513597, 701421691, 115980820, 71416763, 579528587, 987804530, 484822013, 243444711, 880587221, 922859164, 884909783, 851959317, 29399536, 369343603, 505732731, 916593763, 510131119, 540801054, 653184030, 187753011, 928711041, 709847553, 506088485, 782679315, 522839078, 418168965, 709002609, 90270500, 248660466, 560190737, 32571711, 230044390, 932438923, 976817630, 939838531, 544197230, 775711724, 333606106, 671129638, 597233748, 883892508, 669845183, 261336736, 922978719, 795998337, 50608423, 246799393, 624467322, 59178255, 24046132, 703440979, 712409682, 85546089, 852088556, 42170354, 948651642, 984162856, 237823862, 421154555, 199897334, 558134773, 607149313, 638523761, 833666516, 991948550, 249494963, 757449586, 442347429, 76119307, 390260552, 884504379, 392681516, 166416488, 649194582, 218541808, 271187088, 383291635, 796279794, 274196696, 684405333, 548472713, 906051184, 751054300, 485586257, 144386271, 888344929, 74748512, 447809936, 583446762, 19581893, 894152515, 390460861, 488528169, 652798618, 14444536, 175632075, 987455175, 295097537, 973540034, 460323872, 105249470, 649043995, 776676652, 282150216, 714310662, 718779979, 398223952, 299198175, 328991635, 36393279, 340221541, 827920729, 457381378, 684680628, 929119244, 22354383, 789137600, 650408687, 444549636, 553665248, 582612189, 555590739, 212253201, 965989973, 594239168, 253608745, 995768864, 457435154, 543035078, 2248885, 654759280, 834849662, 309274846, 530083128, 366691311, 660961255, 58619697, 728295044, 587707606, 102357175, 310094318, 288080786, 321338701, 1182051, 220156242, 328295173, 592034956, 901287287, 747865792, 188106321, 589912844, 852171067, 740059286, 357949380, 384644691, 588978300, 523094135, 217788490, 89494962, 180234948, 736656731, 318943299, 160499898, 291398476, 922693216, 777437558, 624086432, 148456182, 830642854, 251624795, 423970932, 202949644, 491732252, 565132469, 456316311, 27294474, 10035858, 53525883, 451859416, 643412752, 733328874, 969411146, 822300500, 762025683, 207013906, 770417506, 488161061, 463677463, 322997933, 315725620, 319380490, 85540312, 434546554, 387080446, 197991575, 300705099, 419718760, 40408396, 478262670, 871427645, 310941319, 648344704, 891769098, 237210541, 144998535, 650827289, 24862955, 856412834, 484581405, 770849262, 607348091, 844430826, 115986906, 425338034, 674728775, 778769777, 991953447, 783732657, 982255925, 836946564, 681235788, 798397769, 363445362, 925820880, 894609452, 131751947, 918886485, 167128016, 776091654, 902179214, 670994100, 889968414, 970130491, 862844392, 934921294, 290641727, 263990486, 2864898, 149750784, 876099263, 128683527, 886820246, 239679034, 949634624, 621345277, 818023832, 990247814, 435235006, 48977319, 453399809, 750024669, 285359138, 114144531, 807555322, 809491321, 162756319, 52291363, 934341339, 207246222, 118035422, 171790607, 857212698, 24839663, 499620264, 578997501, 345718438, 205937020, 82673247, 453471154, 231577118, 303131208, 39853326, 518260968, 569328908, 63496602, 488358763, 910109771, 21360296, 558002536, 704131473, 697249226, 711301632, 129597963, 388615960, 943869557, 143350160, 988547273, 676227895, 845462245, 886626767, 528137195, 513788313, 668898292, 269084948, 551154063, 807788613, 26103586, 310426727, 311339013, 834380238, 154493386, 483695126, 289318437, 586280190, 26548261, 7283416, 89245440, 360280220, 952577866, 816747470, 557028923, 802131872, 508060257, 620521231, 474537912, 744825374, 69604801, 308525730, 84695174, 591867610, 120212845, 175611464, 231751606, 446624590, 845826964, 430374047, 527783653, 969359864, 64822786, 841062228, 316631041, 826138528, 852049229, 412712052, 561206530, 121570441, 444847715, 840493482, 709945745, 848677410, 245960863, 479574179, 472697818, 715320524, 697320624, 720393157, 747239366, 729294919, 924468096, 295101091, 652083784, 885843515, 13371458, 148593491, 205359243, 734589082, 59728493, 884680624, 18457062, 822863653, 507946405, 973450327, 773557980, 496486605, 255558398, 706776931, 145377721, 406410711, 79570497, 939529110, 306324733, 486148326, 86785080, 476541897, 653840476, 757250851, 67489028, 126182943, 69140492, 29574647, 949491848, 252625109, 73599928, 672348729, 149095247, 571889151, 489380583, 826090102, 851865426, 848630840, 831143770, 927940860, 619503143, 129907681, 772739462, 794501576, 31304554, 311155653, 332351895, 333654826, 116503577, 73710831, 417918694, 368975389, 133068778, 354758169, 248430663, 15843119, 336985152, 295584574, 600987564, 636887706, 838429041, 188235390, 324880755, 388380709, 336657773, 879941224, 848384691, 36146591, 600276757, 728053496, 707376712, 111507621, 650811524, 575452974, 152463533, 490815455, 416086578, 168615573, 481769626, 952616323, 471489029, 735902093, 470005652, 652087958, 579245266, 616320015, 704325889, 969504370, 914774334, 503395228, 718377621, 800321314, 662138244, 6305005, 530296332, 981461091, 549347225, 599600263, 388860091, 186879757, 438495100, 617857424, 385653770, 90478742, 671507059, 254842250, 135901418, 733491512, 150922238, 379157592, 799451221, 233502622, 625804484, 466305954, 377490104, 688288485, 273241383, 309478424, 835594738, 720842300, 982357554, 115656373, 834676933, 430478248, 503143171, 173238472, 427571859, 921830248, 137338547, 821487827, 201615458, 886867187, 793265870, 367463903, 984268128, 298311787, 933911332, 565413266, 268896445, 839990026, 666091212, 881359265, 580118873, 678283023, 842096409, 170481283, 140151982, 488301253, 79449612, 456525577, 600833054, 468411945, 736193161, 204745685, 37032092, 370242281, 13723900, 706597542, 366170135, 553449206, 569296242, 123730591, 374694847, 699909675, 288651045, 603067735, 738244691, 508276561, 174868985, 490936549, 633658369, 463863416, 557658950, 170838087, 682390346, 808653635, 943357045, 550973281, 216486041, 225356018, 509775253, 289879348, 301573230, 959442725, 97256980, 142519622, 182283062, 9566189, 200082690, 866306861, 752394944, 759729168, 980275533, 420244172, 238861132, 906712901, 295687898, 404613276, 427586780, 381750141, 862864683, 1297251, 692368336, 331106344, 850796084, 299866963, 523052043, 429288334, 25186276, 356164021, 728677867, 170361583, 672968286, 575731929, 651875664, 309149936, 925208609, 262290293, 932961282, 982315072, 360354091, 299742556, 329332864, 999362836, 28981786, 194400579, 772952052, 470546122, 537154999, 169370061, 229859370, 965311921, 193023775, 742834672, 530940332, 421685641, 381773403, 232062151, 335332054, 892876981, 760258017, 85394643, 4113555, 464698385, 596152962, 71958802, 788346187, 454850605, 120047356, 516416623, 999972, 895426000, 728187299, 406064332, 782153642, 893692752, 594531964, 563093747, 998362760, 2470949, 745610253, 371912117, 864002068, 336961344, 667200436, 887467851, 596158984, 710380000, 705716631, 400482622, 88539067, 316535414, 348370305, 688635391, 589424065, 608234029, 859934335, 388684826, 102248102, 578087852, 493001442, 828276357, 687740139, 222207346, 508622193, 881707278, 728572102, 175115485, 815903101, 979166259, 882084880, 181803828, 848406949, 754930462, 284981828, 637872412, 927494091, 810928174, 488106964, 842874688, 950530136, 663699859, 136630003, 512462453, 57083877, 794411550, 128563213, 232761918, 342805214, 266664459, 944621031, 144624113, 616825274, 819704090, 110505496, 327014583, 188440279, 952664801, 400320523, 964563963, 873409756, 146866028, 828094442, 768323002, 857632658, 161127238, 315726244, 876211356, 22685653, 996418457, 326989922, 640691378, 217881742, 799952346, 969841960, 13203400, 396902194, 173428387, 214927456, 368687246, 933091033, 162047364, 888555110, 268534779, 628182257, 275119034, 712025845, 924630465, 680414136, 50237978, 82220767, 680036585, 344010712, 809251897, 708560156, 638102011, 197079394, 911366089, 253657728, 986003455, 796774641, 246833453, 948657485, 301873356, 945127344, 13951295, 513744554, 798339102, 741189932, 535287569, 613469297, 253605547, 1800560, 520562570, 277329926, 589477608, 455945981, 710430285, 582489850, 281384298, 503497045, 511891915, 327161488, 815717416, 152401285, 286784010, 905234567, 203714002, 196367122, 711385025, 381521303, 212867426, 808606469, 201490735, 571210428, 411262499, 487552031, 472149612, 303203536, 941803373, 782042650, 730217815, 873280843, 704363366, 274999822, 741983096, 81083702, 612976873, 662209987, 755129588, 747170078, 958476579, 573875679, 158311987, 923340080, 591023194, 125553023, 669213501, 675141580, 358827979, 810069312, 398593225, 214054304, 97179496, 402183501, 704891888, 408470632, 62893040, 850751525, 699273128, 638930668, 777603883, 178499229, 548549432, 863950270, 113794654, 54988280, 904685702, 553679790, 187502790, 168858834, 458023718, 268917259, 187500090, 449289589, 662285318, 596185633, 838091909, 913938334, 254746751, 693613635, 216642677, 822697343, 845363251, 495885321, 601677789, 839062432, 529507783, 64434825, 124296920, 987029009, 680068745, 127374444, 118834555, 2863136, 661605656, 303973869, 290671081, 268081302, 191082244, 105040655, 221594662, 852198801, 990747204, 350369744, 865784729, 92617364, 189209287, 877466513, 464106106, 837478816, 314890040, 99640989, 599094142, 532323373, 141007793, 494106325, 314313824, 494957658, 610530720, 445565194, 977675134, 4162831, 690435067, 304133372, 310901006, 295135660, 509659227, 76544957, 292505392, 268905771, 94637348, 2141479, 591349, 999751743, 50435268, 438766902, 319327131, 943603117, 945932314, 851492293, 353266066, 921916622, 34607418, 535111543, 779045629, 939234255, 704958178, 152340085, 803905944, 851486590, 764036824, 335530310, 141690159, 57300842, 978841652, 654983930, 577948888, 902078083, 11946615, 645331410, 673198746, 1335135, 929713321, 124805759, 781712942, 801702334, 60398301, 295550045, 808315346, 712263022, 893729223, 156088814, 896992956, 445648173, 281250759, 68744316, 111605468, 2694717, 811568672, 308290290, 667784634, 790379514, 893833336, 304567376, 546724975, 930197338, 188093331, 865622934, 437728777, 738051237, 949881258, 582849525, 421634580, 358930384, 433522582, 997444807, 835962371, 80001165, 703265196, 313693843, 883368708, 687318883, 350812536, 59419419, 319853683, 883314210, 730431335, 431816450, 654909009, 180773041, 817249814, 591226173, 817098197, 642037801, 164700715, 903855940, 110382893, 764489475, 786116710, 904138969, 684286306, 70076604, 688581605, 726297464, 875997579, 607050254, 988457175, 346361738, 94055062, 301162263, 468770888, 619303949, 924804096, 795592534, 472202399, 90961313, 862543137, 950915502, 702164228, 31069988, 501982936, 576484821, 123640743, 57857243, 760091545, 365487923, 131861923, 945679602, 968529643, 515842042, 143240508, 66563648, 468839898, 614832714, 379845205, 91238117, 20445027, 762640657, 214381176, 793464743, 326816402, 517970761, 86736295, 495731745, 256670885, 214985148, 644645537, 900415129, 833914612, 367176694, 990901929, 617592137, 373887206, 73800046, 787723641, 530025531, 303535023, 500286414, 183716150, 575715844, 216829638, 579272370, 772185652, 465263202, 183765672, 635682593, 637777438, 992250701, 365940458, 924368015, 368262148, 528051475, 235237149, 81920684, 359616699, 158143666, 716277680, 646724350, 976010441, 999016025, 758331349, 873601511, 616385299, 576177104, 716411532, 404772990, 123753160, 206365718, 556683294, 38244380, 228998209, 361418778, 918986179, 619334480, 618354149, 53220092, 687276283, 665548534, 409701167, 460966019, 728043238, 544502818, 235621922, 974329286, 20768706, 182976962, 427180766, 533108884, 104547960, 159552897, 416392405, 887195713, 782476209, 815802159, 128584236, 120446613, 656565750, 308140529, 80421937, 538256581, 400067688, 586391470, 709818641, 175442272, 776423691, 160106332, 52141345, 187462193, 465280658, 240836361, 953256800, 115517311, 650268836, 211828638, 581591878, 448597769, 653030367, 113127542, 136099181, 935743748, 785003456, 671853642, 314127157, 347543101, 485539181, 337266127, 137005206, 262483544, 89957397, 956274660, 489851308, 509217124, 699870532, 722504877, 687288149, 80958156, 923593965, 218068021, 779683339, 40191735, 904853798, 64763288, 406745783, 149493121, 640487989, 560485689, 776971579, 260949072, 312976058, 797959177, 926147519, 552226611, 840171430, 269432475, 803629266, 424979420, 626903683, 28257564, 449393180, 944641834, 559936177, 678731006, 184083533, 878856587, 269480454, 200299500, 667373228, 924250489, 665721615, 960238012, 6727635, 379260533, 572573842, 385211721, 475175265, 497021086, 358215404, 817942701, 929188049, 503698688, 146232100, 576432156, 410889648, 112733364, 356303678, 842731274, 814370712, 160788762, 126499371, 939376998, 659977549, 402128272, 607092080, 434298277, 967084681, 352728549, 758358634, 776552580, 755540341, 567726687, 530108302, 146170195, 874700841, 121065119, 68045983, 421747073, 583020202, 917379575, 97835452, 181505544, 499338528, 243817826, 948719477, 555265455, 553672009, 200744656, 51474650, 328683421, 629523782, 785899411, 168351678, 668699603, 831769140, 17817315, 425505758, 193139191, 598521512, 848386535, 199706918, 304962698, 941580207, 735919415, 972257645, 100240947, 508565612, 278143450, 705328572, 665316131, 276050948, 588010910, 469642376, 341002875, 484688645, 962061392, 583830187, 309310593, 926272169, 428866272, 354652023, 3942377, 836012099, 842534737, 579243385, 101811970, 675727877, 194676691, 713007107, 633957873, 528418921, 11853540, 74639221, 762966141, 952860996, 948616442, 235546288, 21619697, 417013153, 214490225, 799646544, 574538880, 64608604, 620334747, 313074201, 827563971, 285238441, 967787908, 834579147, 483507992, 548511006, 365595377, 897113666, 681185187, 419441343, 481039056, 701515035, 47359321, 711188860, 771636380, 19611126, 171606143, 964319888, 502443315, 85594931, 666389196, 930019124, 288342833, 280348017, 364967058, 1114430, 975099259, 157220170, 679655924, 242877600, 575757289, 919657510, 744878398, 355892191, 18217738, 903011018, 792775856, 881706992, 423320604, 794069670, 22744826, 317460690, 88979808, 510574340, 283456524, 708836627, 377388551, 823555837, 404458093, 670189368, 217893605, 517860330, 644814471, 193938569, 861430452, 7541238, 352149717, 460773988, 970420740, 126404776, 274799131, 597160490, 469110459, 191452113, 41674181, 665876165, 468257306, 367842477, 77877011, 766812461, 597496308, 227052279, 791398668, 941197176, 166215242, 943538232, 150425716, 794878484, 83852550, 76248764, 820932037, 822283190, 720308108, 963179387, 379901064, 204021943, 955364626, 708629417, 601716868, 945633726, 839883133, 519892166, 86541654, 903686202, 849233582, 671085109, 772010318, 674261714, 832231313, 352999885, 364959731, 467354166, 502094587, 969322994, 25040656, 81269788, 421601736, 536289868, 403165159, 633125706, 66191573, 436375500, 384762019, 8921969, 672114493, 309651440, 264117317, 196012653, 229300836, 419090827, 928629685, 620488182, 154509852, 212913607, 282020715, 816040296, 23919458, 332585290, 39807784, 421912483, 919148346, 114382555, 760429159, 608556106, 272592431, 9053834, 525518991, 810500871, 793745584, 167857753, 57890245, 271774821, 586873049, 348538384, 501250451, 800425893, 673200903, 908156854, 15077525, 577253498, 912815107, 38719967, 689821603, 840208776, 83744557, 12746769, 854356059, 12181646, 858503027, 203999927, 668765690, 878500513, 514946667, 876769137, 462915843, 920628539, 490646110, 617220827, 353842501, 797121190, 616024083, 317078773, 243343900, 433201206, 465311347, 71422699, 621646320, 620977751, 256953687, 768171628, 647404300, 536760161, 590991802, 121997223, 991614184, 923935749, 403638127, 355119757, 252331200, 434433516, 212430714, 322897592, 611649303, 798782990, 701933181, 155253372, 804778446, 486095096, 508308132, 185516057, 82078922, 531829953, 922361573, 561752341, 53546122, 882329757, 229680135, 100915974, 180043077, 734747946, 4649066, 837110082, 151157004, 160569416, 77680700, 191945275, 636200935, 746366588, 984738294, 959655455, 767135935, 128813184, 721623948, 371194415, 917347567, 525631953, 52106338, 765163843, 192607547, 913379742, 962891345, 187127876, 893368590, 735274037, 445718245, 623538902, 824274989, 458367351, 831845406, 239866828, 61216781, 740792994, 552661556, 251975811, 977836669, 198953679, 657600918, 351028560, 725906670, 330646327, 965458296, 246360167, 430574159, 791465144, 56784092, 102906328, 912843226, 733180937, 753327985, 772302032, 95114603, 450698020, 144309864, 614947917, 384920064, 781898902, 468321491, 746076617, 109265572, 773188399, 788684627, 268094882, 200107432, 460856640, 441692513, 891622547, 259011624, 509212290, 197603734, 174132604, 345871572, 981277905, 296265665, 668984997, 369997733, 490771800, 859426004, 954629915, 70508933, 392742724, 669046615, 575801843, 943982442, 351252792, 125208151, 199434927, 649343486, 354794837, 630252174, 213508909, 414154929, 228136371, 747422508, 777271407, 231117820, 138080547, 241423211, 24660981, 382456876, 369990211, 257661449, 125358109, 67859854, 795970385, 550974713, 188650784, 763747994, 120651132, 752872598, 137262124, 347455152, 934836254, 734641298, 723195800, 874312962, 40452319, 750784029, 40417494, 133686508, 255699889, 166405532, 152678625, 303370737, 621360569, 262871481, 954522004, 958894350, 453734831, 858477364, 163704476, 276040863, 708844007, 261808036, 757747159, 865376469, 571839548, 786741102, 138216288, 488206849, 836952556, 331226441, 597548259, 727195858, 224799813, 933379038, 222311115, 198059580, 763091639, 315258616, 762807618, 156958323, 766430167, 390052946, 801085747, 317258593, 817771064, 313221220, 481923357, 216483786, 195244521, 301970597, 878019175, 347649364, 227143920, 485764253, 671382009, 715911573, 176275146, 861348167, 85153845, 182100314, 347827171, 356951269, 417391666, 414547360, 546214212, 403662778, 603668638, 502834124, 853075596, 621937179, 316443278, 244946576, 518623090, 384688490, 840289246, 307052973, 969461252, 433218338, 233614531, 328397228, 356937106, 744713093, 311071671, 265062676, 354362246, 804349512, 621818942, 954035180, 638364979, 900466667, 567918230, 136369507, 725174468, 940771380, 628182590, 525502392, 127828451, 680802163, 107320586, 722847079, 879352904, 67804011, 427032431, 752692420, 702695838, 243993679, 977219270, 89722660, 185364942, 248944230, 830842961, 521142323, 33320390, 84717306, 789923144, 800297145, 927886118, 187890744, 634774578, 189544765, 129015342, 153737705, 628957385, 365099991, 174167704, 828007103, 121378649, 503935726, 384270805, 621804634, 225190181, 468631587, 517802716, 567113793, 826443952, 71195003, 163162644, 484066064, 673227034, 647206986, 854992382, 692629741, 51113320, 362804389, 709591499, 186042154, 599346491, 240168884, 978926693, 682674797, 210488673, 912868543, 115661545, 754348883, 12501460, 706703069, 226475791, 552120482, 845514533, 357882665, 982554282, 411457457, 593984292, 7495405, 227890338, 821503315, 673524178, 423928623, 451996834, 456163685, 548300219, 514954106, 925905043, 212748475, 255699471, 729916721, 112632435, 127778159, 223477947, 466095464, 184224332, 572791053, 270608009, 741375617, 753993159, 664793086, 579474172, 231951067, 658023479, 431332106, 754365140, 388638432, 164011880, 280519771, 501629435, 801615536, 185871542, 455314293, 406509295, 616482973, 961961178, 533425923, 701294183, 515940007, 546133033, 261226834, 50645875, 72226894, 942554354, 618813181, 170313925, 609993303, 865042731, 446998825, 656273234, 965285769, 93372471, 330430010, 235389234, 853140923, 262276171, 576711497, 370941423, 893709138, 295750035, 158846524, 885857280, 770312840, 574914795, 167358944, 377805141, 699519489, 937368857, 756570208, 495067860, 781471765, 18258168, 775618568, 288409504, 138380625, 401571496, 424479609, 632741739, 760874012, 973499911, 412606301, 294615803, 185458985, 534337307, 481048518, 422283636, 489875247, 332874892, 685069586, 863233151, 776952014, 182302781, 511798179, 627927289, 581795093, 857247500, 355819022, 684638353, 599793718, 553254780, 801946269, 231197388, 209437007, 408585612, 124231183, 729927899, 441864381, 485685119, 90268775, 715544370, 247200326, 678901835, 415422119, 853164222, 165836622, 862690615, 229412853, 90676573, 894615566, 566093630, 27103899, 830920047, 891975149, 278489498, 364770977, 548852133, 602105921, 699850000, 794738747, 364949085, 607735083, 508464425, 262147291, 200797204, 781768270, 840329073, 17084157, 452473519, 521346987, 176065291, 356764634, 990214226, 416219162, 136911897, 296393774, 200811956, 317948221, 566102589, 62059832, 667568085, 544619539, 37259088, 761920369, 935370720, 317441846, 772588905, 127039326, 913389303, 650564845, 124756034, 319784165, 920925622, 298540510, 925542641, 610229503, 466803539, 739233061, 879675865, 684556377, 247349489, 666448556, 820967198, 547051237, 878748982, 487998796, 340961324, 938236037, 467390262, 630834080, 599213990, 802071175, 652486501, 86011465, 930311830, 65625327, 929080173, 240323694, 283181862, 27315929, 369839716, 959883729, 466978872, 415118073, 194785891, 443556270, 885326618, 100201939, 311032592, 183147826, 993551520, 402165744, 779956175, 739531034, 931614863, 290056024, 387469522, 386737316, 469126581, 698099004, 647375485, 700321345, 10038863, 406472585, 827217933, 622633663, 505720368, 988041145, 670112062, 500978805, 962738921, 642513765, 4621962, 301835372, 380393792, 155569208, 854365325, 615468577, 449306177, 81064894, 320440343, 975797476, 891832603, 227744831, 592639657, 227362568, 182432457, 344480080, 527249201, 310883716, 498458614, 477381485, 556383432, 996882481, 576267725, 799009273, 919257266, 852216064, 693860348, 275960216, 545670326, 368303977, 787399212, 237314144, 740120178, 544910277, 470769903, 879081535, 435063642, 192268681, 637572398, 164013629, 86077978, 94052914, 640301224, 245846347, 725172430, 770741952, 646324465, 872055719, 356735052, 334377377, 265436215, 809136749, 336446787, 318389058, 747357288, 271695953, 914300429, 216268272, 114685468, 859013212, 721196002, 380128039, 878718673, 311611536, 585506156, 457271396, 758677730, 389262679, 835862255, 48224013, 295105234, 460945779, 436259030, 173327372, 59885531, 306165110, 878444256, 903284231, 115560765, 677599439, 661973445, 746701163, 889803963, 890623234, 302162456, 447920254, 898197764, 574863291, 783583678, 591908792, 910470572, 826406487, 711469212, 40725902, 115483710, 55568779, 59053864, 676038743, 390929481, 18042476, 541362473, 69910719, 411146835, 103686822, 728758379, 510873321, 236263533, 124605221, 12929519, 596542311, 498732104, 35393780, 301902724, 478915245, 703280672, 533420085, 136447718, 45285853, 231770302, 837485122, 607094990, 361189843, 851657971, 404964952, 754432585, 576148363, 618819799, 405174915, 87298255, 772213436, 901863523, 753202946, 255843261, 963562272, 848366989, 786502775, 878178068, 177705958, 322807567, 894557192, 398734605, 346053307, 960916765, 565637429, 315445994, 587177009, 682416824, 746417694, 376278453, 612503217, 726115593, 830106423, 958102776, 953368189, 388951068, 747270736, 453447764, 860586903, 9991163, 121583837, 210906045, 990615624, 46162323, 210510833, 526996144, 980303915, 13817129, 759962434, 687202276, 25931626, 400304508, 58366042, 603759553, 671696775, 956157741, 898319879, 785978393, 756273788, 203468197, 790454803, 148480688, 47330838, 118209117, 100645001, 563092961, 918063661, 446356274, 156823576, 850528315, 520921802, 961200664, 826117357, 167140244, 615734701, 437169593, 443097258, 418614500, 715380517, 866945532, 511793950, 997258022, 531659221, 481453467, 305976533, 368416260, 145302375, 217754477, 424956265, 785141777, 538135517, 133916451, 193914643, 135884502, 538586411, 628619979, 988463000, 357909847, 634809572, 952847346, 631390208, 538408178, 85541566, 302244234, 905687573, 109257416, 111954432, 409346984, 48885269, 486631813, 820601187, 857481590, 252943304, 190513841, 359962455, 555918245, 222738361, 566021234, 660980946, 598103995, 348438305, 330688431, 847094478, 728324818, 299028611, 690265077, 999757978, 278999317, 586646403, 671335545, 992907265, 773375886, 789203887, 187321288, 950513819, 254082918, 85873463, 443881849, 568576368, 423455640, 313600472, 640232875, 744618830, 526949673, 684715101, 627722425, 956786619, 886408251, 390848192, 351828560, 125117381, 736593769, 327244043, 157746985, 877370998, 674587392, 386601990, 465175192, 468879152, 197494104, 999540253, 507855139, 811892856, 183717337, 756130956, 746121641, 549781844, 619118225, 650915194, 588089709, 348947314, 798202983, 394895921, 40420098, 164561410, 182035336, 435959536, 654791410, 917615623, 217038833, 28448867, 527223582, 730885934, 714436004, 968330152, 815433291, 961152238, 162978789, 717332277, 514342618, 754816274, 112802993, 840477176, 353423833, 696223149, 880989637, 508379926, 311958768, 148617510, 953316785, 939671874, 635573014, 698041793, 2090401, 148543071, 435933186, 627107629, 176803857, 637473307, 802738224, 291544471, 730239969, 31550680, 554833965, 437939187, 150697339, 156942867, 544033797, 864347471, 645061705, 519656175, 65126648, 810361137, 939596723, 742977122, 624391739, 702678995, 273056605, 607371221, 585731355, 880776136, 25593310, 560506959, 514394014, 642672857, 457301282, 726080388, 199707958, 677244936, 150285771, 129983140, 396153090, 141327050, 913923963, 435648851, 365001380, 493110758, 70166917, 465374480, 318394835, 631669322, 659695493, 242529544, 440066723, 285904618, 366893681, 209236263, 148092110, 387467015, 921266147, 467694369, 896311577, 571938345, 647807418, 812010802, 327058955, 996536064, 480866620, 38495645, 460752683, 389765416, 58411395, 940751096, 585024614, 113674812, 691736925, 572345219, 809757567, 169404638, 906886551, 159738863, 779482409, 247722451, 460342514, 114319116, 50689064, 532647549, 177707461, 757817807, 505813667, 207373386, 796632240, 802522240, 907123957, 51881847, 279956140, 921535939, 573841236, 766315280, 920234919, 757005215, 872763637, 704196636, 494744117, 396277975, 296307374, 591765299, 346181866, 192089689, 851202199, 758848708, 689864125, 940790344, 383715371, 985040208, 309171320, 59707461, 957620305, 107645189, 117397342, 586312611, 129044029, 8219979, 372638351, 191712898, 994420557, 24283022, 945733553, 413305392, 989254409, 333325158, 607557234, 767197509, 802631897, 463425641, 582605455, 567497737, 515603005, 682016960, 59729496, 893627408, 314284828, 797076221, 670506861, 877439626, 752369868, 198730176, 810932189, 928770848, 254457092, 122836855, 308740091, 891617304, 191520147, 241924709, 387211005, 547900444, 937669953, 246395318, 503560761, 168693547, 228653723, 711913442, 540912809, 94545408, 557984583, 1245078, 881748022, 625176489, 761990619, 114587498, 647809734, 41564549, 227051085, 157593465, 374937241, 105319437, 909149954, 666234928, 359496295, 665351675, 133544979, 975813521, 50670530, 280697427, 276268456, 109654344, 483471480, 298461461, 30643742, 535216927, 157460244, 268673226, 461080498, 272884373, 519031517, 609705266, 347445915, 451031591, 684196823, 537168525, 636681222, 528079541, 696493420, 448119539, 420583408, 642707458, 579304222, 907912475, 984834876, 267924670, 305665158, 869013869, 493496057, 707287934, 367297916, 242878119, 787763095, 692888343, 848194649, 522947435, 510252688, 691614457, 5653558, 725038474, 267917982, 970927080, 714560775, 777596539, 780114500, 128418688, 409984131, 966177155, 161811944, 218581729, 605950122, 696048715, 902192611, 48333221, 300108585, 849556709, 750081974, 531519311, 921586454, 169151282, 780706253, 54591706, 297551124, 513178521, 538794615, 549290163, 624433306, 585924518, 831558064, 276977174, 195390212, 243881931, 694618000, 460886935, 224867618, 19826687, 624714273, 208481210, 388312684, 334899037, 438323225, 981308760, 634520730, 263165737, 53200597, 1999394, 398618132, 401117491, 848815533, 484083432, 133022798, 126527304, 604519033, 354197048, 160113250, 535921839, 572438013, 853904729, 666394680, 4314266, 770035920, 60962035, 646284342, 148076328, 9481806, 431096385, 957009534, 261744060, 258044038, 215682837, 184819378, 568475105, 695673757, 81071933, 87992935, 400223151, 601186170, 717231724, 759361786, 24563984, 965552671, 287563439, 509356160, 735036164, 989412056, 817451223, 159743982, 800142601, 766503143, 81138167, 263344346, 27174536, 675339570, 248550925, 673136964, 746818768, 616594570, 306895125, 136576321, 782373803, 705150146, 583620182, 567862320, 423745907, 458207929, 267297415, 523519994, 20883895, 173086686, 823159483, 732596739, 273341881, 464529049, 240337120, 657974679, 671685743, 864128357, 444296668, 295842489, 133278625, 164737244, 221793998, 267795811, 369622611, 731203091, 482744217, 951847242, 977045648, 715219632, 874427308, 621853896, 526657220, 355094824, 917958978, 622075444, 569638030, 422447367, 690482898, 496339618, 402822395, 726689102, 417078909, 477323880, 151876663, 967053765, 147585035, 274446150, 174440582, 949203388, 493627212, 441544324, 697511244, 488194040, 90684532, 491471055, 707225173, 49033074, 662840348, 62026736, 665474651, 234210580, 985181622, 371061990, 55316251, 897767753, 524518235, 902804690, 329753286, 796531734, 483671824, 642764181, 587038958, 800256519, 386519747, 473850033, 969562456, 56843830, 829295437, 183344344, 624343905, 200122309, 997594741, 701610342, 778061639, 935484432, 635825790, 29787310, 185721997, 616876062, 808267554, 244897277, 697516215, 991922124, 488158531, 842977923, 171956098, 872659942, 874419473, 949136209, 908983934, 747494633, 389936595, 574246956, 911927175, 550388511, 658667973, 529139130, 400774404, 157530372, 64840786, 18995673, 879854357, 144819528, 901819707, 296111201, 710884687, 500237251, 364789162, 692670691, 781499559, 647742203, 136057253, 40877760, 432984110, 605546624, 401812327, 704075525, 943682816, 760415810, 488372329, 204276621, 780909155, 549570579, 324639664, 749962609, 362747852, 630788010, 561312407, 88553019, 935148001, 990230602, 33878177, 429790504, 783518949, 917362831, 269126631, 581220219, 549660531, 286570756, 927915484, 551822462, 539855385, 314750297, 297349519, 884721085, 223396889, 915065779, 176719517, 378124805, 791093421, 161382912, 841208577, 566933216, 454194914, 400917539, 134359473, 370969526, 739567083, 188876560, 317570351, 38065736, 379774550, 627353681, 387315004, 843069633, 208493545, 975294447, 996583705, 680324362, 151573017, 814310345, 974838269, 716270322, 570704860, 284109969, 784698763, 451045254, 895944912, 578827172, 393198947, 256579217, 9486253, 49790293, 381073131, 368145613, 650762095, 441007810, 873838384, 516696725, 326284337, 376396166, 527600180, 328813165, 101098978, 27193588, 239113048, 585344710, 354519745, 771897029, 920810308, 357894431, 468701469, 323919924, 82381194, 270464915, 431102890, 474901893, 436831797, 717243102, 727272610, 499276539, 657652769, 984908923, 47820084, 595719203, 482593787, 165856697, 967152153, 258371043, 565456680, 934093210, 653863281, 625176882, 272983646, 828986218, 734260347, 587053686, 120861324, 647043694, 596054062, 817413149, 465503714, 794080482, 310764316, 356874543, 118988530, 927568839, 403592799, 683321372, 706546719, 472737378, 86278876, 570060712, 307381633, 922471570, 254892079, 825775244, 970579456, 97702277, 708321031, 450421085, 453908375, 568497951, 747547610, 186236313, 648418646, 263353769, 247624271, 649564737, 905787261, 602709702, 620532995, 876488484, 187268405, 335680693, 830748297, 120991470, 90766553, 87948162, 111164151, 661328858, 312584865, 205898626, 822234884, 258531061, 357321364, 15164890, 928068383, 527654226, 414124011, 469832469, 815568, 848217544, 501545418, 67828443, 478410850, 13804170, 419383259, 237761910, 852420614, 422570665, 52350656, 293458628, 726019374, 29800534, 486958817, 14611692, 293978275, 214327063, 604667431, 143696079, 312889213, 325050671, 441677031, 284641740, 217726013, 144709716, 661620621, 949974702, 616654709, 299253040, 255499578, 284238890, 356537911, 86666320, 18958339, 275766219, 326616788, 243838931, 419136753, 952840052, 753741988, 985432100, 438530732, 245318829, 683782613, 628400481, 97889651, 340929468, 598224890, 745027202, 887595874, 300041789, 89590584, 746881228, 31677482, 1671260, 350723593, 11478658, 755803856, 346982972, 536993738, 731222607, 3045300, 561531385, 243423534, 19694828, 371561834, 359292423, 6137966, 352565297, 750484461, 778286239, 174830098, 881976152, 817305520, 598730326, 882119068, 104434305, 264522105, 915911725, 651516330, 51882194, 258305683, 343318582, 867581203, 971367235, 554004515, 304882651, 581331579, 311171959, 956371301, 942065047, 883986420, 321343475, 166843811, 467443638, 446409956, 459454543, 821233981, 753348787, 716214481, 74814624, 521713797, 564221662, 548688728, 733523165, 772429959, 303027483, 751146472, 350507755, 900042491, 934164836, 649105397, 596894103, 604472121, 44997183, 552196020, 83341176, 189832205, 918969369, 658979630, 27463498, 712985190, 752041475, 759393617, 504075022, 31835944, 295867108, 102066641, 43739782, 6950290, 316864104, 454874777, 757219644, 431459876, 394988537, 438443278, 199908797, 418897106, 302260162, 405822694, 987452674, 882352364, 134529577, 104081811, 176742229, 46630185, 611113397, 635298988, 479541344, 521782234, 299698442, 104545091, 99472373, 228319205, 285593215, 219999405, 85790495, 114622808, 85754571, 20761188, 165738126, 99063222, 802223371, 911164144, 978227523, 420603159, 740212910, 73420065, 880554502, 615546232, 627412622, 639541300, 647905951, 326794209, 235885234, 296250347, 786875846, 657286213, 320377820, 580938474, 432808441, 19986775, 358112824, 610893222, 818524154, 254985542, 453417629, 964618298, 106928950, 600374427, 630381545, 579857459, 38545926, 78919135, 237655387, 386990325, 324700885, 996694966, 248078569, 411790864, 692828411, 85340667, 710443923, 592476510, 380934321, 471225513, 324749250, 12484976, 60242425, 924517476, 725195365, 280177397, 794475745, 353518343, 989614164, 197169163, 872111081, 464834761, 776683306, 532554150, 768895915, 62869182, 452437598, 219001840, 302541444, 752835269, 952071863, 445535387, 289310155, 820429782, 237361532, 989877333, 460144375, 448923055, 885265985, 633254895, 530438231, 831244218, 733687778, 27712070, 848740918, 993504663, 326699861, 836103268, 669664479, 310513539, 901522397, 33051821, 632303991, 893736302, 923543055, 834316875, 321325196, 476539145, 685930796, 814224836, 510580591, 459580425, 309047467, 577895036, 597971480, 779788374, 243019163, 923014934, 984597985, 67056924, 439367612, 652797075, 358248243, 444896865, 986724080, 180089626, 397066861, 745639543, 589898422, 365061422, 819781638, 305903225, 757187552, 110266511, 102322451, 812443420, 37885197, 58543760, 91403883, 885580294, 358392917, 987515816, 743332916, 690056805, 360650568, 599156247, 944232572, 141153279, 656226566, 272734265, 334372738, 698043819, 339198059, 237481318, 370691039, 960721406, 523963782, 85646309, 647916149, 861437208, 551171026, 801897193, 597759693, 986657850, 491561650, 430819533, 771437201, 278117993, 853266521, 72943770, 415698551, 660575225, 956009553, 47209912, 634774852, 99368383, 356706988, 95262621, 405257738, 661414312, 713407022, 224992567, 236352605, 876469325, 74205017, 760722341, 489660432, 736971762, 301957772, 918015742, 386751640, 118676310, 331613324, 806378526, 991119333, 593728443, 530840802, 555648938, 845670521, 83163100, 797346650, 132946833, 655597678, 344513189, 148440544, 138896691, 232922268, 758213332, 408550671, 461099053, 299025174, 238560055, 232191711, 1817987, 191828530, 591381649, 291595061, 997659071, 974940747, 414518428, 607302492, 831543466, 286269185, 673441444, 64915778, 832420948, 558000905, 808296411, 296622409, 735203197, 255503385, 616408978, 704780680, 204650250, 492329154, 823257201, 501111114, 335221540, 161848841, 348499147, 540446496, 934363143, 560759148, 448972119, 91870200, 439129205, 667378390, 358492301, 931836913, 614808805, 498068309, 40702231, 817865615, 121361620, 805916696, 302956795, 409829210, 631374752, 432600906, 16225006, 219746147, 580116788, 576951983, 502908113, 675032410, 794783231, 489115197, 270454797, 341424710, 82427102, 12855211, 356104287, 745167169, 103714166, 303830227, 628476707, 599909630, 909435511, 978357249, 804868352, 551400054, 773403665, 571123889, 79267629, 875155648, 624458785, 368702020, 268319424, 670361846, 915551526, 708150669, 183895296, 788572939, 316523138, 526885426, 609015012, 131181436, 344558250, 249463386, 742971139, 710367342, 97922659, 118216772, 112696560, 102920246, 990022819, 412639922, 846961571, 752910939, 819055905, 762407826, 342471250, 100494311, 396911798, 733284191, 338053677, 822649216, 126067517, 492540699, 428338411, 536334948, 742189389, 782967532, 212382670, 933395521, 901020231, 325758943, 74039394, 557012040, 885526621, 222480012, 567430830, 516582770, 587380566, 804584563, 439101688, 247174651, 440394160, 491387855, 536762402, 142136988, 497189014, 316247101, 473509937, 916064608, 723190068, 58576229, 759957252, 943010084, 772799896, 112940466, 739103203, 578289787, 996387609, 735219686, 509621400, 136028973, 897877063, 775495150, 480810759, 21456674, 298360068, 132260492, 205639385, 735230457, 370313102, 431106531, 414902697, 405312500, 633716945, 706694374, 61062593, 293440740, 413103381, 723431885, 78557431, 193508899, 142796466, 897931095, 977088725, 727424382, 284129366, 213429680, 669577682, 158738761, 896511902, 654983007, 755551218, 365390358, 423199925, 351521066, 664859635, 978183364, 839570727, 13018644, 764468793, 629741049, 979086714, 58299830, 117247277, 53050370, 601946943, 178398783, 619087532, 579981564, 482287625, 405347032, 847249780, 99950865, 635527867, 208752096, 139516702, 845189799, 837760564, 894197990, 576706128, 1544651, 325454808, 558457532, 866949605, 790867268, 680683165, 240412774, 414506321, 885108236, 177497100, 555598409, 612299243, 286345659, 108997001, 7773857, 615929085, 910150531, 139658696, 917447865, 352813357, 652501142, 354992648, 900788601, 10386914, 267864767, 479555947, 535870439, 324964127, 93857234, 699776844, 877086745, 642988654, 901591058, 412690853, 4016849, 312797257, 556808620, 804635533, 572467759, 388629834, 182375879, 946286683, 445234670, 79206191, 602483018, 114170466, 134084540, 60512861, 660698410, 378196515, 344604287, 229186154, 333514303, 709149537, 900493439, 510253153, 41697119, 320604531, 693025086, 213796286, 696232428, 235262964, 220208411, 55090363, 800596863, 24931813, 789831587, 952456683, 178613560, 252971255, 330469562, 563181734, 88397059, 173455298, 152663144, 16123814, 61627819, 485448465, 17291296, 443794865, 674778668, 775234828, 235410832, 135808733, 647723151, 134904600, 855135072, 568273508, 762926453, 709695281, 585287750, 484390411, 323261426, 822870619, 182892591, 897287353, 504661456, 444530447, 924016961, 728081437, 243664984, 924572486, 251025638, 338724191, 686212498, 877215406, 111185204, 826421747, 641039418, 74624956, 576053786, 558520109, 732727343, 179533292, 284458619, 257867879, 308118898, 320969317, 914787604, 802078583, 538662584, 680261530, 233964208, 206444647, 581670513, 570088082, 210478276, 62324988, 639060238, 273029911, 775335885, 272463913, 417524545, 786242319, 710805201, 833965016, 72351902, 108426601, 892239017, 905517815, 344827966, 296253042, 620177899, 23355657, 459263251, 606255083, 146112029, 787966483, 783653345, 160214216, 159348261, 968087548, 983867297, 233784630, 184477489, 323759084, 393730436, 151426679, 305904842, 717855455, 211870954, 389512887, 939967340, 827464686, 292841171, 711858746, 823849237, 280035419, 733310668, 173480353, 780896755, 50072720, 301099132, 422404581, 112283209, 573892974, 626579788, 269545204, 765693483, 24323349, 420955892, 65021042, 495388143, 574461368, 271208700, 394805507, 662498604, 221243389, 540635752, 11552555, 437757035, 468935726, 796395116, 487656707, 676163936, 957464568, 36341008, 600765927, 22269158, 457774320, 288374091, 684238912, 849092960, 920036957, 819668243, 800336675, 499168444, 198746084, 817569420, 928329969, 970952489, 371589027, 338448022, 322666312, 519717851, 836959947, 9907794, 164097761, 568042632, 214802858, 678004381, 286430637, 992570100, 19181444, 328729739, 106912533, 606890795, 514694449, 727331789, 895839911, 133310644, 282861013, 623071057, 321350826, 69212367, 211333458, 580717296, 812997605, 81749728, 892522850, 768767813, 425503954, 409886412, 822138490, 433746007, 869070715, 56420080, 592697351, 107561631, 514005366, 38650225, 84139808, 768754096, 566777322, 177010647, 137383859, 385913398, 898303587, 121173656, 701421407, 909058585, 789727755, 977834284, 897310004, 728118369, 335470792, 943511050, 187218921, 22237963, 199497241, 248501038, 659575342, 104235320, 707879807, 720256815, 245061071, 785113114, 537970925, 715267859, 379679188, 685593418, 327450899, 392708680, 920630492, 733288766, 300327675, 476548537, 998639217, 923660646, 436439263, 324205976, 363175755, 403534005, 306883173, 824310396, 869879941, 667146023, 280031840, 796016291, 635041725, 658742833, 491657165, 355680472, 951726916, 989540942, 836326717, 939833070, 776847186, 193289702, 294461967, 82619850, 60860300, 928043127, 477977493, 165710566, 914365462, 995980341, 343136032, 90233426, 13611272, 689526356, 35978899, 463981796, 140801006, 248003145, 835321405, 185337412, 108398161, 548024918, 989149461, 645307252, 5380836, 807797564, 579106795, 568569866, 380465425, 459356618, 73767856, 677892960, 80498669, 195360366, 426103484, 175682630, 437987181, 935069036, 538799809, 633909954, 572302817, 915471643, 388207255, 521275395, 337693106, 457889018, 563778715, 652140907, 179411958, 698562073, 240774992, 248786612, 127023438, 545360499, 746832250, 18170699, 884502093, 37303660, 908883082, 571785310, 411771820, 872055033, 844081775, 704275894, 824096395, 219399712, 378445714, 251395519, 477617293, 671973887, 241518783, 131090990, 840446445, 301177165, 156210240, 333022958, 3192731, 774861298, 155986388, 453267852, 711617, 585630619, 92659602, 864316340, 848628522, 666863156, 830574466, 618944857, 425474008, 505299663, 815220718, 740041383, 816214145, 316019340, 804849617, 420827506, 519546947, 876049795, 654902817, 876630641, 700978326, 61530120, 330465435, 333651301, 566284668, 592549604, 959626515, 583213159, 66395963, 568617965, 686315155, 453132358, 857906068, 687295088, 294060863, 799289154, 162757154, 790002739, 454480043, 12666978, 679801166, 599229628, 468751706, 762738123, 283672244, 977248598, 356951064, 571646189, 264068791, 821903212, 410640238, 256179732, 63594737, 600067230, 207051349, 182029658, 607358483, 177033201, 997899168, 500069399, 168505395, 629110123, 420424144, 949551131, 824165771, 962777584, 373208997, 104090816, 478923170, 221077798, 128570961, 145912960, 981899230, 60583643, 613766096, 1704574, 604542383, 337869993, 174111551, 410613409, 155887035, 686942662, 419154768, 737721345, 44890188, 916593602, 880865502, 799817608, 558378465, 588022829, 569707550, 272090928, 175588406, 299456067, 180850149, 736410209, 671269631, 242134254, 906977065, 841192968, 199781523, 967150392, 865105712, 131942856, 666160659, 537660061, 701040502, 858137778, 88251599, 59142484, 497908243, 420562638, 249311640, 332130815, 807185532, 863987388, 947179332, 127268110, 518677718, 161060094, 359466166, 718661099, 727113483, 511171308, 903610218, 462561052, 600765720, 635185715, 276648126, 590569311, 681268148, 438630396, 350231744, 445486599, 443257589, 788480222, 762991224, 810693551, 896158308, 855827168, 525317748, 392913018, 882761310, 374639594, 232477023, 715726557, 436772744, 358878379, 17279390, 718235166, 551026601, 16838031, 683542014, 67677216, 456065639, 59106736, 66888627, 643899384, 388907818, 965992430, 26921542, 666826256, 105915905, 888572779, 840736794, 863811043, 832441302, 720893853, 79070635, 342743427, 94954376, 642699742, 554968969, 205747997, 871813874, 810011651, 506289750, 83954973, 580467563, 920314194, 527676354, 731374748, 844149064, 276493967, 834314076, 153922382, 807715001, 863117700, 765815888, 961303326, 43293397, 497534953, 693587206, 576753720, 827608656, 167038898, 983166250, 940898066, 580051199, 295106261, 936367460, 983087843, 390323296, 774586152, 959280941, 50388562, 17108282, 218667944, 37119529, 860389534, 504823166, 334476837, 581242659, 918610637, 915545032, 576129172, 800041069, 888808157, 506169091, 514238320, 192770097, 742851950, 653218561, 862601942, 937673048, 673646485, 528496788, 276167648, 318434198, 404859828, 347834846, 841740970, 261598341, 709685785, 158665761, 210610216, 974277618, 879362040, 223843324, 257566788, 536845835, 889246647, 871100347, 946409423, 538941836, 726499714, 660724271, 541179202, 555749001, 328444583, 718498314, 297905562, 841721146, 514883199, 654448574, 448772690, 463082476, 707397089, 437957552, 582806768, 424830342, 56561623, 915601750, 845299336, 768261243, 635349170, 531202771, 842805375, 912631756, 729413261, 566015887, 203395006, 152084576, 90083875, 374147403, 720187669, 688348814, 916734377, 629750449, 95008013, 605543380, 120281466, 494826355, 466611294, 49826449, 747315403, 327553847, 305504744, 139454721, 888716440, 43628456, 185168169, 836217622, 934062024, 31766705, 798153732, 101884301, 348885886, 514183471, 455548953, 107462261, 808531539, 280852421, 628700475, 84435132, 611261531, 989400793, 884409089, 692742388, 204609641, 882063510, 881441942, 753210155, 940651702, 24763471, 195303566, 576116323, 93592586, 832954372, 339386750, 237905318, 117990678, 934190248, 166452142, 818701956, 119401173, 232848221, 920740642, 857001042, 34081986, 524146605, 857196076, 827946374, 906377721, 698001261, 552206023, 97130879, 462926775, 264444091, 546330635, 800180925, 198396135, 918926477, 701060133, 752320110, 734785984, 411488958, 971484854, 383551877, 752918602, 941569865, 883207445, 548485186, 449031696, 462537437, 333062187, 954513523, 483093646, 374966365, 480652023, 225744180, 374507797, 202142202, 448806093, 907710935, 334208402, 919195597, 968577397, 544733620, 56788784, 816525405, 931349200, 659904337, 629075944, 425844170, 806175794, 788368617, 235999955, 309925724, 740664421, 201650903, 495807744, 501844093, 628316455, 989669215, 175739953, 31203847, 719606206, 455665501, 428689109, 851849941, 852443290, 873361332, 181885293, 955514550, 988539784, 655876606, 852593033, 293481642, 847715147, 276057490, 608727799, 460475235, 313040815, 705197766, 210492388, 750709646, 759695660, 430703017, 989648185, 868221080, 808064785, 899239079, 704999950, 660618662, 761253510, 509031607, 847917617, 70558722, 335503018, 477792329, 866245981, 401683292, 212256839, 844122200, 714694192, 345986851, 96248716, 127350197, 144603685, 79181316, 858694947, 753769716, 26220105, 204871252, 672392670, 82522465, 164520551, 957209211, 553679097, 580854539, 277878716, 547693500, 514218627, 818265363, 600319116, 747760708, 472725428, 391037914, 412128248, 593680918, 891532586, 294329528, 427822056, 501022770, 295664308, 943725404, 755817620, 535354008, 11017185, 336883678, 280146552, 54079751, 588111275, 15992588, 213874832, 808488789, 406348796, 97034570, 108947817, 378397859, 690286005, 954829816, 99157173, 166689078, 854331783, 838084576, 435662454, 612085307, 673654662, 75147846, 161548628, 326791458, 477813933, 647331091, 577296391, 295952584, 66197318, 393128935, 696336717, 399292929, 763429637, 310052515, 215206090, 625221014, 684133843, 331354319, 603623268, 994760022, 62016666, 458400282, 219704557, 369903352, 800805722, 233454352, 175605277, 711727316, 179686051, 761614073, 479787393, 261380186, 960837742, 816343412, 634394062, 157288630, 352983269, 349275055, 26795648, 954228347, 629550368, 598617059, 181374741, 230060676, 424802287, 268551523, 807032535, 379967023, 590771285, 935025334, 993285194, 882732089, 861216268, 304980336, 986459522, 365875090, 86237315, 770330515, 522400230, 113213622, 533150057, 290428017, 779254994, 749132961, 203101591, 699463446, 639376477, 369639288, 201884237, 976639004, 256689264, 851438110, 174283323, 759321804, 308508794, 2641050, 356309950, 62656215, 591763680, 463510183, 980362619, 799784418, 597425837, 37984058, 313691434, 32715280, 741132545, 260536552, 17692658, 893581230, 911043662, 471682327, 150964071, 707296484, 98052501, 741516705, 823661758, 298305573, 123465009, 136833896, 954182432, 874997070, 899589771, 993801240, 57841530, 774123521, 844648525, 745311138, 596437631, 375887082, 351162903, 398863250, 429145734, 171314145, 206421469, 553903650, 64749430, 642456760, 929592674, 690225230, 912568402, 677796653, 473081415, 712345919, 539176745, 877420683, 753714876, 155390656, 634734065, 841966671, 663571948, 259134339, 656289662, 959329587, 444615906, 803538188, 376463781, 973787486, 168961667, 129840203, 195854600, 550443823, 255236370, 869376438, 258788427, 624853363, 939937060, 362521401, 153930121, 990859704, 791213959, 747086955, 252210545, 157643522, 449629804, 248982371, 787803669, 847305837, 460872674, 314998004, 233270851, 69826095, 647597278, 862799271, 679105054, 614067195, 591477176, 917113307, 904348797, 139575754, 750499393, 371469229, 66394491, 370339657, 538376813, 327033342, 285305454, 674643841, 593921326, 978741197, 948105338, 229476931, 278774346, 250151123, 910213313, 53520620, 665378284, 63779821, 214883571, 906262472, 356464534, 673925836, 196690955, 687592524, 863874764, 652928405, 398135640, 834915701, 625643045, 652912977, 814090269, 766564535, 224234676, 971335307, 123171080, 307217403, 557644892, 53264559, 971389133, 876581401, 934745648, 555155525, 963435006, 195775102, 682907985, 981717791, 94216379, 310740026, 404780160, 160283648, 95444782, 169591799, 281603326, 275953513, 921296683, 970219128, 553537263, 298820940, 457694561, 951979696, 541214003, 510519365, 413700148, 931129961, 243335180, 736328971, 233261882, 439446039, 882547797, 540764542, 514526339, 134850776, 200391646, 651868592, 382279479, 935875724, 877617759, 572595896, 995052720, 973295517, 964110182, 913612007, 102135949, 656121827, 422993932, 835829017, 166092249, 288776127, 276690713, 110058051, 603842075, 113472297, 68366535, 938477478, 829350257, 290639243, 619537103, 558708497, 768801187, 283772683, 987982459, 408636947, 745899067, 101782812, 431655731, 437527820, 589871400, 214773545, 460094607, 171243912, 980061389, 803633262, 237370246, 483819720, 196500613, 521653090, 724829968, 205342455, 656874369, 354589005, 277684221, 928931955, 465169941, 910125235, 701348885, 110193431, 672533254, 334598773, 877982886, 577317872, 791911850, 864131569, 710977516, 581038246, 99642295, 53434854, 368818996, 919064064, 999272409, 539745108, 919349483, 774944560, 394732037, 588775784, 619090295, 148962539, 284064762, 75930070, 189345958, 453694351, 338475981, 794522173, 30917910, 409265335, 36401356, 375160600, 112189260, 837124875, 619673644, 543635791, 128664481, 616156163, 780678526, 345225407, 734551172, 642137234, 960791972, 507574085, 906359548, 703741823, 251593303, 791465404, 682577470, 116071495, 193186232, 144100028, 387970188, 637741797, 391194007, 264099691, 763042454, 885469609, 138966615, 47472170, 205178599, 934606528, 436997396, 408573265, 234388636, 388670164, 886064864, 444064101, 593700672, 155433530, 860604663, 697938220, 361408630, 421064305, 460528208, 847190525, 465306373, 289005051, 553608264, 508705405, 349737155, 286720847, 955998673, 512047225, 117862021, 695433571, 394540682, 594578731, 547698104, 78411406, 11493245, 665670925, 608491756, 714312296, 845651833, 555416905, 640037140, 821199064, 807146291, 864420857, 831675931, 18975897, 460196759, 729804047, 503233402, 136500313, 365918038, 178142829, 731644862, 143216052, 256243121, 424978755, 620407129, 348125360, 755308440, 994655435, 122086927, 732262735, 160658739, 307139475, 215712208, 387534532, 973153455, 218662538, 477037678, 448459119, 240755316, 141469232, 817266399, 88893301, 827487831, 203218335, 524202113, 147686094, 279580288, 450705682, 999701291, 252787032, 359752382, 551463117, 348869899, 536654088, 762021601, 682483285, 531960615, 325348244, 698974225, 707341267, 780686446, 378759295, 892857197, 499865853, 74128423, 650841757, 11907721, 929160190, 680647513, 792946797, 500886976, 373001739, 616475234, 430181532, 674267633, 256704073, 795616101, 980153184, 28357814, 385254319, 38800672, 333785017, 315744598, 191529905, 86877308, 419636228, 390248046, 936795001, 825720352, 423938340, 819543810, 279253135, 469582583, 38516615, 197309555, 381697150, 488987534, 393770102, 233908674, 778804400, 103432168, 403538429, 121930884, 847646392, 774249070, 980666671, 922083956, 892228514, 102457242, 300730026, 266614747, 682893084, 691866236, 580610436, 814269609, 512681673, 677014933, 550276223, 637680963, 684434163, 619834096, 245857594, 714265123, 856733739, 246256222, 248592283, 979515763, 303611908, 988574077, 887467141, 19373924, 977772746, 678706289, 66846674, 534594219, 743737393, 717946681, 380924214, 681173479, 713076473, 438389436, 421190702, 818266030, 667186569, 511428236, 637970608, 499092406, 882281418, 767926321, 988423697, 694833045, 197643368, 202505976, 61947449, 336469873, 785431239, 390533053, 423575093, 830222155, 883806455, 590968376, 256537761, 655003821, 486095004, 575759617, 760315056, 960952087, 923708018, 452704159, 825949596, 359810359, 49493162, 420856954, 266520268, 740202125, 559410631, 650852982, 24726626, 316216951, 24244661, 240596452, 378454289, 881536202, 567873759, 734940375, 934396077, 605892189, 613151050, 568926924, 105894907, 263593499, 231652026, 251039401, 671649415, 125004997, 95815095, 996413544, 687288362, 2399173, 823134991, 513047985, 379720803, 410861277, 802922596, 106074314, 174011761, 930638222, 677301431, 405367220, 115095629, 423101505, 376896422, 617607859, 69144422, 702808142, 776313913, 153175789, 654898839, 655286068, 733291151, 36206238, 737928218, 159276284, 690424534, 893896569, 613207822, 878724738, 484139067, 221190027, 288314688, 416084474, 606936568, 526090221, 303598561, 767242888, 743342646, 724223412, 871641745, 1359147, 144477282, 941808716, 537031096, 27317344, 720412871, 349578755, 637987232, 27701068, 184347079, 4786174, 846021676, 630418072, 80726181, 773739771, 276705764, 363519261, 11512557, 820838869, 547395246, 13444223, 144909261, 637822178, 639890846, 281278494, 584124689, 410382350, 469194336, 995146579, 281539541, 86175915, 39161265, 369630055, 200525863, 893767504, 556201119, 445225443, 311572532, 973592667, 324496299, 744744951, 660424814, 876678148, 431769353, 909736814, 493832122, 387633548, 58660654, 788948124, 82107135, 328907354, 79146663, 835693550, 720261614, 142307710, 944140810, 913452187, 884212592, 929337701, 894418998, 757154956, 131082993, 688083262, 687376628, 790080686, 494345503, 897813780, 797428220, 924602452, 47814769, 948076101, 485364400, 619155838, 294327034, 338201043, 291419511, 368283810, 70206647, 637553876, 35365943, 526242086, 981154520, 713814138, 594943956, 27327393, 487465426, 892648942, 376915531, 157583370, 639277155, 619652717, 216921520, 811392725, 47111942, 583162248, 602902227, 409084591, 86603101, 794997606, 169388884, 861716407, 979949901, 778877503, 956745577, 573844662, 330943889, 126631974, 616273247, 196812767, 856687346, 732757928, 519791431, 164296175, 770960496, 192578975, 144300610, 885950222, 739681293, 167644227, 184526169, 159088228, 653750573, 572134596, 698276287, 127457217, 559150521, 741590131, 33941000, 273629097, 228065917, 878810163, 520024570, 587907099, 846466038, 485151134, 947548574, 648666688, 886042641, 203128122, 699181585, 898831122, 385185567, 388284692, 562487968, 186433825, 51217373, 722018921, 50310262, 73762295, 37942011, 297786429, 196729063, 886638967, 238658656, 181219359, 371951954, 466281427, 684360955, 476516807, 267869140, 43592724, 318663536, 447577144, 940021573, 426513430, 627014655, 801248963, 976887832, 859104733, 715180943, 672502860, 145372525, 7587744, 808082184, 878689134, 486669326, 346028367, 83158926, 261715493, 642791974, 666754414, 712889664, 582420031, 862331931, 255664453, 734193000, 812613141, 93631877, 951058179, 395614599, 631192176, 820988680, 760497259, 407274243, 740216507, 691389562, 407577658, 304974010, 699405243, 14979927, 974503185, 923084548, 815387539, 920182721, 65929804, 202016378, 585405688, 899511295, 277254326, 758456488, 356541325, 661452959, 729807051, 540698731, 301357818, 808206170, 787714140, 823222657, 758326, 489501282, 992665762, 548692956, 313877546, 453418512, 838587084, 530027872, 269832277, 654506177, 114283323, 265286235, 377194629, 562367442, 918629767, 845974478, 126932906, 751041799, 662812209, 886987394, 70915417, 426904323, 40182667, 76393896, 315507838, 626794494, 867229843, 697541710, 212781647, 494560644, 586082943, 869444833, 64529997, 903233421, 265272640, 50641756, 98144061, 516309639, 561354276, 1241060, 815840353, 285669350, 222757985, 737037860, 690493989, 678305246, 189567894, 523068873, 555585169, 276541045, 403824355, 329346905, 265401828, 993860252, 31730864, 530914274, 999463212, 929372114, 336226354, 547197870, 976121914, 377710750, 676899270, 456367935, 965748398, 565689751, 246932079, 213280792, 778280483, 466551591, 687657822, 866343691, 758805867, 700999127, 949583872, 810656148, 909103020, 493586026, 124518593, 652633017, 571090595, 488751804, 259726970, 44334406, 445736121, 964206945, 357597806, 55348884, 889926562, 513527036, 529719084, 113590076, 550093319, 651523523, 551968830, 215140960, 61621264, 484701539, 263782843, 141735988, 836449807, 586756709, 481318146, 415294332, 655546062, 429270980, 563960029, 544430013, 474670294, 775805750, 712207997, 854762086, 241102115, 280159460, 119563747, 633998234, 310632073, 409370322, 670403338, 996972397, 578190057, 905592068, 627600500, 682666375, 756095951, 899016185, 161607268, 570512200, 442615821, 337613038, 799628100, 532445407, 256432506, 353305096, 287124812, 746365215, 814014246, 245247540, 543071564, 207049014, 798409292, 489597702, 648298216, 54320822, 426258908, 837313228, 135091074, 723387175, 143528304, 321308667, 702518826, 336658910, 234579543, 582784995, 846504844, 824014809, 999321984, 756845481, 842017001, 548883982, 171782161, 531679989, 379890992, 600141213, 977138498, 581120468, 402231604, 833787406, 434343310, 491502611, 93770247, 37631531, 43263409, 281776637, 935502493, 198269401, 702353909, 673771829, 413687828, 658862922, 533222996, 210185529, 50632319, 991493715, 7004163, 829949828, 934300249, 230711221, 200794950, 835193552, 568835271, 636927687, 859713539, 719663912, 122565904, 561737258, 979270477, 504060841, 435651578, 795750278, 365286032, 404861357, 29374393, 375782098, 154680545, 699710683, 944541068, 349368795, 555927942, 145463214, 371532782, 131871177, 242958410, 198517255, 485133651, 527707346, 41042364, 730569357, 349388230, 843206665, 367635941, 746358043, 139788526, 223772271, 123877330, 294425124, 854254920, 523848778, 360481945, 211217421, 549351937, 802355802, 242469909, 711416224, 825197371, 905371525, 591566851, 759871153, 857783078, 735303743, 269562034, 228372153, 18364031, 375681226, 562280279, 124985374, 961273928, 106751295, 34710970, 487938415, 802949307, 826592008, 657032380, 425482637, 243985626, 953205725, 523006441, 464963779, 775542741, 658529683, 777323353, 434972761, 560217221, 71832268, 691211741, 558005844, 282638332, 844142504, 652415037, 717303812, 217240466, 288818332, 846088553, 57580257, 765574394, 53885671, 599604101, 420474104, 524659312, 30553438, 884351708, 109328534, 910647625, 358185870, 73987102, 229496598, 534177476, 757888590, 731649855, 429648858, 787601976, 719435874, 526184065, 511776042, 259622198, 748465473, 811524339, 783158461, 628188955, 211249512, 460759309, 314649882, 394187580, 357163156, 111020311, 301203040, 551455298, 358476241, 136398143, 159077166, 209772568, 734266334, 933910745, 134348501, 267015447, 191834955, 302160647, 877641974, 457885199, 315488877, 784373067, 457952867, 953928713, 14227146, 672402766, 822389883, 906764259, 705414997, 27013677, 792408410, 979764593, 190214166, 684633560, 684601098, 697069139, 422981239, 476775166, 993910660, 543528162, 386953677, 267846200, 108898458, 123580342, 820218190, 147768419, 91801463, 708357973, 482817139, 736551990, 289925336, 116971302, 182927790, 63407470, 209471088, 669049020, 941128386, 30735245, 408490791, 3907014, 150406015, 719620746, 31831897, 186415387, 15010954, 851726842, 545401636, 1061595, 260266439, 226863414, 748056551, 368062603, 545826171, 830410778, 783681331, 340584944, 835329710, 941446401, 283184656, 241722169, 308833460, 960005550, 272646794, 374612865, 148167146, 312454619, 487784796, 891176216, 106505593, 315427404, 731972321, 243778675, 985640602, 90309819, 433529001, 582098231, 949727249, 356783478, 719452198, 665264143, 244422805, 149246914, 996666078, 95224846, 809873695, 254255447, 843504264, 121878560, 526104920, 670705096, 190589707, 648386439, 125353749, 63236637, 867200670, 241432791, 252974335, 583940404, 524607408, 762382843, 203959361, 507650136, 191215246, 395532935, 661318259, 310271342, 997187035, 184757833, 817785248, 680017810, 788476255, 132230152, 327865162, 396471444, 260061700, 591118063, 324818262, 130051462, 598576959, 888312510, 919013911, 498673820, 171388611, 729397402, 500823731, 317594831, 905056636, 762233536, 270193105, 718828879, 735623051, 253345552, 502411444, 83972171, 269752228, 68994413, 966763679, 692149605, 137492797, 244069944, 961435949, 446558148, 617574735, 245262491, 526298357, 98802338, 360104749, 683632015, 246158883, 758500140, 112307794, 893531231, 400226798, 525487316, 765188822, 803969167, 978987436, 234338605, 477255301, 780499236, 748416215, 549887236, 426344070, 250649381, 491602365, 645959900, 522507577, 107317277, 946273306, 272095517, 521975296, 308446610, 692043909, 23748453, 312184959, 310148759, 776413426, 768560778, 532265386, 482244843, 291029624, 779855267, 268736036, 146393241, 181997807, 912570425, 752656334, 867357611, 825091054, 740835837, 125985114, 244449188, 721722408, 871975219, 298634433, 177580640, 32925673, 687462229, 684060438, 475402774, 303047455, 521132371, 765511786, 196370431, 382269368, 152708521, 611058046, 572527464, 829689370, 441033762, 379227731, 946707049, 222291890, 682016904, 935416592, 25671644, 528056136, 73368238, 995687522, 533759792, 539434133, 428585946, 783533652, 444814075, 831217225, 287898744, 99431486, 262912120, 198849987, 869884693, 563445718, 737420484, 818140263, 989100375, 710973559, 9252216, 5130747, 398282759, 366063040, 332291531, 45768850, 959943933, 31335120, 598701297, 389189947, 385757933, 187387056, 332310, 160748489, 959682373, 338386105, 137287338, 883389119, 689876352, 314729437, 657021334, 979261960, 107449043, 930904206, 807590296, 922453176, 734153532, 971276235, 765817794, 797090236, 340405868, 530972905, 183253970, 114585716, 222115108, 431012093, 647369474, 669344679, 569085196, 375567660, 775970510, 721916531, 729344373, 906072491, 88603136, 491297163, 682371120, 214612920, 123673103, 825541371, 842079180, 107784489, 246027068, 469416843, 192399675, 241544226, 580744227, 27177043, 496959334, 490487155, 945831092, 138071151, 102960491, 699087652, 286314031, 103417266, 410087329, 417201823, 182316670, 670290103, 622755892, 525694442, 486026872, 556383025, 322312625, 34743112, 14320643, 157587079, 686078404, 486821809, 297519644, 237913609, 758638609, 803381736, 6080624, 560993758, 989518697, 120793681, 289992266, 171079899, 475755469, 390112420, 949771270, 125859907, 845514253, 48484200, 145488666, 368398426, 307209228, 92885278, 542449224, 436064108, 485594860, 284240332, 33699602, 75246796, 231958211, 356672655, 455582018, 374034293, 200461198, 340624063, 997155511, 648087626, 666858793, 450077716, 40746079, 63796507, 143921665, 182438762, 733218927, 583514074, 838299714, 39166921, 323719461, 942450321, 91070488, 284196760, 865172073, 432852250, 279993823, 791538985, 532034256, 700415783, 287994390, 73492940, 348717436, 529017756, 870896681, 917214773, 413916241, 41856566, 646143104, 62299416, 451718045, 185485503, 953447917, 708741762, 369761225, 341417818, 430621847, 154774977, 896609762, 822205581, 545675251, 796514621, 665819708, 889677251, 708851578, 80147835, 588546166, 415870577, 893155126, 879011177, 386757210, 848874017, 934123973, 147197377, 424273533, 589499875, 578440681, 6964109, 793625609, 337967185, 809814615, 188726984, 558071747, 639178521, 561972153, 726730842, 983135540, 2081235, 879284471, 655033708, 767757225, 249231267, 79265248, 749978881, 259533640, 179433036, 140538681, 515794177, 200457670, 680764716, 143609110, 641866525, 476932301, 236755911, 539515176, 116264418, 634053582, 57144860, 997881970, 437243723, 12714765, 791692154, 688127069, 535806545, 107638375, 935151876, 732803384, 907840686, 393087822, 847402969, 346267216, 254734569, 876849878, 841113036, 608367597, 345094706, 781897674, 956234853, 887605863, 250009302, 400585554, 85949680, 579245272, 622863366, 112067211, 62209796, 30014330, 348441414, 899454508, 786308330, 256787752, 549606925, 526350735, 796728684, 523894677, 592034884, 35143740, 561224653, 395765641, 23966086, 821570352, 944838230, 150944462, 690227106, 170911052, 690070288, 753374713, 338005657, 861597927, 595595196, 488362955, 43976271, 89517478, 601893084, 144622608, 94229513, 689266509, 691666613, 794870550, 722878901, 744170154, 500608235, 874269136, 189032448, 388230176, 670274735, 960101893, 653734062, 436269266, 320534201, 175400475, 503643675, 214029342, 155717636, 910080848, 565475509, 77912777, 68135389, 254624705, 326451334, 741136630, 263110111, 806045676, 494212789, 227212256, 587000885, 880924939, 328699997, 48505712, 73942177, 894452173, 932775493, 689822875, 29714712, 619289015, 74799073, 709419045, 837376264, 151113971, 450229339, 417470505, 680272047, 295353685, 164843334, 799340863, 715779216, 479778783, 19904260, 437709233, 531419012, 638266498, 234817123, 387528303, 874016316, 624452229, 336784171, 207090673, 461678711, 540897196, 352168086, 99904403, 450815152, 234159037, 775482149, 589577422, 974673284, 917538713, 533343512, 633369107, 404138498, 879132426, 862242479, 897989840, 154760470, 103299465, 332371258, 99732054, 18281397, 160300561, 838747316, 194107377, 427177743, 126615857, 700019034, 993276356, 972115407, 838484213, 956018065, 55476684, 347330609, 503111515, 986984970, 138162465, 926072760, 505061305, 52666810, 979756838, 925326109, 214731139, 842694911, 338155808, 837670785, 474724318, 835846570, 547003355, 647322791, 831906599, 201659348, 174527889, 846962649, 852282039, 18974496, 395477248, 601682022, 671303428, 626467046, 310084851, 784616394, 212654772, 384217618, 14361168, 109264045, 570916841, 412275987, 688475336, 360353914, 87488137, 118016963, 878957106, 812465175, 599600261, 415174659, 531428694, 154790002, 286614759, 28608188, 214529482, 936390648, 165554782, 339484286, 773334527, 557239519, 739255933, 234856274, 675835949, 768575760, 939726303, 369730888, 413386830, 6981849, 944504715, 296302349, 357976490, 570588673, 280872680, 406421258, 964055629, 103211165, 957763774, 554260424, 471451211, 511550985, 657495785, 21239963, 737955568, 125350060, 536128852, 684890347, 832296231, 534235617, 73336188, 144466064, 976738662, 361311321, 53261981, 203912186, 59993215, 37822164, 598695243, 447458634, 75822046, 696465340, 151167326, 484837784, 700700248, 635715082, 937199336, 116093508, 408718130, 141865086, 30242427, 882343778, 107509795, 549084528, 113031379, 827957260, 207447611, 79160556, 157206423, 325604057, 431118524, 332570024, 132828109, 194153390, 16285683, 597337757, 141537578, 597164954, 644819414, 548487574, 676439973, 887155066, 408766075, 374064251, 627280172, 881583908, 686476007, 260488690, 459543401, 234501636, 767151121, 767286150, 304516992, 899451753, 413666127, 81381068, 760811276, 11682851, 229369427, 443928257, 348920485, 114412414, 824639638, 320417292, 719604033, 208099192, 661792873, 355604755, 489208379, 720177760, 767727266, 801967834, 697934799, 373979260, 625449082, 900819067, 524569770, 968677400, 959519638, 568653859, 889318694, 392277899, 572394329, 563721391, 78280642, 277687371, 634812929, 383653244, 1616646, 341182599, 767499673, 977704935, 455950979, 797182583, 692821049, 903203194, 740271495, 894536712, 85290179, 42844791, 644749591, 757718515, 612949254, 458091034, 831395515, 944748208, 536173620, 812307699, 869672483, 715601222, 22982600, 957516465, 130948594, 608865699, 431473383, 633367288, 151337003, 715567693, 831616464, 250093093, 343893741, 147873990, 367153030, 315137205, 851098290, 443492342, 41075170, 721717104, 461908009, 987971305, 968100371, 71306484, 658917665, 447461343, 198329190, 742103031, 403801750, 547559475, 270692480, 244243852, 958002533, 605012317, 249605865, 627489474, 558646379, 436918545, 758600232, 863514135, 680991348, 102358884, 100736632, 944869588, 864842023, 239080140, 88617790, 580786333, 398371367, 919695901, 569156348, 125404541, 60334877, 512654382, 361118584, 332195569, 899827025, 315075125, 32303356, 159523070, 447797144, 412457883, 59537268, 468789987, 400367419, 382445870, 847229782, 219896709, 35280270, 519209758, 524822066, 3233310, 547716377, 953918557, 620592083, 744937048, 666580151, 884822616, 847930429, 633681921, 358278295, 315886561, 952205226, 19912593, 415016144, 980881829, 189853511, 917642325, 631479521, 576068353, 844964085, 675816850, 435696466, 663350028, 121972998, 346292047, 482300635, 89532418, 406226974, 186090623, 462572278, 669375369, 5408488, 752244415, 850143099, 592811818, 877360436, 816585041, 267807363, 928359340, 490279915, 879454965, 140047357, 162866020, 521186048, 686310037, 896098661, 145718718, 910491459, 239452718, 864690449, 283246290, 256832224, 712164024, 292750308, 33461981, 936339733, 443340585, 621803616, 215827426, 404292443, 578464817, 864099455, 673847716, 698485360, 120501175, 254883510, 23893532, 972265483, 166773984, 688026346, 903074196, 139340168, 903871254, 915962556, 376194413, 239215062, 747637726, 691450567, 614536958, 632279476, 313162116, 946973310, 914098190, 354101917, 333146126, 894716540, 499692257, 695303328, 671758223, 269663143, 553832402, 109829107, 547498364, 959396616, 936494093, 267398087, 803502298, 444148085, 186432654, 568443478, 128036394, 869405998, 676956845, 323497183, 368841210, 331874643, 468833548, 238938311, 727440452, 352338021, 196183083, 923794085, 647620836, 423128551, 566274816, 942898140, 595533634, 373591247, 503450648, 301916466, 8708120, 642390020, 960366268, 417079708, 19505217, 718437283, 994272337, 576266953, 267978380, 620876115, 560503150, 104881744, 588577337, 853021532, 92773150, 331318249, 40110799, 537465878, 99091266, 715165496, 143295717, 559433274, 232148910, 646022496, 753034835, 511186097, 666038148, 21304319, 640529253, 189355797, 348960957, 861505285, 772465162, 106856831, 276835068, 553306661, 594996372, 301654227, 572507808, 78309419, 924568234, 98232032, 793021913, 711613980, 178313275, 248950636, 175842426, 635103927, 648551638, 149175721, 106929333, 681295125, 195268085, 777020239, 545394095, 952433086, 431032492, 33199450, 639097493, 674713037, 373250856, 965884177, 808755756, 799244766, 874813906, 288041242, 972752016, 56146326, 570362108, 935808679, 262328559, 215709345, 919935644, 833924640, 221800020, 449290613, 324667430, 878602819, 535946140, 808444930, 230631535, 674122035, 266791111, 60396163, 921155403, 821742062, 476924890, 361644767, 72403480, 49853218, 747630009, 328061877, 417439488, 441033656, 632159512, 507820721, 522538070, 402865791, 855645408, 573952911, 283054350, 765745744, 537792458, 839929118, 554073294, 59924421, 136721373, 808381582, 364457444, 453435390, 402637446, 753919866, 960999911, 119331766, 251289717, 436669280, 182959411, 756668304, 200061312, 639127990, 595742744, 442025654, 763865471, 45364622, 984634075, 24386047, 285076211, 553281647, 36658000, 403978309, 146293223, 293518758, 39242324, 602427218, 955698155, 291735536, 425142178, 75573636, 460266447, 659879658, 544628691, 943659730, 491755148, 584904449, 414747421, 65881365, 976418335, 361809044, 328089179, 964390969, 950865970, 17441554, 991030273, 339159023, 590015895, 277362288, 697562806, 106295843, 390948291, 632721428, 185630689, 897951902, 142045815, 558379476, 444337643, 44745411, 161987194, 226963391, 911420654, 976080276, 893233652, 868123763, 333580982, 456166449, 553226012, 429155676, 92484550, 307074065, 410004017, 889360299, 565314544, 241794172, 436631745, 174423984, 852262193, 710263851, 260431951, 546490030, 785215293, 503322380, 109051541, 311081459, 531805277, 831672011, 457192453, 741254711, 618690461, 58033924, 458754281, 361402738, 428617505, 171527688, 86775423, 517784449, 258114637, 258639601, 747565466, 130007837, 3824845, 93132914, 233111935, 259801548, 149413240, 983993691, 797668615, 918119212, 64008440, 727563489, 312748211, 806530225, 866354155, 445614416, 903652120, 203652303, 886830107, 140246481, 263444821, 487926631, 642834126, 430543872, 797090506, 318096696, 507881666, 913908099, 11604038, 127172645, 357073165, 927274288, 707900290, 399462925, 207720041, 369532459, 713115912, 435903218, 890799763, 359602672, 936757949, 53399469, 863989773, 753734723, 212994396, 614085, 891786927, 370823381, 566691107, 718646251, 442898749, 452139134, 320961586, 354088058, 468086759, 706349926, 53032139, 599933231, 446990631, 444222755, 372571834, 698225119, 695399666, 773574399, 357184755, 776504072, 732137473, 709119495, 636698340, 844173280, 82185779, 539007567, 9446286, 83539706, 442043065, 112979215, 770200179, 968899491, 858582385, 360788009, 591691548, 389559186, 336045146, 534624429, 59063331, 715080752, 113577201, 987124861, 641187180, 724691310, 213828395, 360706711, 719910163, 856165805, 996203522, 952128882, 703174068, 232818133, 634861302, 251314743, 576130620, 891228599, 486125878, 347373354, 52345979, 128590367, 623188252, 624162653, 962840768, 191294364, 913331870, 154984041, 100738988, 965337639, 66372124, 819650510, 474557643, 236107285, 789901808, 228091145, 557034352, 973535882, 299116824, 586760351, 919651985, 961388014, 543399430, 766958569, 894780133, 82087971, 590419346, 925531041, 579062029, 720235956, 296886807, 807992629, 614995145, 598264088, 243167457, 397911710, 61253677, 91652372, 379127543, 273371304, 873818489, 180069344, 582614778, 450787111, 439930485, 301994391, 172207571, 268398348, 890519151, 324178453, 49325071, 167737300, 469953303, 494682128, 863564786, 379510961, 689764652, 920206372, 84701663, 536313610, 238050325, 839640831, 596351160, 167564077, 982270299, 970680906, 516740209, 680315547, 485981814, 345284543, 46138708, 260154757, 951418001, 87190965, 684993063, 407087809, 182928954, 86958420, 785384537, 598499837, 497547438, 733147693, 996554609, 483929121, 298046403, 280071453, 182201137, 258234946, 519357495, 775316726, 481500777, 378576679, 213015413, 925743368, 27325096, 807576244, 479734205, 258359972, 967227, 911207975, 265318437, 476009591, 667104769, 186032845, 659780186, 875108674, 354291436, 126810023, 820601994, 295726725, 724979290, 567579013, 122925213, 332448980, 890660336, 194800023, 796117546, 305476044, 132448718, 297922480, 982015526, 926552629, 329339295, 880758407, 955707493, 404114257, 479776440, 416277834, 665259754, 967297698, 895668877, 765533058, 644604533, 19766440, 937495159, 374871503, 759097578, 898219041, 453288928, 940326167, 596071104, 213452496, 251154939, 120981557, 143450911, 729162194, 916388434, 915918014, 636253694, 673753950, 737828766, 253480748, 611332843, 473403153, 83130062, 186440894, 862301875, 709879494, 155794511, 309553452, 583303847, 373194393, 997182042, 534294410, 598556869, 663967431, 53656262, 780834477, 953191418, 713183738, 35773636, 206857349, 960533711, 530527494, 737030882, 697351356, 40991260, 489215176, 792718472, 606782076, 542403926, 724173148, 238621950, 435022195, 488311403, 436226960, 314979943, 193558304, 374905406, 870519144, 981998494, 693000922, 988395328, 797987201, 564663247, 883618478, 122371689, 275580554, 796079454, 598785764, 434225902, 795750553, 393578899, 750770899, 686313468, 822126843, 782545868, 832183920, 671106083, 144341797, 700451317, 682448248, 286482938, 857962572, 580347433, 654803229, 20331307, 192428094, 241231025, 666908657, 640002483, 488858255, 307392177, 36891839, 759451533, 278546701, 413682854, 538439375, 791577454, 659576628, 468769084, 24871781, 42851931, 277370287, 942962095, 940436075, 674662222, 223154700, 389087925, 288949462, 956671979, 784701640, 605593367, 992701530, 486496081, 305008458, 758641137, 465275842, 956463323, 939876469, 610897834, 599358067, 415940385, 504626416, 328576710, 17217047, 419754822, 671319092, 932054257, 984890464, 806855482, 417809640, 177148459, 440058847, 539278363, 653060463, 955068168, 593253126, 887756207, 787136554, 361893918, 354498579, 150772784, 31699000, 84003374, 169566356, 429598682, 87540963, 71516326, 447912785, 792729602, 848795911, 944124125, 251091054, 590379615, 237696705, 287462036, 417933260, 848542971, 487557133, 74428201, 485713542, 513593751, 336148722, 448567158, 290922947, 939599864, 299746508, 76523942, 75042446, 736253934, 994781062, 171272606, 699574402, 435585880, 851279441, 652000345, 474764919, 397625217, 163742404, 693953240, 861222428, 88102557, 986263237, 508710000, 991568119, 578697098, 193714424, 387517530, 992330945, 63610347, 912565908, 990635183, 290701184, 454301595, 403512639, 70307908, 857107123, 762394623, 841902486, 666159582, 366230066, 221898371, 542082790, 854669158, 965136461, 202492638, 793340909, 690142410, 231776610, 926449425, 910977129, 230300040, 750549056, 419675764, 110247652, 945269000, 970911039, 63396117, 424771911, 741862566, 231717581, 266119486, 326694898, 745798081, 810752844, 230616021, 254245882, 186054504, 807808752, 453254538, 328163355, 713796846, 711538019, 551722277, 923601592, 396731197, 197256270, 231184816, 915983645, 484609966, 276340230, 664565909, 555698194, 741410215, 94295545, 245588591, 933569526, 108396010, 72166270, 957300702, 673149963, 688732366, 601669809, 495959351, 701770904, 263323826, 275253286, 124367722, 2734600, 420488510, 80913777, 326269489, 106918400, 613319399, 934400777, 439737807, 680376019, 799638715, 707167213, 955356673, 157012925, 551588408, 419059661, 873550859, 491599467, 941527032, 727612131, 139892498, 949157918, 757483275, 624436025, 529363734, 143406928, 909198936, 748072490, 634327877, 18104425, 379430137, 118084030, 827048088, 710799903, 623524562, 991691175, 358492755, 67591133, 241090140, 503549537, 457175122, 350921434, 750497064, 64988700, 859336356, 237058357, 137144775, 343793704, 326505408, 497189043, 892983307, 237131281, 935311269, 359309429, 80239012, 24801479, 501307990, 624878903, 265940849, 306422625, 52500088, 482848509, 132717108, 921646677, 513754830, 439585270, 529799753, 245920117, 657433183, 387778822, 935556434, 377164569, 773224679, 391455270, 917325682, 805970655, 22766151, 531614558, 325602180, 428727683, 343339065, 326973139, 75700361, 914606244, 952587246, 515312109, 145961359, 997273968, 144564614, 908274600, 726530551, 655006923, 788305502, 473829797, 678169028, 813486710, 742409090, 248239602, 239286729, 343829113, 73181693, 596205035, 399138277, 449901593, 653701684, 851323690, 812905215, 536834390, 251498622, 191559987, 429210439, 333664263, 272405973, 243333569, 816625282, 394969278, 526271870, 157390056, 823739262, 174032266, 53097163, 546286788, 934054524, 606528329, 604306554, 123031184, 66519386, 935274240, 322720622, 461829036, 971124327, 283023026, 313003892, 600600973, 619035885, 973374058, 39825, 200206299, 42347269, 73732344, 273228295, 532791109, 847358537, 361338355, 371344527, 376952847, 306044107, 857936433, 257853609, 4139262, 880192936, 946227645, 277191246, 984270515, 384483395, 554834928, 579025521, 279133744, 44418629, 177523319, 933508740, 239194651, 224648962, 956979983, 555467453, 221553626, 332609125, 914506387, 115189144, 119353705, 301683539, 925350999, 985227683, 828707860, 293511065, 721566560, 841822295, 889991993, 404259123, 787204592, 512681495, 459844120, 114282188, 254653429, 211636413, 555080057, 469882947, 87028688, 221499898, 17167209, 516576539, 547609455, 581198527, 857996296, 653031600, 679175475, 747692458, 755721184, 725398568, 747772763, 345131604, 617778793, 984802228, 658791631, 533883228, 989469540, 362321013, 612477206, 563470021, 417577705, 936512024, 246856648, 167541860, 186272290, 734169420, 941479057, 523255211, 862427987, 489019477, 549742769, 629794235, 1145583, 564674985, 459175465, 341343488, 748692303, 391698902, 759073987, 214827023, 225939692, 672683471, 260578935, 602733683, 946632319, 3911113, 534103402, 449077264, 132129961, 389758864, 671513637, 439904258, 190170600, 685417699, 139894268, 258040904, 200334579, 693054931, 895493180, 114454729, 8972787, 341758372, 26343267, 555367778, 690765421, 580958384, 337409685, 149366458, 276875064, 695048460, 36518971, 734884482, 831110138, 764364067, 86060433, 299543698, 636158625, 720725846, 160792987, 88725375, 923786212, 657934936, 338469792, 834367976, 156012032, 388862765, 493568946, 373442644, 748626922, 992931962, 79694534, 132985725, 431510537, 60233134, 948127898, 457540049, 345597233, 985695178, 780191773, 605334852, 632780312, 48939293, 273148917, 120368028, 516598947, 785875825, 551225051, 287247270, 218549497, 732195266, 970082344, 327083142, 329278064, 701551283, 161785731, 587128510, 821944980, 30556133, 273212081, 827874491, 577829261, 253863588, 716825404, 149417073, 212947487, 393458078, 570170768, 158868666, 21531319, 416836166, 94155425, 375415448, 848378056, 64156827, 291416978, 666546806, 909675659, 495715432, 586548240, 881674190, 345839218, 143007099, 327952575, 856311612, 976111976, 625108241, 76989415, 651451962, 273090621, 744577107, 405200504, 176434506, 956103016, 248645083, 390437760, 867778426, 19834824, 181686803, 372485690, 189284301, 526122275, 572375486, 503178770, 963761103, 971635904, 276050488, 393037525, 754309357, 680312567, 596724844, 719467883, 614914612, 905901249, 377493859, 990639316, 154190033, 670432958, 274367469, 313081679, 102418800, 26694346, 185660012, 218877287, 213852814, 441499435, 72566398, 899972694, 641963663, 580545800, 990874750, 199883995, 351599201, 487131143, 457229429, 404670433, 4933619, 898026554, 703484347, 535581311, 9286018, 144353800, 260261518, 566325691, 970513587, 768310366, 889023785, 173601812, 535956854, 455093153, 87811404, 843076176, 473985374, 420067528, 990636626, 740993649, 157246543, 188195900, 712200246, 374142337, 901937928, 26928655, 653291552, 579185920, 277247977, 785834624, 549113930, 517204936, 498616755, 59710653, 286059960, 964334576, 565856428, 6669806, 352360630, 965718402, 805245336, 243698995, 523587938, 577110944, 689588996, 331265609, 451742345, 788536690, 947479573, 871534312, 719926444, 233402639, 238195113, 246449268, 265230572, 953230183, 491446333, 671197979, 7047587, 16671666, 240888335, 140062060, 706895620, 748977270, 492530109, 434987277, 337162560, 470316883, 933383345, 252244776, 618959246, 827493296, 875942867, 970282902, 626057245, 96970027, 849099662, 772759510, 197098674, 306681007, 709803829, 836488570, 273442000, 115598660, 488702261, 870194750, 57652682, 997416473, 529183324, 75867853, 972531095, 625177687, 184421291, 330967023, 664200861, 358399965, 604445608, 882599504, 752623657, 496937357, 59750851, 621788307, 635789161, 275679622, 827635235, 289610650, 494972688, 258562653, 737295809, 226287271, 645231611, 75192320, 572911455, 60717784, 978696221, 682879037, 677786264, 948675474, 339238334, 589041248, 549125039, 485298582, 883874604, 864965847, 765296099, 948768527, 30104772, 454492007, 914855627, 861330003, 842381341, 226726667, 929845260, 980551468, 762214052, 489320256, 798487203, 662900436, 469331233, 161680823, 417168944, 669871431, 127392157, 250111371, 35246008, 126868351, 93711287, 305079419, 479688972, 304702453, 811415452, 658185243, 845080895, 85843304, 155536938, 118173224, 315968584, 766146962, 638927549, 813042777, 855183675, 271804840, 40717076, 885105410, 899857241, 434664830, 568735871, 657738442, 737943427, 328894351, 301572190, 696956033, 921457996, 561507911, 179689599, 985087370, 113010601, 341805605, 388225361, 829519317, 417724430, 699915482, 647193869, 987594114, 453600658, 266979551, 447159341, 877716100, 925427966, 300958648, 518439270, 727859569, 103708812, 28678347, 180676360, 171236096, 894703194, 92730318, 330297317, 91761973, 299039419, 148694167, 183039391, 748013797, 384273839, 845895751, 248195479, 18678431, 910423700, 413743872, 640810030, 33029132, 759135589, 949820960, 707188691, 127782889, 38798486, 470943920, 479633874, 702175842, 455659636, 126615266, 914983365, 132614214, 110470652, 761578387, 406060959, 11665895, 945773959, 90172252, 231781073, 493975115, 431388485, 905854703, 887223348, 496936186, 907649222, 584330727, 947129128, 203553671, 131425463, 873114819, 55013211, 407245658, 214762788, 365795404, 306691043, 568516961, 883138457, 417862974, 103583370, 596659562, 230376807, 676145482, 124273327, 33394490, 592164444, 602580791, 38801531, 556212389, 458194518, 622410982, 69369731, 653380598, 136528398, 618185117, 653364674, 513255390, 623933430, 442731736, 30561095, 981128012, 366784173, 159083276, 497651837, 175107924, 580012839, 547417685, 253066693, 288801627, 534234275, 880706689, 300143322, 564726276, 275553459, 406040272, 254495329, 987048813, 64676769, 441978557, 18678310, 525394761, 704736501, 432613354, 138851392, 122731129, 268766057, 569006584, 92775041, 948529335, 457619443, 230544756, 368515958, 342035753, 544229607, 238065117, 778089423, 806268241, 804874619, 263830987, 796610254, 117971509, 409630931, 829234682, 170183232, 63611100, 290135020, 525840971, 841288283, 95450998, 331723279, 652540450, 145016640, 78754803, 499886419, 374588182, 763217486, 72985237, 631031776, 213628056, 537188227, 306985253, 270297719, 497551303, 130823181, 757229236, 434626408, 719231760, 2107453, 970337367, 561391641, 19862835, 926180724, 407224549, 599014735, 804131798, 187969252, 731515992, 576234532, 175091503, 847989924, 39441746, 144149740, 399059542, 347267207, 576982081, 773749599, 905394895, 762226404, 56316634, 694295387, 746469779, 588676842, 290428562, 881086864, 474519769, 395301284, 994260220, 219811629, 855669593, 423365268, 74956469, 41087431, 676564891, 774949322, 596125750, 361071408, 293807262, 59431982, 662741489, 238317414, 45635406, 78701409, 848233728, 389037534, 131990294, 385753469, 894296061, 127964148, 6961099, 926257214, 13606838, 288864832, 580484331, 328777804, 151793963, 46476220, 717619171, 476688550, 290763997, 133169100, 709318920, 817205736, 371308225, 216511838, 654058190, 766273647, 784750066, 82277349, 659157946, 671372437, 579478278, 661691965, 665452412, 940904569, 378404277, 124143660, 285540609, 445198491, 715025402, 850832303, 805372353, 906635976, 247592222, 422041744, 339962339, 685210079, 294849456, 969554398, 707248416, 415851669, 657166265, 551379698, 519306776, 942357103, 479494570, 330541528, 707175884, 889531663, 765718562, 410643499, 411120600, 341595009, 857973460, 426088457, 312090874, 233046156, 102203318, 483072844, 70452268, 855440285, 636070837, 289213814, 864401731, 614773833, 309532466, 136241264, 909955027, 768283164, 398899747, 143498127, 10298813, 638856350, 859305241, 988444009, 553679392, 475625993, 296683191, 899546659, 862473069, 965182355, 336080293, 406807507, 206989007, 111164919, 942654374, 790947806, 29288221, 308781338, 386575578, 345191776, 441499348, 656157602, 45399575, 12743002, 896705128, 427461829, 506017903, 413800572, 367078252, 755163095, 370222472, 32861513, 217123679, 665714528, 778019878, 435751675, 5396732, 538597818, 309296166, 427362408, 723109521, 205558549, 10610330, 157850236, 422076531, 356313780, 344014077, 834857092, 531728948, 586868394, 777699105, 650567871, 142441761, 40357451, 865195956, 25812897, 543373533, 272215813, 894545126, 506504452, 941189035, 270508314, 691194995, 107465562, 444367467, 292883603, 26355706, 631607108, 695896801, 823593707, 902125059, 723540215, 165724695, 820874619, 1119028, 220427679, 944854213, 596428505, 297812539, 487328974, 768779587, 42776395, 140933790, 806931407, 199274019, 410057843, 346808765, 11902656, 343786525, 235822876, 68536062, 813750181, 739344538, 276362132, 290445247, 973832303, 161741708, 945622133, 729389152, 647446385, 62055997, 951971572, 269529971, 861423586, 701857641, 646959077, 849836966, 221631558, 387410648, 737522450, 928832683, 441161933, 623747643, 161135186, 679325491, 35263619, 34331665, 296900038, 315174268, 709532697, 857444952, 72512175, 615048453, 392760515, 251000549, 851653551, 812811299, 916002590, 807064686, 352749903, 769492970, 403130321, 186472067, 358201062, 622150681, 102217839, 634077878, 112464426, 678527775, 424136870, 612871883, 624841866, 176953403, 32662543, 242967993, 413587288, 407687239, 701741126, 170231212, 90688079, 787374492, 170743596, 99814796, 522138546, 197913327, 634617715, 409077045, 23232132, 710881604, 979691352, 335427626, 130980036, 376549076, 363894247, 863224224, 39887408, 947612893, 591537483, 579071448, 547420641, 176961251, 593533372, 100710319, 197905558, 549243433, 487560458, 856012353, 92858828, 268031614, 106561053, 292479019, 137705667, 38404934, 263993986, 270623413, 252996443, 261198080, 81505637, 483192496, 822114071, 417973381, 12363819, 983149243, 262883037, 731770525, 748984846, 214008342, 997477368, 21451837, 82987402, 246417397, 539365511, 303200603, 571516278, 213313155, 844034031, 27068144, 47654270, 704165313, 5384975, 885909595, 685370629, 843713832, 138090601, 642299875, 369579267, 203249845, 897606310, 406097082, 461930214, 193067956, 158444122, 369010689, 102676234, 719861112, 454469117, 242335545, 367778122, 124727016, 408437834, 717868072, 811828370, 449685984, 106915902, 675324413, 67966548, 958085392, 983324420, 846982732, 799102816, 632107202, 812521382, 6998837, 220467774, 523992766, 552145359, 992499811, 243564559, 176672883, 286572572, 727676748, 171912138, 1645269, 975209769, 784444730, 238364676, 161502667, 643555889, 603667075, 161313498, 561586229, 784095248, 961994337, 199183995, 112401305, 733356380, 164698451, 943972660, 465760920, 937304417, 482886930, 787641689, 487364624, 492325445, 560881066, 626720879, 478409260, 442604523, 510307711, 142144579, 517667013, 225046983, 372928109, 109478568, 5788372, 133723643, 331658583, 630888125, 949172858, 691176458, 244567106, 440356186, 454866234, 723047150, 589394822, 568253074, 379032528, 557491456, 337743229, 399478544, 824716973, 543623412, 929415675, 878487134, 717395207, 766758713, 463256069, 416147906, 692932119, 743175440, 640141727, 195213756, 283555840, 503475194, 31297715, 105694466, 561557824, 603800342, 264398298, 118003881, 229860239, 242685699, 280313003, 261067443, 975932615, 612370496, 893616279, 114660049, 189880611, 836947636, 223925977, 694134179, 61714093, 103070592, 256755548, 690693090, 744634665, 669541531, 364361776, 781067906, 359337672, 524759852, 681700560, 911258055, 258043379, 266175187, 985376969, 973589039, 810404231, 686681047, 344323092, 469777972, 781698442, 883768045, 511900378, 403479762, 612375921, 458905518, 84941273, 332013534, 232007092, 467249726, 954843340, 578832620, 817841058, 444936974, 238492450, 531495949, 287668354, 675127408, 646579508, 80899172, 47710479, 118710441, 529475683, 697062486, 499716447, 140216163, 579368545, 207863190, 454328013, 631060148, 333526232, 454390932, 578440410, 886593987, 407485147, 82803372, 872483961, 172429053, 937714213, 169899755, 912122690, 666097923, 300399522, 145558576, 322040263, 661984132, 869977213, 77359005, 204741640, 625345479, 897462625, 429576551, 818925970, 641675195, 509518216, 486297409, 935212456, 255407310, 46810908, 124824973, 701999199, 77237166, 743433009, 825580231, 737510583, 869565914, 207196350, 239076253, 160854101, 703726033, 596463714, 482311055, 319622580, 251834275, 438756723, 798803795, 930329819, 653482262, 583085529, 429994051, 164509089, 524286169, 96527711, 273608107, 679359232, 461050380, 711903291, 957720900, 794623679, 247518526, 210325577, 178762415, 293406800, 572166436, 299455134, 644264207, 51068042, 358068888, 438503499, 583907627, 660873371, 153415752, 654644497, 673441363, 274571347, 932774038, 858751290, 907473082, 770924045, 603891004, 543392381, 72989159, 144240368, 464481639, 567576461, 208811886, 110025818, 344615131, 504836743, 689126601, 549317663, 256536350, 495055434, 637044827, 755680189, 710441033, 147463796, 72866024, 198066979, 950410639, 536920136, 817741101, 758811627, 894788114, 71371132, 203049376, 469348813, 244252933, 112978402, 593053730, 885617757, 251035480, 54924876, 976775716, 584502941, 845294171, 859322242, 327093806, 300595057, 762742782, 521255506, 366648418, 892252027, 843135189, 336375028, 87809245, 277515346, 423947390, 670011693, 602620390, 988534805, 100529074, 297622636, 128738783, 344608450, 518154926, 205357396, 647386568, 11413129, 273815071, 605745772, 535735529, 780955902, 238803305, 72160722, 488308642, 254210590, 719264294, 919889283, 282888952, 764466204, 84447424, 562552172, 372458069, 653243988, 107784996, 777947740, 525818672, 711547447, 610787417, 801221002, 889581736, 948028183, 841614516, 983296831, 187685710, 977272772, 280635424, 961847129, 998115970, 111650337, 570073136, 384637571, 797638626, 203603489, 875974552, 840444424, 5022121, 214667817, 422601550, 700425990, 950332521, 359699644, 477349096, 607903255, 408628230, 454876987, 925057165, 849290208, 844265666, 110547659, 564221413, 633072914, 459626433, 756990032, 247348989, 594762037, 251297917, 579784396, 215609723, 359577477, 429290021, 415521575, 220837271, 953900640, 438301732, 713833296, 65149534, 698800827, 595362851, 494746879, 262815013, 144840150, 265189890, 566926127, 76993334, 898333765, 17835830, 452704474, 301650402, 663567847, 428298444, 253914148, 809191640, 535886960, 479435984, 844894150, 487345423, 933498496, 181134868, 125345268, 42389657, 131653715, 807251423, 75043296, 192499230, 950313524, 249016569, 433675012, 413811030, 585822183, 609598034, 998802123, 970786381, 88230554, 855761103, 715802736, 741668651, 199019742, 300470243, 103541565, 46958035, 949825512, 19901023, 665694592, 398101488, 360291240, 479347567, 740914572, 325984764, 96515375, 391140858, 760356982, 162065718, 514902097, 13446798, 934842282, 47446945, 643481845, 650916997, 274827440, 60466703, 46039594, 622732027, 108310410, 374054937, 232598898, 463676976, 689682400, 726709547, 100101887, 759162856, 854559174, 970209121, 711617925, 223297725, 200010650, 855372343, 266700872, 186143668, 861030039, 578932284, 136075211, 13860939, 264400199, 416497929, 267037432, 83928378, 334419797, 51877942, 475756272, 778643761, 567767252, 279837233, 31567238, 936661748, 705028642, 763003623, 689505706, 907169773, 526676541, 981787899, 707360774, 305123579, 362150653, 32104807, 43551195, 994610608, 507210610, 226904779, 801658538, 592341185, 196399429, 763328448, 91766588, 961581196, 275225487, 610108454, 593106130, 566955320, 721662006, 692080609, 671707026, 416583738, 630245801, 124823101, 374487246, 248869401, 449615721, 257812372, 265633643, 390390413, 586517514, 546500372, 134967171, 768898918, 818241403, 45291630, 472610130, 390205777, 670852219, 167555627, 297912798, 770570567, 189748836, 108244698, 71445472, 91384760, 477716838, 854112346, 735945341, 378570791, 839134244, 275391526, 648385503, 911909974, 497615668, 186615245, 91037685, 592780235, 853572035, 9797248, 342681649, 164795852, 813142915, 233984455, 871484828, 428615449, 984751343, 814144315, 511943614, 468913955, 14762012, 473617234, 797719504, 634252201, 181911721, 536374860, 102497828, 790226011, 961068722, 908762303, 192125859, 5152282, 304090475, 617042054, 333542195, 329466202, 740960306, 655430558, 126815976, 498936276, 695104874, 955246424, 639659030, 137529027, 81802103, 232412960, 701096386, 974449929, 270228346, 186699289, 609632173, 487581217, 743996948, 985671186, 332634022, 485147903, 581478281, 219301122, 214850589, 475346600, 163073452, 854253371, 234509338, 496502069, 468855818, 349503909, 110610291, 381766387, 430080980, 842068923, 810841829, 10534682, 947195913, 844034129, 388075488, 512926636, 769590924, 641646561, 695462610, 27217796, 741867446, 650039840, 571763822, 595958268, 989627691, 942041751, 488620850, 906725490, 738659722, 171561129, 270150340, 157114286, 617892299, 196453740, 159775636, 294108940, 908735610, 781733846, 822314023, 236389617, 403793850, 603083633, 150720172, 504899484, 56707488, 757139369, 132591128, 854594007, 321310475, 96085648, 542789368, 523808403, 191853681, 688341705, 961825771, 44470840, 922087614, 110671299, 423160459, 907832378, 482389967, 126433630, 96027281, 58882129, 82663174, 601514573, 762275316, 971256592, 425337727, 668207519, 799665504, 234432250, 627014335, 575123149, 798932362, 76338584, 965156190, 176550005, 613917587, 546869503, 343050890, 424858864, 447827426, 347840103, 378296488, 136556931, 70633094, 846911428, 777655324, 991601292, 455291915, 789130000, 54330637, 837202109, 414406718, 993938425, 858559165, 703477429, 100808944, 77327735, 928953259, 561548283, 623227478, 951048234, 365643641, 252818517, 167510814, 587699923, 625586777, 473445632, 994728525, 284061703, 618756217, 816715560, 195231343, 421210632, 399800135, 694306088, 867095275, 74757158, 706512125, 866273470, 823656937, 894998246, 946362500, 189757114, 763717318, 445776142, 704467706, 516233296, 826183297, 570029020, 45508413, 399693792, 487298899, 872720635, 519724819, 605201757, 297021988, 444368982, 791740706, 592337095, 970969186, 257972710, 34630406, 983503446, 958825765, 461389725, 516812538, 249271600, 607004560, 167402967, 745492167, 196462803, 593822841, 371790444, 781601286, 838974108, 60304934, 501954236, 892339806, 695512128, 448888016, 844962805, 159162079, 31990836, 74774561, 141762230, 985045977, 85428377, 631563270, 79263494, 122317028, 83091838, 487472966, 177744204, 658507978, 481550271, 671728345, 305355193, 278568645, 502350920, 408610745, 568870957, 904104068, 733082030, 899456087, 200404018, 815058429, 171510374, 390681569, 480670329, 239521505, 772637339, 762848247, 26204659, 490997674, 153497037, 302542444, 547208525, 855511510, 17138392, 277672652, 74312849, 105069448, 483708873, 564390146, 711522650, 581005579, 466510771, 674519362, 173665206, 774365810, 976059071, 979769339, 261729816, 276408921, 534494439, 912640083, 880942367, 744850414, 373264082, 74809778, 989715410, 814604227, 138669987, 65617468, 283072707, 655117604, 290440286, 547721166, 799753590, 130111264, 764268253, 880385360, 438926761, 191066578, 744889889, 510646920, 35113863, 669821795, 568044641, 502992385, 844332774, 720124923, 935836626, 141884343, 83388794, 240776551, 673604019, 556412816, 408495480, 832511325, 864094512, 177093337, 242878916, 146080110, 706429040, 742829728, 517372071, 802578300, 30021023, 721027265, 367952682, 700566292, 337412108, 921065223, 2134172, 809038105, 179615095, 854005182, 650837734, 76771753, 944366236, 681807780, 94304479, 886226586, 979297603, 91047196, 392854741, 156791855, 60413431, 211564522, 142778973, 114485690, 504550092, 635733822, 518684238, 582214388, 319006625, 355831293, 286558341, 126340568, 940496988, 507180674, 763622231, 216451034, 837564003, 496021460, 393563231, 683175185, 975147219, 888744232, 937136627, 558018917, 141731169, 159826664, 512908375, 140343606, 473158324, 996338101, 592530785, 27061833, 250500901, 536192559, 69167655, 12488416, 276469737, 230188923, 150194085, 308567598, 808723012, 540153921, 635674218, 34364258, 573138692, 840083591, 246611605, 195674985, 322082282, 244902852, 254271007, 959404815, 374370074, 826457376, 617986086, 116498511, 57472933, 972365849, 273791633, 455945512, 523848134, 690680406, 824296987, 154743246, 238173559, 384393062, 28365134, 232912843, 300847628, 357572239, 889225029, 226717400, 52107095, 405474347, 427066161, 79890213, 103008317, 343414535, 210740736, 604262010, 679861650, 958056075, 946064859, 362162542, 221470715, 457854510, 118285399, 381566030, 792770094, 18934426, 142471862, 311487466, 836564918, 572520080, 671483489, 742321783, 687751958, 97064296, 756175661, 241019977, 154957972, 775471998, 304130498, 978405073, 501615246, 631332944, 64651642, 641029548, 660936550, 714033081, 500707835, 349162421, 644670177, 771160647, 872158566, 59207420, 671681386, 205747918, 518145722, 566827151, 34434070, 979169753, 559716998, 178410760, 100358641, 201318003, 439958104, 914645294, 233640120, 363985409, 840947238, 564881364, 257260688, 623440134, 688218924, 424506755, 638716814, 391362324, 600646935, 663237090, 694453177, 444767053, 384869803, 163063315, 425525399, 227105528, 94246437, 773703429, 49415571, 136116233, 400274283, 761034313, 220459831, 518975605, 435626073, 503711042, 224520753, 172158033, 169688476, 900391298, 457214657, 671655332, 92602477, 980673671, 404061464, 935534236, 849913394, 180425345, 934883624, 61880852, 645318303, 146641092, 86538392, 433500179, 359787803, 874144540, 139718242, 854425290, 23420694, 660818224, 644037340, 313731579, 218062397, 102161569, 28606413, 759825581, 248199165, 586678882, 914699551, 452648297, 515957833, 761562738, 233162044, 346326984, 853862644, 830841070, 425014203, 562235498, 49060902, 553788784, 640501662, 108346074, 220109081, 939152917, 239228713, 751798769, 226135237, 140376977, 399425437, 268426567, 764260268, 916098316, 809768337, 716730684, 681816095, 783870310, 817266580, 633543718, 860295118, 926929740, 679169149, 18285285, 687416226, 10675125, 655258309, 327587502, 992508473, 776465403, 423853303, 490551611, 84446753, 960494381, 959501583, 593455111, 434439739, 168520694, 1727406, 908945848, 803095277, 125371173, 334499687, 426374081, 902787252, 440197190, 333120704, 390014263, 807200810, 484971867, 157120824, 283844808, 90210200, 947611324, 494343818, 587813812, 274427504, 852316689, 667398766, 346655400, 740140061, 509352436, 636311733, 793205157, 183270123, 528821580, 83135772, 29784188, 353879407, 698287736, 463055531, 564759558, 261309523, 348463154, 188680933, 278609499, 288812098, 850382605, 978769896, 689671583, 370541353, 815874615, 42891369, 670704124, 988952538, 361216582, 200377097, 600601899, 403660617, 603939276, 145915267, 806932541, 353991720, 222739090, 368586496, 173009804, 541341575, 346398930, 233248410, 887591769, 755018233, 972094345, 420828019, 538842465, 251467951, 352864990, 895353714, 827680807, 381477155, 602468267, 937358463, 432578363, 389537277, 876644867, 771044036, 734977046, 412657570, 760256673, 3778120, 11409995, 62626762, 691073698, 807698748, 224926476, 129902797, 656649283, 259687750, 741591549, 595472273, 444741943, 80897351, 768544839, 596249585, 695134512, 651476099, 798592604, 459952429, 49958669, 679208948, 95615299, 940424773, 945722672, 910918817, 77983391, 98843349, 421638127, 489044821, 870903145, 783663356, 309232266, 609634888, 442417798, 722235924, 602236470, 752705151, 780987207, 743293532, 768550702, 674024795, 211633468, 353267069, 2192426, 881314049, 33473358, 518139082, 952775281, 681579622, 270065564, 616703943, 246953786, 428995132, 24565273, 167351238, 148186602, 174685767, 52000683, 476069772, 361436109, 585231658, 563618451, 469679252, 5357701, 89196354, 519323895, 685961090, 673888732, 286132475, 828058982, 112822276, 946475689, 257905571, 513023089, 984656276, 262605252, 779796802, 234689154, 329092184, 859106879, 474501900, 833568449, 993043778, 18201492, 529381955, 566675611, 981534613, 467270010, 872478329, 587798813, 879023023, 374380701, 670120309, 420572517, 346193120, 667691642, 586359520, 760217374, 191071261, 621641053, 194159506, 155133331, 995699089, 373945392, 760431064, 20474637, 345412485, 876654472, 247775530, 21134216, 292794244, 70881705, 17033248, 916658589, 147444337, 89432692, 414386538, 881071270, 547837434, 473533446, 563950592, 431464745, 973951109, 540099399, 297605937, 855141676, 811451846, 340000763, 95076030, 850913523, 429587891, 430009729, 671013372, 390731447, 347090843, 205520092, 108405652, 8610937, 898419346, 679778687, 823005918, 435834196, 666083490, 813686475, 657076421, 96022775, 511309328, 259539729, 586430999, 454335009, 51128306, 163494169, 798637904, 663557173, 641640227, 315750491, 300951877, 103033855, 558307683, 171414822, 547080870, 130034656, 139351265, 952833102, 313882127, 23194626, 723498128, 670016452, 863901018, 65330993, 149852124, 46095124, 966692630, 907631208, 179131687, 782141004, 739706942, 921071125, 580715527, 494175560, 250520200, 947503187, 935725320, 624974152, 932145690, 635108473, 583925009, 943993525, 732820609, 732185565, 205759698, 971483546, 818437156, 883818758, 648556857, 160853073, 347972701, 411936259, 342610326, 1583739, 260789691, 705388948, 411638707, 341823653, 201611905, 59596742, 19420395, 829664336, 101542335, 926730051, 647207668, 822562499, 830575229, 357823481, 67082947, 841007040, 19199736, 629848131, 785178192, 664795997, 650479804, 144711375, 969495797, 201903980, 469031270, 101126290, 601811841, 414972091, 707938410, 134643942, 316648721, 932553373, 196677635, 135823324, 285873888, 314258620, 849644979, 372485299, 144800388, 636534857, 486838965, 718959822, 609313283, 705527210, 386171173, 331314174, 927358422, 207060650, 411448579, 32060993, 82457790, 288165960, 569773236, 353415590, 489710214, 64054706, 662995368, 317744951, 133556477, 855690340, 76844890, 349078405, 636207779, 623873857, 986020275, 642789184, 775474463, 652034446, 412764484, 974653379, 219073536, 996179841, 579599740, 544736897, 622116016, 752676433, 253468856, 908940458, 631694511, 115245490, 961194666, 636914407, 120024094, 191172505, 656609393, 439224085, 662729348, 447492693, 546350823, 549068015, 255372250, 507793347, 168052206, 858606855, 38444516, 921628436, 509294223, 828094814, 850712306, 483075159, 349290839, 25623876, 748647883, 29941391, 862166371, 801032138, 617966500, 820599758, 3845746, 966326335, 777675275, 929792510, 480798239, 363340941, 800229477, 213124118, 206806288, 131423021, 2281237, 97345993, 240648033, 389015100, 997747899, 356757178, 821534044, 594625898, 54811103, 39965058, 853597808, 241375544, 574128743, 11988362, 908582406, 385618665, 157134844, 738833123, 613934601, 384663001, 322510831, 603178342, 293491005, 460701176, 284882285, 729110766, 42822167, 391564854, 562866607, 162115114, 245214488, 246562286, 691170784, 954382783, 678736710, 806486448, 314522524, 93013353, 599971230, 652909220, 964715955, 537175757, 445585318, 594260771, 843813462, 106748220, 716660103, 215228868, 200074526, 523646807, 597740086, 632114762, 972274742, 835482772, 703219355, 321798326, 434651574, 517812114, 204509924, 20101817, 227375654, 945639057, 926993978, 892140081, 33971387, 54769575, 343017605, 934533237, 652359679, 815572911, 946344014, 672916635, 246297237, 849036821, 914611642, 950759803, 859713779, 929340752, 654393783, 554300867, 336981082, 483922886, 248419390, 480989368, 417067735, 762990504, 835987161, 414281166, 638817093, 327949304, 6159449, 107960857, 850376189, 962053620, 99700399, 758889168, 988237055, 768654083, 631850309, 88507752, 96261689, 366891115, 68309398, 408303516, 46761286, 54054152, 749430428, 634462018, 487034145, 486095792, 293671586, 151810236, 112682459, 875405756, 407312380, 873856218, 903341692, 50900359, 643802165, 146511745, 308666783, 808686714, 297501769, 695548678, 843896752, 381994355, 56600070, 182654381, 573560643, 841926965, 664020617, 560814054, 172709570, 681490423, 192108237, 303946857, 60149072, 987681057, 604468031, 457280141, 277267148, 533965698, 800619727, 76691781, 92257236, 337794491, 239052716, 626317700, 399510502, 251704325, 670752218, 927152936, 889038015, 626736644, 275265385, 515648766, 19125327, 175166090, 568750119, 625501153, 470793115, 52455375, 801639694, 175190757, 316077270, 523877302, 955136331, 938114465, 726979426, 199636440, 608250040, 108896504, 595174659, 792356602, 463936211, 851690826, 238053897, 392791052, 305774738, 684591519, 135386936, 346051059, 183362569, 75586124, 646353433, 488679784, 832989845, 205664941, 113532124, 450993716, 187949277, 256063970, 337166613, 199202670, 872612406, 553546333, 903170555, 69845615, 660588872, 671122490, 563659156, 801725995, 355501935, 909118553, 939839093, 644663952, 347383679, 253593685, 523963999, 557203202, 826147604, 194666331, 861708858, 87952087, 883309353, 874998483, 91830423, 897276229, 129328519, 72811858, 770422665, 461455678, 485809884, 494883436, 837186598, 373830270, 631622730, 773475492, 275179508, 650861145, 355000439, 91562598, 629646276, 552922439, 713183278, 240019971, 175753795, 635093383, 584349041, 924850517, 54904519, 376147794, 210923883, 509987679, 441078164, 827377036, 698866406, 587171652, 575786123, 31433110, 365428766, 760895433, 43030326, 347978337, 886647197, 512325820, 691911219, 404955085, 289301521, 520045940, 237563121, 184761742, 89310806, 64570804, 952769912, 182768669, 819422692, 110269467, 527506347, 893625949, 143027389, 24016234, 199928619, 744422043, 702035798, 712667944, 289662759, 964554929, 933993721, 417058552, 210486592, 481812223, 666167156, 873934605, 411519672, 852799097, 515744464, 480268034, 16742969, 878069178, 33913, 648360237, 336920253, 220617059, 574545230, 566016563, 505981993, 643030446, 695159288, 255391908, 23004834, 176898507, 618476019, 834890391, 737275058, 417092945, 747097167, 834541403, 210034475, 216034830, 379246087, 809542926, 29333680, 292639856, 383070222, 570221408, 530397967, 887534051, 328850434, 15819775, 572402363, 47665037, 521758585, 623235406, 559513937, 398928652, 912874491, 932348188, 914108299, 727804030, 999497402, 113000817, 568451540, 798657516, 64214238, 13480936, 433132202, 730799475, 546728116, 823505447, 123465792, 833277600, 524947339, 935537821, 408657250, 445931457, 227996233, 111001807, 607457728, 22556178, 412910714, 647256143, 682939959, 807986364, 453424801, 155355381, 853278697, 868267312, 671536125, 716790991, 690718391, 24556365, 800422475, 200713387, 776949842, 640329486, 539718390, 892073081, 751106587, 465603578, 350979859, 392774049, 737668400, 337781649, 570031836, 166894659, 213634696, 621884176, 101687818, 647970667, 32660175, 407636294, 751408893, 898195838, 925428591, 491078134, 263892285, 693472314, 647131976, 432943337, 475860198, 741421708, 654638364, 409628361, 598518393, 276826709, 397764515, 829935787, 932166470, 929454380, 291181797, 239800944, 656409758, 828442922, 218293656, 715363236, 395858827, 656528604, 376428430, 910174862, 382446756, 816261707, 474529246, 254393697, 850736311, 814969485, 76623738, 807265106, 567179003, 852666402, 26368387, 243255783, 862174826, 437660763, 825663719, 153473943, 673815575, 885346838, 749354633, 227944176, 593180822, 883085309, 679358201, 101516744, 648517780, 558709793, 904250848, 135539008, 985417751, 890798682, 216080864, 160707469, 212818325, 936020194, 301272013, 917294257, 317856443, 845923707, 743588957, 452575338, 377267369, 180952367, 66228360, 637335141, 948476637, 273905796, 174664111, 775529891, 42269585, 389061649, 175304981, 791483882, 551138888, 981290016, 933465151, 136041626, 970828595, 881805865, 530659302, 131673355, 468312513, 966230113, 220075904, 574202430, 683756221, 691183272, 153652951, 391769245, 424822563, 433437484, 50033463, 582763591, 253174742, 497131125, 714012973, 544521248, 328421815, 259113998, 466040839, 361920263, 173139588, 137616624, 400261575, 427515164, 4512961, 626158842, 34495521, 938588464, 756817567, 112550928, 304678185, 47448887, 585855690, 709244664, 543616341, 507125650, 595913468, 392626496, 918477618, 303981209, 55545944, 327167138, 796348769, 999784642, 143124515, 869754010, 167008457, 540184879, 309886119, 810775485, 580121227, 621495520, 877405498, 978263781, 103176482, 521872626, 329576518, 21608418, 429930262, 61735471, 149962604, 707910970, 469969808, 809872010, 472286967, 604093798, 425499879, 937162693, 422644279, 128594315, 204673093, 102980943, 835177027, 502096004, 937961657, 258061152, 793960662, 514271535, 196523326, 541852562, 873091852, 536280675, 941856090, 665958096, 884888438, 887931749, 874413065, 850801270, 850663872, 51879632, 541168347, 293326047, 290895036, 874140601, 621956792, 52275751, 921478781, 941246745, 618333118, 445663310, 77091212, 655318097, 873077286, 267888560, 408025260, 18981265, 353135826, 775806289, 864073917, 603167328, 68268439, 856966592, 776452587, 716263954, 661943485, 526717345, 572613561, 984853298, 51022864, 389549047, 656088993, 922427077, 441440945, 653224936, 448980070, 623140515, 470763907, 599722944, 635319127, 159019238, 529939552, 270046392, 748818360, 14437834, 38036377, 744026374, 733758616, 589084785, 895697964, 308267335, 610700181, 417220922, 268299169, 517658714, 800494851, 790246018, 323437723, 419380138, 784530573, 786311667, 477348032, 886514368, 603053356, 8875265, 923126023, 67859664, 2263262, 81564628, 637668245, 405075398, 530065509, 516342684, 15161318, 679283480, 506446342, 423948098, 429864327, 225407091, 168705688, 822101875, 79145248, 588164816, 939238422, 472687075, 813777170, 209361154, 279961691, 426352515, 625176354, 436604018, 593656104, 385132221, 27457216, 422052678, 599456011, 977122858, 951149860, 134405162, 785476015, 683677143, 616292005, 592876387, 894096286, 788352055, 295190069, 262693923, 512958449, 653249094, 671314977, 563751364, 295612299, 885434715, 958402259, 327361439, 388685829, 190462685, 914374511, 37776931, 109622274, 635931261, 693618332, 737985184, 326378667, 771310969, 72792512, 121082634, 638910178, 738663801, 966524305, 886428042, 903333549, 139867712, 329635506, 454807900, 273652613, 948204337, 306326077, 680382991, 701957252, 709181371, 430040294, 646374135, 743138503, 784354119, 397902614, 980888582, 943024409, 469558249, 537402058, 365214551, 519765683, 902709049, 553352164, 137637347, 907447972, 492351595, 500016349, 853610680, 60210362, 555343276, 803732280, 977608150, 493311126, 667426308, 426868627, 876886125, 976520541, 340188918, 74523507, 231073465, 169232856, 977317553, 763305913, 874597984, 804314702, 365008874, 605724694, 166357858, 175474443, 760139402, 857101038, 880885333, 440492653, 120547624, 331179985, 598956111, 36961273, 382329770, 61313774, 903809554, 945582656, 603250083, 949385101, 101043564, 434069502, 741951612, 916167639, 41246808, 611429570, 796742463, 550610914, 855229128, 433359938, 395193663, 77778212, 741047582, 176850694, 948623426, 952477399, 117484004, 528373876, 126617977, 367414017, 354475843, 67433983, 117429056, 476800567, 886396872, 891911371, 199448852, 441790094, 66946428, 443042301, 508711359, 229056599, 82673902, 232183014, 199336346, 457468359, 422866886, 526609574, 123733560, 347225114, 923271917, 657287052, 401006520, 847395918, 440452473, 63820512, 861323514, 758565543, 371265610, 517960709, 175129097, 117311493, 635797644, 17281900, 429756483, 506461929, 144828127, 859719673, 644796141, 827465377, 580456718, 148887143, 17429279, 907614717, 163853720, 82475201, 308587042, 981207329, 187793974, 926167332, 86726967, 888737798, 67019956, 375639746, 597475322, 786503026, 402902817, 262568862, 960353906, 866336899, 607091050, 590957068, 976463473, 120265767, 644839530, 448102962, 54295965, 477178996, 52989616, 190430595, 52011201, 586395626, 68785690, 601268903, 642317723, 314572997, 891545643, 983947537, 901938810, 736840262, 587774671, 54152973, 214586270, 861629380, 375888993, 792128660, 758805434, 610722348, 652260583, 482882316, 609175648, 884684702, 767347504, 336326620, 980888766, 151313345, 144944714, 160879586, 348325435, 220761873, 292399268, 74509641, 821087756, 249138467, 57586107, 499141761, 681909765, 895343661, 383998405, 385054846, 697772610, 264686654, 537728762, 927037010, 337109270, 45063887, 995195801, 618825483, 58929949, 276959075, 23587876, 914564694, 339702450, 604099902, 393966428, 376107011, 851587520, 890345473, 258642304, 932864771, 158665752, 339652727, 650186666, 270649104, 65197338, 662303000, 15858541, 569732331, 866185578, 223798270, 825764245, 843024789, 101338031, 834345592, 71544288, 904700599, 118338327, 964307475, 594438972, 288590904, 214853027, 145110207, 209897947, 939130459, 421663399, 197831322, 324476394, 583048009, 917410219, 60561505, 641215483, 574952656, 886919000, 816078377, 65318921, 782841805, 747501604, 676311251, 799133890, 976868059, 877038081, 777666581, 739769252, 10136799, 241979462, 722892501, 857047564, 404427106, 832677272, 585390712, 769285413, 906031543, 349457511, 721635917, 927345330, 772364528, 209577357, 555120129, 4695168, 474495672, 143482042, 932472003, 745430531, 458513346, 651362574, 598785325, 353207018, 93314772, 603236921, 979520041, 788404896, 560078389, 780473405, 296242445, 752161002, 220526906, 539137168, 907574311, 403478485, 805337219, 58598089, 878742722, 549395077, 315942498, 749481217, 135708856, 667148767, 259852233, 984878579, 987103894, 976269887, 303403900, 808792230, 600338356, 652246795, 792897565, 650428497, 762615000, 738791701, 688806767, 590832939, 686630628, 507938485, 572952486, 825552348, 919231805, 452861061, 483028085, 217349787, 947455678, 364148776, 56493453, 316277170, 31574773, 595665536, 239736705, 549376748, 316952644, 284495528, 212114030, 813421410, 116411703, 523668683, 786614230, 304726939, 150842231, 948448954, 34737850, 493604710, 731446594, 622597283, 332155777, 364083193, 193205747, 954212009, 117648665, 974856949, 327768384, 330407921, 762849413, 140293167, 434601332, 973565189, 627083534, 653063100, 634332653, 386853928, 116191635, 940640576, 258620498, 114318003, 853979089, 91719532, 692518439, 792326132, 937904356, 529723730, 490990931, 277067415, 86607700, 677037103, 434003989, 201599970, 649445958, 324970611, 999537882, 251090903, 11342933, 516918482, 941334890, 415313024, 95764654, 413128439, 108701547, 368856990, 972235813, 675853728, 669950736, 267662711, 822747576, 945139068, 996580991, 589168745, 359273257, 594889446, 824721692, 390361406, 223865396, 471633036, 691222512, 471409414, 523422718, 98001234, 498086030, 948552917, 489569846, 23669927, 557800862, 692740353, 373568236, 755027028, 982277692, 351987067, 196035754, 61130376, 975378300, 222823560, 242484661, 460401427, 793609977, 537519358, 69276576, 712146486, 307076371, 995253598, 633919947, 580086650, 606929191, 48353269, 783009465, 721581714, 668116121, 153850855, 626082663, 840705934, 594125188, 500923878, 448800818, 185831989, 704189761, 868088451, 380692905, 863853789, 656449090, 324476482, 60254016, 837900799, 452725656, 659128754, 101539499, 109467980, 155891588, 12668296, 450520351, 707603304, 762377913, 118543020, 819422606, 224953226, 137940282, 157114551, 688954616, 248333325, 912805632, 98708017, 651095395, 664533352, 744976589, 573544711, 977532380, 80194429, 908798935, 744326218, 455044147, 971540534, 451000305, 943542245, 963557281, 582450696, 215352592, 488474896, 378125462, 397348884, 448842889, 142377177, 661147398, 445673740, 15200016, 998593620, 666403862, 742124295, 882357119, 840293485, 247896681, 238510772, 72077097, 790191782, 29349972, 444514156, 60055191, 357220223, 979465404, 213448912, 93620179, 998112855, 904557816, 726980458, 662114361, 820709172, 604268576, 488994209, 322008906, 834762719, 932202560, 740259420, 184447499, 473221960, 334798983, 665080520, 24273087, 784268332, 533649868, 530197265, 205873936, 206599033, 266021515, 998694492, 469589730, 42437456, 28871806, 763044667, 873180659, 678279234, 837553236, 14862073, 271226825, 113309564, 281589712, 739389790, 889650511, 208213166, 110841140, 252055549, 663348023, 477732817, 7429285, 252607696, 131403048, 701598584, 497892468, 188471695, 611866056, 826896571, 572974253, 127095626, 724147526, 231357599, 31807592, 24922946, 688294501, 53645973, 154082972, 396763680, 773230225, 830184377, 78574159, 355007890, 44038892, 27804658, 633282355, 262090439, 743135846, 249950277, 192811674, 757764405, 62917549, 703165987, 980510195, 792376043, 180718987, 661013269, 526504162, 551175253, 865845592, 212475506, 477412448, 724187955, 842055161, 625270760, 956331704, 517596657, 97916410, 739193309, 869802411, 528315079, 360053809, 791207767, 882453767, 665452919, 378750740, 797041299, 862416661, 935701931, 821397038, 753651411, 841721477, 234942511, 996583632, 408198954, 14034632, 461612983, 188296368, 949255785, 332549182, 819710392, 807244647, 305828812, 783388050, 607019126, 99353559, 257546142, 689457037, 990133928, 894447613, 545445656, 653747779, 676054528, 217278583, 124993572, 997153662, 937480216, 39349814, 595138638, 337393021, 211550234, 504307969, 533248999, 129438619, 108570227, 708148417, 772152503, 267364797, 524640969, 325993560, 998351111, 469229862, 730441223, 655163648, 868649092, 518031005, 541225412, 270251999, 548125803, 10425728, 525185222, 9204728, 131213515, 130379067, 446123568, 927010661, 155732318, 203909777, 434524902, 100554826, 526707156, 497831019, 262196685, 437719028, 179120960, 392856653, 602082239, 323312790, 913478482, 894886692, 554348994, 463452016, 649855437, 144865710, 427376073, 133240608, 594239105, 322230373, 613679652, 510444121, 460603812, 111683891, 945694476, 777131582, 843885076, 257664933, 615111746, 267339385, 200872157, 146316667, 142074036, 370236263, 92122618, 225056129, 87570433, 571232247, 381912703, 940394360, 593327812, 567063392, 676159957, 234989543, 742841948, 166529760, 225086103, 913079762, 49515144, 967645431, 896918959, 196011864, 584923654, 570315000, 150408083, 822732739, 537686339, 408592887, 783001547, 74518797, 373960945, 244844335, 330536997, 226264460, 721909404, 247772145, 441264015, 131302296, 527771816, 785797208, 212875804, 365168372, 208349576, 608825116, 793684232, 433802337, 39697415, 384438798, 388853826, 49701207, 398984205, 757659637, 796349181, 994312700, 627122121, 82435278, 493069702, 515248501, 546603785, 965834786, 526914898, 115138670, 985842370, 909078792, 151634822, 321788442, 906852944, 987383519, 49132989, 698976144, 672622668, 721046966, 729027142, 263197472, 249512040, 137370994, 521026422, 364426817, 195958050, 16299585, 425890527, 625702258, 335822777, 424725500, 488877154, 685813074, 296319954, 565670800, 287696728, 167066321, 992409332, 934496703, 99158810, 900312339, 97498111, 169685884, 521937130, 765513359, 124571992, 203584265, 672693836, 972858163, 440771082, 989344401, 588486979, 656400850, 656739676, 400164013, 335522317, 957086244, 66512514, 358881508, 292329301, 847231903, 887585371, 492071164, 306445174, 289743471, 969552904, 979238531, 166750197, 197863223, 210045584, 684778819, 508077053, 598622997, 465773284, 892792175, 965069659, 945623383, 882285593, 689327749, 479874469, 767695076, 527297791, 876383747, 518501490, 236982142, 907826709, 654711977, 916402673, 431452070, 562261673, 472069762, 359557263, 64810834, 109374255, 478650822, 467004910, 658094620, 491274748, 740460451, 517543485, 170765760, 67514164, 189397661, 897754899, 698916301, 257869149, 585911865, 291081959, 355807935, 627699562, 672697863, 378153285, 310892216, 905756458, 800338532, 100750514, 262183716, 385726789, 515212062, 846988397, 741374778, 935501440, 537816412, 314664588, 644113669, 805423838, 667183662, 133982075, 16537263, 833930839, 805432347, 894702606, 670328405, 721316608, 203701296, 647642986, 766493404, 833396174, 206548314, 914613230, 464595404, 773892338, 176327344, 9907258, 501134437, 119424939, 960574421, 346776928, 93566189, 128288733, 347961755, 811468230, 877106073, 644907164, 710382873, 869396556, 562782076, 271765576, 150138418, 519977004, 311698311, 473295216, 558074020, 902864750, 63041947, 167981179, 681493415, 922625311, 139430698, 384836998, 244776809, 107743744, 758449660, 916446839, 540753121, 278640466, 866749835, 629090566, 401081817, 572463831, 841700278, 848981752, 237392150, 725968333, 710444778, 957935789, 644064172, 223760774, 318145713, 281506276, 898237029, 323892409, 159059807, 190134405, 294689647, 546793765, 415166119, 804075443, 573070018, 905183941, 218117932, 530716709, 652063303, 548801894, 927902568, 808006137, 920933209, 500073133, 647776322, 659772860, 591719804, 403266533, 762923556, 73290294, 234330065, 169646963, 32726695, 276139069, 619517579, 94969208, 573126573, 475169877, 785419071, 91259602, 925628376, 770823169, 731619344, 397469737, 394041073, 407440988, 400544707, 508555515, 622476745, 631173025, 632188256, 671261913, 491096014, 164228752, 35354379, 425967024, 583889894, 823660279, 660854351, 882892134, 634823066, 683965824, 610667142, 911936924, 833326313, 574395477, 648618034, 38695149, 812640761, 47975790, 43669278, 221004393, 611878368, 972110440, 638775488, 940561069, 129650387, 862979767, 37892033, 592547251, 253500791, 96549002, 851210732, 799875318, 42775206, 217785275, 839517296, 485435343, 301341764, 699605206, 954809569, 831990133, 725019958, 845531437, 366243854, 516759022, 74913138, 722525954, 486903351, 760142955, 371742760, 955699818, 574118549, 686924598, 257711843, 428446660, 766898099, 809633088, 630538084, 734137233, 286724018, 461627394, 870153680, 165372175, 345946907, 209163746, 910524368, 863268309, 803113671, 497557351, 926003720, 109385640, 163507920, 714769276, 182892738, 899213809, 516621674, 289514672, 848715525, 84721576, 753001950, 350550842, 812998504, 610300904, 523736468, 817253803, 336975471, 371593140, 785989146, 497109701, 206544816, 766441671, 99786593, 133215921, 878373245, 58170562, 606637933, 315565907, 850625031, 254982504, 2322375, 673931608, 103146591, 889791634, 53859513, 236213539, 754138773, 546612172, 941402980, 592443110, 86066893, 277639763, 162332751, 86043732, 212529565, 441213095, 360491824, 840785602, 190393423, 642379966, 80721313, 402355242, 927781196, 469799245, 590172299, 606339937, 5413578, 146423737, 148690376, 243111532, 829420215, 697815025, 636806172, 743365981, 460814626, 871812196, 504718439, 862071287, 252586500, 993619929, 479977191, 631733445, 52870513, 743593306, 741570060, 777667534, 128151224, 771329306, 41041332, 10597413, 352729929, 251188185, 225372418, 12479020, 752477331, 3942053, 125814946, 70913120, 720200933, 279271291, 566848753, 858073122, 940910986, 877798775, 871508440, 614062856, 815594058, 876059723, 823279457, 480929260, 40352357, 988875365, 297921063, 731759155, 603935241, 729487379, 817871668, 668187609, 929237989, 449086970, 186122534, 101142710, 929675463, 135089418, 552210928, 315426627, 5233712, 917921754, 657055609, 550266139, 470265096, 883827453, 729646435, 357677816, 845952811, 571117015, 913977204, 601693284, 529006886, 932917762, 481693141, 698906180, 387959675, 260035439, 842171277, 824516600, 518015700, 542728175, 577998960, 101069416, 805388411, 766447926, 328929560, 751656721, 544965822, 760463448, 198196402, 842324505, 804735228, 462418359, 335418143, 242105522, 281665241, 659291071, 347839273, 356046462, 533799667, 828569252, 512190786, 702549287, 260895952, 381315749, 769239368, 882609635, 584481294, 388448206, 407451586, 293198400, 270174447, 120208446, 241748147, 483462515, 776793722, 622388507, 200330775, 967010761, 250576677, 726513472, 726069485, 725439316, 200261002, 718960545, 34542321, 549026667, 660725122, 5422737, 57121478, 842793349, 291340232, 287998312, 721236850, 785406424, 748750705, 439322697, 517353480, 75322660, 585021555, 136739227, 145850185, 885888503, 422838996, 50741698, 48628260, 839771517, 39389077, 528131123, 14368544, 350171894, 238796002, 245854429, 947070820, 45132283, 543993151, 836508620, 474595641, 558050520, 782193545, 156670437, 234184698, 892054889, 145761990, 704569628, 224043634, 206824689, 393141268, 723310233, 832981496, 387984497, 40052999, 104574663, 813746006, 817384975, 63898040, 486318506, 260064465, 592943084, 23240710, 847527467, 376923286, 259246087, 494098014, 782663012, 329419024, 342227885, 62768921, 611248875, 246285944, 402000507, 442687545, 975034547, 207136541, 191403959, 529045989, 572879496, 165786144, 493192255, 847716119, 119224490, 627518886, 323209929, 315718783, 916494290, 585702839, 841464216, 520932310, 348489811, 132390501, 413377524, 540371257, 418168873, 955036878, 920608636, 540154184, 508876743, 920740995, 757782801, 310874249, 42913631, 242879670, 158677242, 738144214, 344828545, 939390462, 197869905, 17670721, 822852448, 368984731, 258867973, 23457688, 387258074, 929339415, 509717426, 951194537, 644767317, 425955444, 636212887, 879960645, 710756791, 669166455, 179292324, 550357170, 948313561, 476945344, 194469336, 106095815, 6855386, 418771434, 11548757, 192304716, 354748364, 979469930, 915164147, 501698129, 273809447, 946197186, 829167286, 6569904, 915403236, 592658407, 779327442, 965554044, 201160114, 626496382, 143101120, 467741750, 83550289, 957113319, 796441276, 403558241, 452000951, 501480131, 370959945, 467091176, 206068140, 873309189, 662471285, 293941493, 925133724, 927881663, 724887858, 128222908, 665734342, 101477207, 573121739, 62293481, 140592987, 838853678, 192757746, 659024968, 961526019, 719306213, 425334014, 877597363, 23620544, 801210194, 723505418, 512102487, 442685714, 167435703, 31418071, 836770231, 480734294, 419979204, 635484044, 908139479, 176554736, 181825074, 322968209, 139909800, 253322862, 490170426, 136350592, 649358312, 302574281, 282348063, 155512751, 307954016, 473817489, 654207331, 5436170, 325483422, 300442500, 456426061, 159594368, 535209988, 979458828, 985836157, 807354866, 983177844, 879879653, 868855174, 572852449, 263839686, 898635347, 109095469, 719294624, 593498332, 365882058, 871630404, 784843924, 944376771, 417073129, 990310588, 925143393, 666279219, 23486219, 283420257, 103641855, 518238127, 922990123, 95033471, 361689283, 27046571, 750803698, 664675800, 929772949, 835429007, 448952546, 329167451, 940031872, 730000965, 55981542, 705416127, 212837235, 36334507, 358262807, 297452244, 190474851, 892271380, 397812639, 840169239, 661632956, 341583785, 235284456, 792636700, 993381847, 409644560, 231217622, 676533253, 335609291, 206675057, 273249101, 688936209, 499971347, 903352428, 922367950, 953126803, 587591703, 45969420, 291330793, 624972603, 603655752, 818893524, 64714672, 380762708, 906415028, 876498239, 699719436, 484929292, 609934802, 296958649, 23073869, 709142303, 408520799, 111061964, 803572874, 711826541, 166166274, 594694644, 350363955, 553825098, 632161490, 94517549, 685210653, 944398116, 38503506, 453895113, 667927695, 645246018, 752596372, 181454665, 331458940, 10102572, 123200794, 438733782, 328987668, 141403688, 59458490, 516081376, 642431121, 941952532, 868287545, 319415044, 49122833, 757057612, 708357766, 790421965, 5217861, 66414072, 924885090, 304545843, 459822034, 42465726, 387934381, 785675694, 920267660, 537434082, 576966922, 813718009, 166029160, 794120106, 516643062, 60164841, 564372781, 459717578, 722913673, 161064642, 852147205, 579346661, 953891836, 588221117, 136824443, 515520010, 313576656, 714496605, 328882696, 860464743, 724643122, 302908750, 872755722, 336438801, 37660795, 380446259, 651591349, 607672690, 992932972, 951372211, 386124193, 140953678, 992674336, 427825601, 198394579, 508789731, 340662251, 906587698, 228275429, 914005210, 699733997, 768483920, 336742232, 103303366, 573215799, 316210908, 892578609, 539215582, 895428114, 928963798, 219288042, 501555439, 478176946, 276956746, 519471578, 334295531, 926375044, 345063213, 23875692, 686149556, 367625240, 923240099, 982239442, 741830844, 971996363, 91092087, 125816144, 438264806, 645522119, 995380476, 204340647, 36511733, 667260736, 568561194, 971218134, 178918322, 949928767, 789381313, 509264196, 10263012, 476890522, 382824839, 3218061, 999536627, 700400549, 572949255, 57886355, 487664935, 731446068, 322009859, 210070872, 635250343, 760441464, 417263317, 220352282, 304817437, 315068744, 446843190, 490017609, 343743367, 105476786, 434737547, 994554761, 125915220, 258844933, 593206606, 992612478, 460559537, 821406314, 120308316, 125228877, 989891967, 763247003, 730689118, 750112393, 269886315, 861612147, 629495284, 995271377, 913623282, 978957667, 380748574, 530486543, 167045933, 937239766, 160580490, 345465742, 740087287, 199648178, 653218537, 72489425, 476356938, 915030851, 369847305, 488603102, 748491983, 668414874, 588278894, 839084007, 313513944, 823900588, 528754019, 465405229, 119394206, 764564499, 781682760, 768038805, 283974265, 919991884, 286246575, 411639386, 718738709, 942980697, 605508594, 829933671, 195292656, 217779951, 859693672, 454573827, 890381626, 358387257, 123208115, 784600970, 242228379, 521302177, 108688846, 257769185, 170722859, 611742154, 454304626, 120429193, 638727409, 712185096, 99864273, 982797992, 39289361, 802458098, 735885733, 138084382, 672038835, 429532229, 755424421, 11925113, 541359535, 3851220, 710612587, 859049326, 226824303, 378084817, 880905535, 512639926, 398079207, 476111746, 465709568, 111165360, 888093349, 203252506, 723749908, 203424701, 825026113, 444412103, 922233310, 560210290, 263342011, 185902702, 374098121, 714403466, 579892033, 926077980, 881590611, 592431918, 535563527, 660205382, 321451635, 650161553, 188291674, 475172216, 432182421, 136427279, 8881214, 33065180, 980582541, 830169402, 897741831, 833919490, 388757005, 209625960, 562298219, 841198286, 387086913, 28416165, 536234169, 936261092, 869795200, 633732255, 583690402, 912909935, 139543276, 295173807, 369212592, 128305827, 496678049, 601911890, 430842764, 192944663, 744982815, 458347151, 299367511, 841537730, 896767969, 590883800, 853102476, 291073748, 38199782, 169877189, 278260782, 6151558, 538848297, 3269711, 778799547, 216863126, 877732019, 40211908, 395565875, 848362778, 943910443, 960162466, 101405102, 355603238, 135225239, 557541527, 904773738, 342712166, 246845344, 699751661, 911194592, 648096980, 202600981, 321991432, 831954226, 405563561, 235136064, 101066582, 925943261, 315656633, 802292044, 755633593, 70336119, 692592701, 508200218, 340826610, 1750178, 287346399, 582669040, 18613000, 603477370, 429182991, 152439405, 548373113, 941685992, 122525121, 311596229, 677929072, 686740419, 551174646, 975646265, 174912871, 332086941, 835188258, 104665797, 923155760, 690799581, 463316525, 760937361, 408402794, 384524154, 238999250, 664811069, 34623069, 99809581, 791750190, 540255705, 831495122, 664024318, 467793965, 687662630, 505195105, 679195454, 712640518, 404407807, 18305707, 408796821, 94745392, 987122058, 359243208, 940404516, 349437398, 700858946, 245834038, 960239156, 804893602, 414277640, 524434576, 937737849, 862822848, 241356490, 448653891, 774625363, 700047766, 858170727, 468696270, 371169750, 812305172, 407078248, 319459080, 14575559, 869916696, 605051064, 458270927, 381614459, 220493295, 669826685, 76699142, 742313538, 578655087, 99348549, 638289611, 424994279, 483573056, 266479939, 311283706, 809813501, 306650477, 651105684, 111914806, 693116795, 906857002, 399146430, 786713284, 58050971, 804773502, 737274400, 334221521, 525382798, 480411780, 64547304, 830430168, 613743921, 810720079, 711016591, 587876780, 227859896, 79903628, 337415814, 766925192, 413953085, 968071044, 940492735, 859606382, 819704046, 12571521, 514887247, 43987415, 279859886, 994722731, 328252401, 976037706, 275183007, 230168557, 828639678, 605959544, 734868936, 388402530, 134605131, 34448834, 907706720, 474480183, 909648787, 296872443, 281198647, 209099299, 150879910, 859487805, 614744388, 951273151, 488629713, 747176645, 708701155, 770402504, 82304468, 272665620, 714995640, 183339898, 167226600, 992408582, 762936226, 656294115, 598872996, 13998339, 6350989, 532873732, 937248614, 778562626, 897640513, 615948966, 792820661, 406858956, 546914080, 588869072, 426952889, 598364892, 191297659, 120704582, 644852405, 708465877, 775149887, 945605391, 506612855, 717259397, 191960151, 415460960, 995152594, 53517496, 635862395, 783703951, 118419086, 333273658, 202619752, 956842788, 828608954, 247594391, 486314327, 935831027, 622762407, 341722913, 626166471, 453606090, 687925155, 509417196, 294712725, 604592055, 421356081, 9058670, 779205232, 392055054, 362551501, 426148834, 860250353, 519977462, 906522317, 930415726, 552084938, 616437629, 576705321, 7496740, 121488452, 161109625, 378495403, 107966941, 269582524, 873652229, 963390414, 360032608, 680211738, 30528034, 975781893, 947178499, 795226803, 723332746, 644660874, 505460180, 974723066, 17769636, 496865400, 88582682, 702819664, 450199753, 52486241, 905400247, 324565347, 897553650, 103472998, 88298964, 55675070, 349775971, 544690673, 731527179, 698848609, 885487562, 265062202, 18901143, 680267630, 598718277, 421330350, 814137289, 263434356, 841012098, 153092659, 667394861, 772141886, 945357666, 951279095, 909371941, 748956611, 6518243, 267842858, 85476437, 328802615, 800045310, 808027768, 771030694, 698097889, 430292786, 19650646, 404998264, 967260041, 712251179, 181992048, 347634203, 816234379, 117822975, 127505309, 747563181, 490934013, 557395675, 211291887, 223154085, 485661142, 711988747, 490386362, 668940330, 114222388, 21711786, 15885505, 498726207, 673204654, 71176026, 542442118, 161717400, 299082634, 995073525, 328189, 92569138, 997852171, 908947914, 813913506, 124349194, 789749376, 769205401, 269562832, 186636431, 426218102, 987439960, 544658443, 479448402, 359333995, 648863668, 239938482, 976105248, 382163585, 656693477, 622243287, 504517466, 190659743, 860406322, 768925516, 511815339, 458942205, 678796225, 416040575, 156452195, 964068510, 842839309, 905514460, 11144761, 432563059, 176911966, 456629418, 532858206, 34590659, 214199089, 147703879, 545256018, 978060125, 65582640, 149467035, 918430291, 379345633, 622068290, 396545312, 977416432, 63842925, 184455097, 204992624, 510279037, 614875420, 428249734, 841258722, 408456495, 647480238, 261208502, 65797812, 14725872, 816263207, 946661533, 542184888, 684113035, 84437586, 894534273, 254331636, 796284355, 672810683, 819989474, 500256200, 459552541, 28567396, 214257117, 525729166, 150776706, 586271576, 790295716, 626619327, 209071485, 489447744, 497595435, 155169688, 445608984, 776099390, 524387058, 852225576, 159753875, 813052077, 402968709, 762130352, 186273743, 174523603, 79216871, 192007964, 225019178, 35652806, 230036032, 948807646, 303228740, 951629767, 536049215, 966846327, 692095613, 340057254, 603574174, 915550365, 825315163, 882691915, 608723687, 367601953, 112038743, 13274181, 831989424, 869841685, 577819159, 259189514, 549749748, 810136887, 729113868, 690884449, 317160218, 823033729, 758518981, 307563808, 309914537, 459685973, 969543661, 663381326, 540739901, 212920707, 561781550, 504426141, 335301075, 955692024, 927550140, 405804021, 434328713, 59782753, 778018240, 984942164, 289451232, 634204391, 832757962, 121992967, 385449186, 344371929, 392184443, 365252327, 236371205, 878550105, 49434950, 261401138, 139863554, 334960475, 663375380, 449522204, 628030918, 640126330, 153095079, 274176702, 17137094, 622718747, 198225209, 896215535, 196291294, 788104982, 360945542, 482199517, 61780664, 804733709, 842723295, 533175212, 193714219, 146606031, 554831158, 740931736, 981235034, 385101037, 324038389, 98081803, 209652112, 524894538, 556906949, 598381091, 365604455, 818344672, 145038560, 659478050, 260009568, 319651343, 954795731, 280146749, 853755722, 219352039, 953565398, 90255264, 393981532, 346642972, 532744470, 310389855, 190245913, 328470773, 424054072, 403575815, 558839948, 334518467, 769231832, 12081507, 997455998, 771087184, 259508275, 868017645, 605782230, 686114316, 59878676, 512238943, 400104445, 321510643, 462025001, 603044277, 328512662, 600729499, 686569708, 81202808, 827955695, 90701616, 168089048, 683429175, 156114411, 604926801, 151662587, 499929537, 493827720, 509738148, 301464705, 501122521, 249712851, 30187108, 710309730, 586920958, 927459710, 401474459, 301164580, 633391583, 257401333, 259356285, 754962158, 892424132, 219763360, 509118939, 750925801, 861610700, 327005274, 381364486, 100711487, 347593386, 662209524, 172152635, 476244143, 322120484, 871870739, 719287612, 868609561, 651082445, 73636870, 255939116, 864788918, 733371060, 477885549, 447515979, 260996223, 132862823, 9583465, 559904138, 842922601, 327726928, 775409066, 354271631, 886723820, 420128334, 213515576, 647417009, 230672650, 454593239, 726203152, 936692197, 416445300, 456949911, 221639320, 685988178, 394522022, 262465314, 685031777, 902499325, 967273575, 719722451, 477426687, 462064336, 240435241, 808718934, 185781824, 832888331, 366910820, 961004930, 86059875, 956313269, 784726490, 953237198, 837845776, 214144929, 701312907, 262779831, 739743531, 892270841, 466574750, 1215306, 768824917, 746555034, 400290052, 559339803, 949538691, 969212821, 778764948, 367796259, 971832334, 318690822, 152208137, 488621157, 198313074, 638012602, 482728992, 803205947, 359705174, 410867432, 228602165, 352547701, 471210182, 908030487, 543127353, 296263554, 970864038, 62671823, 792301093, 70880162, 385321664, 97480719, 55827638, 477772880, 658189900, 120651222, 674288129, 333015276, 738755540, 405660289, 688503710, 639721734, 267102902, 315516912, 355321378, 389200539, 305027369, 787939731, 964381539, 451299247, 617738212, 670213495, 218233848, 832899665, 766846933, 898597988, 88124389, 680213005, 556496917, 451665291, 656825152, 185894453, 32044409, 901205796, 519326973, 960333651, 890480591, 434446711, 257679847, 830873669, 760349119, 603681116, 122837758, 320013743, 534585140, 873829971, 525098623, 505708863, 440206900, 323727428, 527038408, 649288459, 142139231, 290935411, 691579108, 198133237, 160094525, 701840136, 296034162, 563056640, 190092175, 139509085, 540792072, 344486466, 863838282, 600879284, 179593093, 187047607, 26776479, 168378073, 899360405, 828269168, 465261643, 781888369, 931994288, 834939308, 426677928, 647208354, 402244955, 730435532, 959581419, 996373017, 667014808, 657901092, 190731110, 711577958, 232526504, 333247853, 176727046, 10180409, 724262278, 502265987, 329312512, 18124509, 282124519, 630989209, 453709216, 177263908, 413111933, 289384921, 970880912, 182489879, 339211025, 146656008, 959513366, 629064580, 352030355, 414154639, 496749821, 627145848, 223333156, 821016984, 781966258, 261044075, 497500688, 16667341, 824170953, 597569546, 521679983, 400713508, 542701004, 357782139, 465914297, 927778533, 753680607, 257000935, 626393737, 965286183, 920432992, 252504013, 313553372, 107790045, 418907980, 510190789, 891476421, 769614677, 553500633, 199432169, 197001773, 365693610, 457245626, 366300036, 592104168, 130404670, 417948251, 603475688, 752343881, 323385396, 758556261, 220260721, 43169261, 846445454, 217129972, 639523751, 249537432, 842533304, 715835564, 368029558, 966763665, 196600356, 808554525, 630966134, 964575832, 175975053, 198385658, 691905999, 82557518, 650962536, 371470137, 733322132, 212450549, 598348818, 277425049, 625018232, 488610139, 806632339, 112046032, 490099843, 668142910, 8007771, 926932865, 137644597, 927858069, 967603834, 808921704, 447448488, 553292832, 75358558, 863777398, 386448049, 54718169, 18590876, 984857428, 6637357, 849668307, 966842061, 298091282, 405675764, 215956096, 302894366, 373660859, 427050783, 994494367, 123461746, 34863209, 320582400, 228039657, 227350705, 66932536, 927138285, 960435012, 777500193, 841763461, 958742419, 834611620, 597628234, 310277554, 549557507, 286537570, 168324710, 382027750, 480056019, 474276066, 964016314, 662968498, 466477437, 302044787, 385988225, 283093622, 134174236, 901225469, 533357237, 66107851, 932033817, 918427370, 682193199, 303783850, 536505584, 378436218, 884577741, 928760840, 756449245, 868856148, 146924578, 347061919, 43368932, 759003892, 254700498, 525319813, 167652958, 576862186, 568230661, 808175752, 681090647, 517335221, 115744491, 360093158, 195548411, 138863758, 255320134, 140781891, 3355627, 539127692, 477485984, 279642756, 212827439, 32411215, 375957696, 168360979, 827721473, 765078939, 519684530, 594643045, 608411770, 145571995, 624288942, 623497818, 686964868, 865361812, 368261800, 281062241, 676833381, 748659474, 63013760, 888319126, 273041799, 587057113, 890313461, 436125113, 334011451, 976651848, 641666783, 166676911, 68324818, 912419925, 885991185, 179084112, 152067355, 967964379, 665223433, 99675017, 940652080, 857890798, 241337956, 631334966, 554356411, 798617746, 462884304, 810305103, 865743755, 918301077, 459666900, 390159346, 861328577, 156938956, 924210844, 563610348, 675733506, 780882061, 254902242, 351884033, 218470579, 979702960, 918168918, 320142815, 510354946, 569524481, 831895169, 219892530, 955291933, 963487946, 593756316, 751803878, 235933334, 137372912, 701414471, 350178797, 840331820, 292255250, 778437193, 855730466, 949950907, 974426110, 638057666, 682528141, 173960658, 974426050, 130942661, 3680728, 781900206, 791752262, 570788434, 571937500, 576024615, 403075295, 325671507, 190549184, 51834131, 118931851, 777112959, 161141967, 431933896, 742318868, 966554051, 778590512, 595387941, 278276709, 369364210, 374910175, 732931033, 201132020, 816154433, 78344512, 171281219, 451949233, 95938798, 254429112, 495235180, 512190917, 788661771, 834973721, 769191113, 555989504, 634697822, 324023915, 54262728, 308268164, 963956317, 211215494, 965265015, 402168919, 942494763, 878356628, 665355169, 433200613, 593116082, 236650719, 610998783, 898596515, 820072024, 236299123, 32817204, 411369606, 660294239, 735398255, 828308462, 132688742, 860263456, 541041009, 643348793, 814442662, 57362740, 11329437, 926012197, 663274395, 365912189, 533682378, 86778572, 135840991, 804220326, 84048633, 567340831, 192877861, 878162670, 447153359, 869405959, 816583136, 837220686, 181511185, 527501805, 416855095, 802090772, 415264997, 206304779, 782998589, 710677099, 223001194, 821648496, 270480589, 539379758, 488220563, 663598987, 631501906, 255877717, 782518756, 582356745, 885145815, 564724824, 621925157, 981798228, 91670940, 537759214, 197313470, 712428637, 623713602, 95145503, 444888862, 196619380, 325269265, 937493096, 115028125, 690774810, 239349383, 30821591, 409016739, 331354324, 890720411, 165657003, 27230839, 518787189, 159291152, 981547325, 478229440, 438859980, 892943203, 515654505, 963680492, 813241553, 640581525, 300261270, 710772181, 681939296, 420590285, 773339736, 793648975, 708778116, 163098082, 17549131, 858269909, 679839283, 689574744, 41315473, 985524857, 431721804, 643009839, 653751640, 366601259, 852967765, 922073647, 674259799, 761557594, 479497336, 503459487, 774387232, 521490491, 343946280, 144326602, 686613915, 47523945, 873439231, 728096341, 579807018, 324650987, 604209431, 579272279, 658101437, 206619557, 520861690, 665576216, 753652646, 106162474, 972830054, 380650122, 743904305, 595929529, 832318608, 371421576, 921277200, 255115094, 669431855, 509724319, 780262251, 725484202, 383474789, 633449601, 817609842, 640875929, 90479798, 479683021, 309961059, 185939515, 26995084, 123719640, 59608052, 891831668, 18880936, 744592664, 118473497, 778359442, 401075572, 991940936, 310032576, 85186445, 203045131, 10216235, 510378255, 648314933, 22414366, 331306899, 947770658, 566069733, 821178108, 192355461, 278916308, 868222120, 432043350, 927694790, 850676265, 960083044, 877113679, 231687443, 245894775, 161437782, 11446780, 527937160, 489252326, 425075925, 779636025, 449832115, 850345230, 110959884, 45759193, 396290457, 739906746, 387216725, 96740726, 412704644, 613663447, 233554198, 451393215, 333180277, 749381727, 420429054, 804005615, 365635367, 828701495, 897281833, 332289135, 342352660, 924863360, 800029429, 405197566, 852267221, 15553068, 739412884, 759207705, 225942784, 769765320, 352884218, 727240571, 673028344, 836647418, 997907022, 53270279, 615012218, 324285014, 188148567, 39755019, 541480765, 135301229, 296236929, 538053163, 43120328, 887568298, 558802393, 703220411, 14714989, 600393119, 786489169, 385593632, 485970884, 612301041, 762741371, 345742264, 965666631, 689308706, 620567942, 305606042, 970182378, 449966262, 240799549, 890693131, 776850910, 282786544, 837092811, 613365693, 108641867, 501198772, 136167331, 675371821, 414487787, 837312155, 707109856, 57098028, 9117878, 197390236, 42677803, 961767030, 594580270, 268121797, 126723520, 85771910, 341853516, 965550367, 229817214, 417947403, 500697139, 3127973, 992123677, 800478457, 296325601, 518773894, 326517120, 145740299, 459029650, 267194016, 809465484, 261813774, 803872925, 127767352, 913436581, 947878354, 143743839, 842286471, 343116392, 952213924, 338774779, 192237450, 376995044, 750862309, 490022394, 170341363, 904319579, 949974926, 167656208, 645638757, 417204586, 498857434, 906498546, 111267020, 454841716, 887414828, 399669462, 14472622, 433560446, 4800517, 251755819, 957993788, 855591153, 212887191, 150335458, 222265015, 415296976, 561171222, 291313304, 734067320, 304959534, 792179445, 433750803, 505166871, 269487290, 262894618, 722062083, 139053914, 377187456, 411579969, 646970603, 63988099, 873407461, 757701349, 971073433, 370404265, 51898932, 170839042, 820177162, 859478686, 600060624, 88073697, 739885325, 580288788, 501248824, 247700339, 219505966, 176127525, 663257382, 161345183, 576755242, 997958465, 994292983, 40527858, 458203678, 142412968, 874483351, 572490801, 708171165, 480409401, 573943067, 898066525, 940516554, 258849525, 79768068, 653383275, 260585182, 376002286, 612802742, 665570956, 989654522, 824911074, 810038468, 645987213, 62252684, 875075297, 920638117, 803817341, 926587326, 399611854, 378455057, 46132028, 732529522, 305644483, 543588468, 978831166, 396146979, 868783688, 671001188, 593845997, 682412411, 427829909, 643698429, 165816640, 718503498, 704548770, 937509236, 633600719, 938362565, 20962985, 385649936, 820187364, 990047237, 834243732, 831265717, 741746258, 642309471, 639253120, 350268078, 522002454, 731680013, 887979839, 248308010, 498261779, 964439456, 135903059, 904136862, 172702366, 407105093, 124190940, 170891629, 510560155, 940887897, 660722101, 922946116, 928230895, 171193876, 40525908, 900880200, 322980942, 638140230, 965109389, 874455640, 804546654, 461173153, 658915494, 990231425, 552623684, 589927703, 104317791, 837392234, 801606919, 275880666, 896884885, 762720947, 362319725, 509621094, 265427423, 295814863, 470904878, 714843908, 331291711, 119378391, 569770270, 672690372, 854571984, 6930962, 704917879, 501308132, 150619647, 397515277, 926500799, 571360012, 289862974, 340696179, 389260147, 94876185, 972722124, 968801650, 512124642, 974316414, 326990167, 333508455, 171899811, 71722612, 399245390, 257237170, 550216708, 166929968, 659861227, 388873521, 7574921, 817880396, 654219701, 818979811, 970859529, 594887552, 693413423, 383185351, 649108248, 433320235, 67318238, 755626199, 544734524, 902970712, 236756220, 402372078, 144333028, 371301172, 613373423, 892504393, 801666364, 182775731, 119064113, 763555806, 952994622, 798178999, 660123158, 250165799, 585344343, 872499825, 999060507, 423062459, 317882325, 543399080, 59442142, 519706369, 630732065, 742995184, 754971468, 625677186, 316509102, 421355817, 154805335, 651052733, 67636401, 483352400, 498687117, 777681639, 586993828, 113254447, 892925419, 556152862, 890165736, 520703448, 723470494, 502966289, 158973500, 665720295, 324304134, 673096381, 956537903, 850361396, 529352931, 68430996, 76060786, 814053882, 481355148, 884143525, 224951044, 71575982, 406687634, 158209218, 226719703, 691048661, 474018696, 852600965, 532151719, 581367915, 681135648, 409625739, 252464427, 242025498, 440473532, 995215672, 74304806, 652648017, 355491018, 202256371, 796190630, 34513888, 205112298, 884379361, 516820783, 54669368, 937038661, 535744418, 83012962, 243649573, 235547908, 346534450, 841621802, 573781413, 636037209, 410395845, 402071241, 363368652, 856680971, 132186158, 278627411, 121882250, 767962092, 240267525, 602007691, 647082928, 16748044, 773377708, 655518175, 800191948, 210916821, 266303998, 902594749, 536426446, 759124394, 528311637, 950374430, 229060681, 507075345, 394113195, 679179716, 473759977, 204073467, 762006714, 91939445, 282786337, 353467175, 624217837, 435593747, 790162978, 923401492, 240430545, 531845469, 750853653, 792449081, 171708216, 64959730, 440301816, 124966473, 814853072, 601552376, 706270755, 605835611, 69151234, 95449075, 326075238, 508418557, 495003661, 60411780, 944637723, 964802212, 789043752, 351186360, 179203322, 366785206, 151202005, 529457183, 106006515, 369173395, 131754091, 841721451, 705027357, 705610894, 51932186, 906589056, 996806869, 691096145, 855335882, 551578511, 398322750, 538652645, 521800701, 807284618, 9473955, 587426959, 765372820, 316041618, 509010011, 765008154, 637695696, 333506864, 225595067, 996669693, 923414023, 693195988, 437749955, 21223914, 530850116, 563713282, 193670253, 435899585, 117131283, 670997449, 258272182, 329835087, 746735328, 433308169, 547506901, 16507599, 906340384, 433715339, 954583768, 973927563, 223632896, 538169183, 152618538, 233327644, 501790442, 274042557, 738589732, 641856025, 61275691, 359820368, 79881906, 264852298, 866861811, 698393031, 891121882, 375257927, 71603060, 375498828, 674065880, 248667492, 591690644, 987037568, 860867619, 591458687, 75745686, 311555871, 974115710, 284735483, 72289402, 868887207, 334921290, 645731832, 250228829, 258864393, 424041194, 613870378, 608907524, 883559915, 64645989, 35852669, 224715684, 681674326, 497460600, 230633221, 838628204, 559890034, 544845073, 499553112, 407784937, 61516738, 251250268, 851089621, 798379387, 462192239, 211371140, 944817496, 833657135, 923595266, 920237252, 648236942, 888258575, 582578257, 24554175, 71765556, 854572402, 367164957, 780438302, 243338929, 139460243, 882815349, 525178900, 13212357, 62357480, 938576035, 164207670, 938176243, 861339046, 730695535, 122741174, 19199668, 995278601, 116982254, 360967510, 371654701, 804072300, 545377003, 562947735, 453060501, 818791051, 957116304, 386520358, 525223270, 814380764, 167954065, 402506840, 169559538, 287576956, 338543678, 753668107, 640640382, 128110665, 260277174, 625845840, 320070580, 344580130, 30059073, 698790824, 819551520, 476046245, 581502179, 144260516, 199657619, 931999680, 244616813, 692982318, 297691257, 55778874, 515023732, 286819419, 186762386, 426284061, 797835817, 828835999, 61275512, 260220870, 26019778, 193334276, 352876054, 37465669, 128867722, 224095476, 575347488, 120708878, 381987737, 613085063, 93434485, 98806168, 390682050, 20641518, 608602520, 380060713, 911366398, 289159427, 897086030, 273868219, 318976501, 155916481, 683586629, 450950520, 61507971, 442208973, 41896123, 662992686, 68024608, 9146796, 851996758, 982371110, 14351093, 425840877, 45261906, 519502388, 497018167, 208741213, 51582483, 722481391, 263391514, 160126229, 831636947, 178511717, 527956136, 852389889, 231997792, 981179597, 669256815, 901874374, 184997389, 141360946, 797994333, 537387314, 399748672, 995335056, 659323824, 979119413, 769669380, 81636731, 337603155, 837990697, 988464949, 100711904, 939143858, 943682457, 716681431, 972646704, 145893729, 573573411, 292712043, 548356851, 249812066, 861308885, 127288583, 587553940, 420004777, 582832936, 34668385, 496989116, 516319137, 368057363, 806013465, 521333093, 818490427, 157021662, 851633376, 837298065, 607834863, 954878331, 885610307, 913721839, 837303318, 760747588, 59341387, 382289215, 711530673, 406873621, 420813265, 665740550, 677370913, 422326752, 648600304, 233780428, 458690253, 327134172, 459998990, 443077449, 559522983, 884005420, 900499342, 792390682, 928977931, 999640607, 165364968, 346274691, 285425388, 667786913, 83354706, 916637524, 754438708, 756190130, 417057738, 490796456, 643431908, 179746787, 147350850, 588325909, 603595610, 573040056, 774788865, 919310445, 243661083, 791195574, 105948787, 840322859, 614425714, 142496740, 207383251, 134688139, 460713073, 40161181, 160492821, 687252205, 983906764, 604441736, 878866742, 139302410, 590115682, 747586754, 820272123, 292046902, 655449154, 236380682, 958171329, 511186646, 751673063, 129707770, 112959947, 34133681, 403886652, 182755083, 933093911, 523553878, 92341063, 366202319, 446744952, 244216109, 164822363, 229134110, 183955064, 932356814, 288967448, 662286217, 815197887, 705079582, 896458201, 141214707, 673608353, 704373355, 558596024, 342999057, 820802995, 288115374, 324430790, 860700036, 695891226, 426529412, 15074735, 164634624, 587041625, 776225742, 471022279, 745839236, 981995050, 772911100, 6517183, 607111356, 585542854, 812969548, 918468428, 533146941, 603112979, 96618682, 860978800, 875728393, 864903378, 732189925, 63253060, 232473509, 204045808, 944899811, 635869866, 242093459, 482215936, 237373925, 81747981, 845764046, 452006143, 428844609, 974599461, 25210292, 519976777, 883511797, 959066663, 135127754, 44953230, 802206243, 694079055, 775620984, 260411207, 879925733, 930797492, 536490396, 545262951, 153489140, 102675311, 303184317, 49732346, 846830842, 652308367, 445135204, 29173843, 907558186, 266647263, 959801368, 182740900, 598651304, 563665788, 805132695, 396254361, 881957752, 247418345, 123536641, 270170093, 118761487, 641777545, 908889640, 413935293, 649795179, 908301166, 110384506, 983431747, 88646001, 23614606, 356422024, 545478894, 844295063, 787357962, 319705864, 818388187, 775806008, 387502033, 809556221, 823402615, 872740607, 265759102, 984851792, 523598928, 552288213, 761844285, 542165323, 383373802, 90265658, 454803279, 218974847, 947340731, 47595343, 974948758, 808705530, 590189370, 16044126, 803789662, 863080470, 230785862, 725030443, 211172950, 378622358, 75201463, 571299534, 343959417, 12458275, 17461928, 461347535, 96752543, 184087840, 837631442, 922657290, 23914372, 308787395, 817812888, 796988251, 828982230, 788774067, 145922823, 748144796, 31722420, 978153541, 703883730, 201442618, 995441004, 133307168, 29299268, 925468629, 573331215, 194554362, 276237215, 5331475, 137273581, 414117114, 486589381, 549497388, 312915281, 531479198, 894776148, 239933166, 603377714, 405601885, 623728281, 334370212, 47269450, 418762275, 719711934, 346710009, 812891758, 608348112, 107712361, 881223271, 918535620, 376366986, 379989253, 548264522, 656015370, 400019032, 796166579, 477178431, 408333136, 569799737, 779092676, 705285158, 868627191, 56448683, 591095524, 879859368, 690381258, 973877706, 225479496, 697704665, 752637380, 508416197, 301315146, 934404738, 892909462, 300873405, 958968097, 318483217, 158952553, 15657124, 240452923, 795663263, 123537597, 376542338, 990934333, 429535162, 937496806, 658455862, 495991173, 236903023, 182138149, 40611345, 255176346, 268350763, 367637839, 877059128, 447738260, 900919286, 743796030, 336422502, 478383906, 9816114, 350453674, 303130403, 369753971, 500701621, 624363370, 962813474, 931766866, 455626043, 279923726, 90942495, 498308625, 949235931, 861148008, 113271668, 936390947, 959256104, 81152383, 597065423, 713698587, 922937996, 203065046, 816626482, 890732369, 210853719, 809311754, 988856620, 97548080, 505149780, 847145268, 619479021, 963031661, 866122104, 549543562, 956201273, 810867958, 259637664, 162797287, 976602300, 135987752, 385086066, 527908318, 399889432, 428832979, 955342589, 146754868, 913141719, 373545825, 620705621, 998408405, 419657690, 207634565, 417751595, 874822290, 702682289, 551118143, 642648365, 843183184, 45387985, 850288161, 248224341, 887999920, 374169120, 848448480, 515827964, 435283358, 150592661, 426093659, 645533438, 849968471, 145768982, 900174400, 460750274, 288532027, 167301535, 138946216, 606590551, 60801000, 551986166, 441916118, 566033850, 86215233, 6445526, 552309808, 388167880, 755509496, 250371316, 504131602, 777554820, 51575130, 518565300, 256175871, 46924114, 152510771, 49226509, 785781152, 467148285, 923443492, 97601917, 42984097, 193993455, 230744252, 835867326, 160338666, 662374779, 335528122, 773022958, 157397307, 391348650, 682289606, 731179123, 916216292, 9484551, 155076848, 152631717, 290953485, 439559259, 349899713, 548099413, 367194243, 77920839, 436072474, 82264043, 475307504, 570814209, 544018533, 933030607, 889607341, 662432446, 80929264, 816073035, 274529858, 521776000, 600819459, 991951287, 539739627, 239228828, 574429987, 357592554, 885757690, 149365611, 174880517, 787834086, 536418053, 737965665, 791477844, 971155716, 771594531, 240711157, 729172316, 497019047, 989407143, 971282585, 510567662, 628182580, 142003534, 215032880, 434638202, 446845940, 31138963, 603873675, 66146380, 95499896, 744572773, 721534263, 308323933, 662972527, 136269107, 388783054, 104569918, 839524051, 907653243, 600020884, 862541721, 590599358, 91511545, 405913024, 396061738, 66168487, 596223699, 554678424, 458611316, 362403682, 850265886, 467663210, 694535840, 62207080, 375384240, 804693898, 770211511, 911608875, 243961456, 78410278, 358778223, 225509058, 650314367, 880852567, 867724692, 604381471, 610352103, 261731435, 608079215, 893562093, 37565996, 563510910, 939837714, 988315062, 78005146, 677503721, 29719927, 214570148, 484475619, 936714362, 51338661, 624569961, 367826594, 181125765, 505918631, 806158105, 642017093, 744104480, 269775488, 860172452, 80842168, 233255196, 350548024, 492010950, 939676579, 64458685, 956858495, 484766956, 397939091, 192748820, 395312532, 21197199, 128161443, 730581329, 952150375, 201670853, 83308639, 196634839, 375919963, 800707170, 781780257, 823343747, 522904943, 424913835, 59344486, 917959064, 667608688, 966242876, 236382204, 410320911, 499503331, 956957206, 646126345, 724174493, 729864778, 520498316, 496658578, 792248697, 854884956, 528833893, 410515730, 75601560, 101892351, 461851802, 444409508, 223914693, 608818727, 735190743, 691144323, 909650044, 226554431, 155578086, 820990307, 732816182, 574751190, 203815486, 296860145, 262626466, 176659134, 929414341, 504895267, 529864002, 220186464, 521409615, 724796178, 86600674, 496316163, 840817344, 7501278, 837669075, 985167443, 164575470, 72101795, 83829206, 469843777, 672060839, 93050435, 832905072, 618941095, 691756125, 431431003, 973262256, 689859886, 127951482, 472532793, 961145326, 217595911, 428196914, 560021241, 858514033, 824943010, 904045119, 402392115, 647892804, 168616521, 414407257, 641198895, 516120939, 508782054, 38169324, 2282850, 18586565, 405918365, 249762990, 690109167, 212979142, 430455415, 730401489, 264720777, 961702435, 62493118, 653544339, 857486652, 45021247, 415968930, 966602309, 304563776, 832671808, 969970729, 248597259, 62274505, 802965310, 535440916, 767251575, 898576137, 875976288, 789486196, 699868753, 201391171, 72211437, 447081022, 837938631, 915315130, 615579428, 284761557, 667743056, 617911618, 121322331, 627789796, 378607091, 78819566, 860651293, 607609515, 76717090, 843949774, 382179113, 123256883, 806808661, 176765770, 268268285, 824219900, 28539558, 423039125, 826948376, 250588129, 250800611, 839614253, 172466989, 622890385, 432201480, 208443434, 976813821, 874521396, 431939454, 138807788, 116917263, 71465593, 927177425, 598897172, 1709462, 134111862, 492411615, 722524731, 591799471, 649089409, 70196528, 392992952, 566093712, 282599348, 270431385, 799168849, 70338882, 283747375, 756431565, 794008162, 196641128, 974796693, 526808165, 872767742, 335392724, 749386486, 489152078, 429493777, 865348061, 164614889, 163236818, 269580463, 702864204, 663365614, 79374258, 152018394, 885441872, 961657917, 392380888, 228938363, 109646974, 537854819, 249756152, 117340232, 592622604, 143236157, 396813664, 911803591, 619966231, 544925703, 406459285, 456503416, 97640851, 552376968, 515108972, 72531436, 894101302, 711785260, 346785716, 667692416, 895274495, 967714982, 913452629, 351293404, 568595338, 14245729, 605525224, 817301017, 223724282, 668494018, 373068946, 512943399, 881558684, 200108455, 828728729, 808671015, 538249867, 377302086, 90579142, 75849605, 697831390, 27084027, 207824870, 804450427, 278703640, 643267166, 375300705, 224857742, 198506987, 214682551, 48761807, 745862469, 402239956, 687334659, 575950247, 730101920, 579515959, 981182131, 338638716, 560856917, 46633298, 10690791, 165875041, 45796935, 971972506, 45065100, 87578479, 663374284, 163681429, 682357081, 481248704, 930273256, 181957240, 788300574, 223070017, 847216328, 107635730, 685727707, 151178505, 507049609, 383889963, 40023228, 996816032, 509741872, 14115847, 723062844, 264100379, 296588253, 68980736, 15385712, 90981557, 25143707, 413701365, 531244170, 586090424, 346268998, 611388522, 81095689, 343569350, 548336024, 557962984, 333296082, 507110664, 64774327, 159075420, 28321383, 782344507, 203688878, 58371119, 564110362, 900451899, 426557314, 19822369, 167748377, 987732437, 575764410, 406318239, 653294409, 665955118, 554522684, 159348447, 837380891, 171201590, 247364582, 641383340, 304813270, 75118424, 214577476, 619924602, 360076570, 359846465, 121606488, 444735646, 926309417, 745335195, 323960439, 361198042, 991925323, 556958627, 242915238, 31596263, 838311174, 950154603, 494863222, 207590688, 296701470, 959392941, 275981651, 102534808, 838179576, 251383703, 602245989, 458464376, 714183929, 855809354, 131367815, 30998289, 96736427, 251535086, 300787687, 562815254, 229074777, 505730937, 782759665, 928535749, 865539925, 335441926, 266981344, 397520538, 63031943, 889784797, 64863952, 970981522, 498160722, 951945431, 78521889, 530551612, 197490965, 885295, 459403591, 774776292, 695271799, 964868216, 617474258, 788132154, 594019538, 779960764, 640033534, 839126142, 329602732, 599146784, 100001430, 374024420, 666350935, 443308813, 375842942, 831730331, 962112046, 732410117, 166771301, 522999415, 381587655, 428996210, 713271658, 481031579, 451831695, 566570241, 332122325, 89932323, 462068757, 333523170, 176680743, 215264392, 873508203, 523245504, 621309678, 391191762, 459323496, 633106831, 25104680, 930558052, 87886622, 251630726, 945848058, 832710854, 75021570, 588492176, 910864480, 489651731, 872239799, 393134255, 73851295, 483278459, 623412685, 665970618, 906172616, 618340723, 959644371, 349028573, 454240721, 700924056, 630565112, 970768050, 396645088, 850710448, 174351519, 22501931, 572141979, 458440688, 890213751, 867634900, 508113257, 994571096, 631377261, 693091753, 519527198, 322544272, 927659660, 476743132, 379583920, 459462450, 177492298, 558976360, 994107857, 489224340, 150829351, 53527762, 637520943, 944076542, 308012624, 205693031, 354348429, 615139999, 406830855, 69620400, 159478446, 240172044, 766125364, 280003971, 904063705, 757968916, 325223380, 33270092, 667178987, 777484406, 140240865, 403617518, 467020657, 424230387, 608839231, 9999534, 966505850, 667035798, 812879882, 140122602, 727218504, 275826576, 91930415, 659644388, 222387613, 104649326, 633683778, 250055314, 92082319, 680397896, 225830032, 610976207, 862263613, 249349791, 192870435, 744740398, 296808190, 190019030, 391478679, 629189499, 297663965, 619248346, 340278600, 689370749, 806864057, 766408980, 47653494, 745385445, 462080799, 681332164, 713754247, 456837407, 368629709, 115270735, 502383869, 408010657, 461299316, 144410168, 414177529, 227499952, 825537471, 182489226, 38652724, 182129796, 571753330, 71322038, 260543706, 802113946, 363166673, 879557250, 736852393, 287759177, 876136245, 112206346, 175624476, 438349878, 238300653, 546370687, 281679260, 433318855, 514496110, 74260745, 371732741, 921536200, 501400003, 882234981, 238065963, 893916423, 644331215, 893843204, 207216870, 31390715, 459894111, 715880228, 401021161, 296067737, 653142445, 746432399, 497767389, 583953400, 915869743, 166993547, 59527503, 973031978, 668905713, 373235937, 960521336, 345548837, 82896564, 620000234, 798158927, 199586094, 784528988, 143253903, 344391963, 438733875, 705023834, 492217490, 273424259, 67979183, 721041820, 488779193, 476024373, 256420469, 393086715, 975785022, 844765083, 712069481, 371384848, 885012191, 326603804, 631719382, 122276312, 23676002, 449615410, 943241127, 783595435, 264155424, 752199756, 929779718, 793646891, 898145153, 378126969, 174052281, 967599680, 499306095, 724592272, 593255613, 47588133, 290378367, 80872648, 976400915, 409852479, 67992532, 179375748, 930906108, 704934140, 905770088, 82809776, 993812612, 69438726, 59721079, 898729108, 790201280, 228307218, 238076460, 576205268, 8394152, 50735319, 724979183, 813597847, 39021255, 255269817, 387015767, 502177797, 522877337, 822060945, 435773160, 677063779, 88761571, 698027986, 205937150, 58578813, 960293741, 224694252, 481375727, 822694588, 846431930, 691398141, 385445692, 290628381, 217417572, 400317471, 204987283, 197123434, 369504332, 713151480, 982392520, 174184598, 357800646, 713830313, 488345111, 536724899, 406111670, 799973966, 810700746, 274304459, 631559971, 146226204, 690883732, 244410549, 65277055, 969225359, 206011929, 147662570, 268262442, 346959438, 193756626, 550527814, 822849115, 554987594, 75060627, 775701799, 797075437, 232648646, 437377424, 520099277, 477666854, 839197092, 34802194, 860681417, 454945322, 362632720, 91482570, 1346922, 230788303, 962708553, 94826266, 178768561, 363537655, 998534124, 584344726, 535135863, 670328769, 109504196, 549790291, 841969102, 238469495, 362039526, 780348620, 890266470, 501505057, 965195944, 752198845, 180614411, 574975433, 746075606, 838581197, 661428653, 364046394, 538756117, 210331601, 755004784, 321270807, 384127763, 736887061, 88242547, 192784353, 430027013, 980545983, 368942660, 98004844, 451059443, 443214260, 324764340, 554954027, 800031013, 272353360, 583846982, 905706919, 30602417, 283464928, 753764772, 746138474, 2191642, 67545728, 848236481, 503884392, 491252659, 498786394, 789596057, 628477469, 163471314, 442873264, 307597734, 70001787, 644028896, 730818008, 950990853, 171129838, 482480395, 874755720, 466720297, 509692500, 836339382, 191861692, 77020410, 546115169, 80315951, 965807248, 884973698, 203167631, 796663249, 443378538, 187486233, 387990852, 595792361, 208850689, 444559175, 958699608, 754269044, 732852513, 973232506, 860290736, 671221142, 989265016, 878355562, 827162688, 340117897, 197360870, 618095799, 935776650, 155095604, 203001100, 183878588, 315034924, 964959547, 480245096, 604293435, 806387861, 680113527, 947373600, 277446092, 459596193, 992782556, 699619610, 922289465, 500660938, 886288531, 395470365, 944864205, 693382212, 367397318, 562985924, 629255011, 985303952, 940575301, 113364924, 546787969, 368299777, 406945092, 62718219, 14406436, 815741220, 61695158, 504669574, 786138553, 1505647, 588767777, 536290328, 203271294, 407160654, 388306208, 292458743, 364239542, 484315709, 926551691, 544939608, 58680798, 993187662, 27953206, 570945027, 598558536, 972392653, 295803400, 616576074, 220310493, 517732420, 937507723, 934923397, 764150042, 155552516, 489106806, 617535652, 504792994, 78663147, 132087223, 298743721, 908587608, 414771720, 556425128, 225995156, 796280433, 372261163, 494231249, 750619426, 705109896, 206269958, 839427919, 468672105, 206815370, 401090131, 367808305, 425509903, 923355222, 882653487, 179006901, 114165356, 712647393, 145883642, 319219949, 815931664, 902434750, 656683808, 495914505, 87688213, 948455723, 25679996, 232498264, 375699054, 793266369, 154606436, 49882529, 36510228, 108603841, 415908849, 840200131, 781839055, 704231617, 584065484, 155350489, 712825211, 913807777, 180279795, 207314886, 171920059, 45234788, 863285305, 306850155, 304842231, 693330369, 949055238, 399411886, 95996480, 706996079, 135642416, 592804435, 865112755, 890810142, 201049674, 374814494, 852909287, 749306341, 165279858, 808442665, 216373937, 220285267, 834053723, 163550978, 128628181, 938528097, 783198353, 357737992, 238206282, 182328752, 406477500, 517044214, 426846433, 16451593, 805641889, 866456194, 746755280, 246515645, 591142466, 637924147, 883621225, 19431642, 33304927, 179272394, 327130490, 894617730, 435187300, 966004828, 347019991, 150889733, 642312383, 494389161, 656371015, 70736358, 624825524, 333112664, 368305759, 414803359, 338114362, 717715470, 770372213, 347242697, 78539843, 990647601, 912791511, 331908920, 436141351, 870505515, 997020248, 738693718, 893152670, 962811096, 479666663, 593356483, 317868521, 604756552, 2295575, 41260452, 2065586, 866156248, 296479400, 618001689, 96658089, 929014072, 50353254, 960801390, 941542331, 356679540, 281066668, 531919265, 953791268, 504329724, 581815735, 371145517, 70379160, 280547074, 330575865, 745595141, 406849654, 759820175, 514496312, 825134750, 716279675, 811200868, 925096076, 746674441, 72766959, 920637776, 713982243, 100516965, 149019013, 639887879, 332345688, 258462146, 329339283, 448883052, 922781796, 786254291, 633497995, 950502191, 716798912, 573286347, 167515566, 191525657, 579828663, 842977034, 813008275, 849590517, 890029518, 422918743, 518019748, 876193272, 152299389, 814164966, 410192763, 108877312, 649183551, 155663332, 894205730, 846869777, 808999950, 548438102, 509958761, 484971684, 756304798, 313567992, 821134224, 992770039, 589815962, 468269185, 936397192, 42317305, 106009334, 192085320, 995086078, 269727360, 556512894, 999654650, 623696287, 131027908, 659367209, 492772098, 905798345, 56498260, 780504871, 174171173, 410468795, 404922700, 247293540, 300453819, 86771761, 241595061, 456803544, 908913161, 820962136, 818275509, 940242413, 195556255, 596920206, 290841155, 720928842, 962650351, 851120282, 747365180, 185482393, 341983456, 957165310, 182550305, 731238740, 90238917, 896413833, 459819550, 62008988, 394590462, 914973632, 654541539, 923567249, 128358872, 373740636, 265275454, 384030265, 181884370, 975870815, 664041056, 588276999, 231768290, 107343489, 473362139, 584359827, 864059150, 586456121, 660010961, 589952053, 90000949, 830707668, 52242640, 514408887, 802800368, 975665519, 733411069, 411023843, 150701883, 506867504, 233252214, 100543516, 699562278, 450334811, 474520512, 50414467, 152313370, 358058332, 576493941, 253785507, 645675377, 390847978, 360127208, 71701887, 506790941, 543944044, 373291593, 249016077, 548016718, 389787349, 863366560, 979715452, 849053431, 569109266, 899288899, 420529827, 225933546, 806681591, 711736545, 25284592, 591401132, 101182231, 242572311, 78668254, 694486023, 15386430, 574162294, 757340990, 502709116, 413448135, 448798493, 684933578, 897001011, 859244494, 855875113, 616624432, 480500027, 722811689, 876760576, 363217706, 297172723, 847547283, 248044217, 662313666, 858437893, 387371874, 921875135, 692152414, 874764355, 332573180, 451541474, 669732071, 512225185, 375471257, 936461671, 245997035, 199386951, 752318471, 689198019, 821418668, 766269485, 702534832, 733892321, 937537632, 202104191, 972415937, 974327455, 114146315, 659985501, 281339937, 24359203, 704270742, 398030948, 587759051, 458902853, 356199809, 856478849, 523252160, 220406070, 30365815, 567011699, 850472260, 825073435, 339214730, 583536753, 608806562, 594522500, 933528551, 303172092, 189520814, 814054381, 113387436, 210557480, 779263304, 811639170, 339573645, 331105385, 215218344, 679269381, 478353651, 350528157, 278106535, 507490191, 654326957, 343661653, 241930813, 727714139, 946088077, 794034958, 208707594, 602524511, 476419465, 956242291, 915356158, 887223299, 625445507, 569325623, 580242928, 838149458, 567403944, 904006067, 998985567, 684076456, 727913110, 715085526, 112725420, 482427640, 788897704, 969997923, 278065723, 506021059, 38298957, 496113172, 503777158, 997106999, 464128506, 571314827, 126911763, 475763612, 477759673, 737383355, 818641277, 727223930, 165430750, 137948166, 945317198, 354976160, 133375289, 590700590, 782199799, 169494189, 299575739, 951584377, 364982626, 444309544, 160243111, 456789725, 607930218, 225813748, 157773042, 76703494, 253989042, 736351242, 472007927, 442568329, 600563762, 92512244, 750184612, 851256613, 236864583, 271108420, 447281723, 62925963, 158503424, 491292144, 652857420, 279166726, 891017777, 373343801, 108209094, 734119784, 498003584, 892727251, 72506095, 488927670, 7450717, 506825671, 769350627, 162867061, 506181949, 42822397, 531232870, 765410567, 834935492, 297179229, 934792014, 706054342, 794823780, 84978239, 466899742, 993206581, 698004665, 330459783, 851702784, 95164086, 729101474, 801088659, 504423255, 826161712, 275217587, 97551799, 326740501, 333400229, 248217849, 883318318, 5523328, 419177756, 701911667, 822492098, 324613462, 269270190, 495917377, 136806735, 324222161, 295036684, 522843008, 554185532, 163757284, 134964034, 650972125, 668935378, 655882972, 886041692, 673874056, 386776814, 573941503, 25212222, 422331882, 561413515, 951170085, 224115479, 400072905, 194092773, 596921003, 427611729, 515891008, 498974187, 641612685, 157798273, 930114736, 456694074, 298959773, 743308512, 960247939, 133889093, 196134433, 469952609, 543586914, 495069289, 671781924, 446144350, 7140390, 378204170, 147234912, 3291195, 630273017, 829558408, 205668991, 546357810, 341337177, 874969086, 112654721, 531077799, 542684757, 40214345, 639659725, 739409073, 746313359, 8350195, 827020479, 778676063, 403495582, 197375135, 11786664, 941112542, 450008277, 774925048, 188271075, 821885984, 885784316, 743637794, 660905401, 971354369, 287100135, 604637885, 296412734, 521220971, 402828864, 51472792, 141426236, 19613888, 806539194, 736039840, 731564273, 143618918, 737354059, 236491340, 77263520, 616776772, 176546391, 381956369, 152912501, 262594699, 412179951, 897316581, 598328556, 20990523, 200501225, 396829036, 486150070, 237770707, 97376287, 679622056, 307680806, 792633934, 128585358, 257905839, 32307251, 581199715, 221515029, 784885275, 714876395, 945925756, 903250776, 317830733, 392940838, 963765795, 487003281, 75746729, 759494684, 822119460, 632128897, 946501222, 210437508, 211574125, 307487911, 91374330, 347093493, 300869199, 629918265, 863398506, 691727507, 556097321, 911245289, 558657907, 831742211, 6197548, 928754438, 394757287, 192939002, 54011045, 462322708, 141826995, 253602635, 676714601, 300398342, 42660931, 314048528, 924880066, 671947283, 365257727, 246002610, 856836338, 601401807, 81046531, 902273265, 580489470, 439173088, 713176159, 544965871, 583974630, 906840000, 334023962, 993048428, 227500428, 82890007, 357271232, 559050200, 500847662, 382909240, 41555471, 482606795, 392867781, 968094403, 614888831, 667021159, 834537318, 475406475, 535130731, 76173234, 897459893, 820027663, 745923862, 197222401, 656373933, 944473418, 682892270, 861330419, 330917468, 805107152, 529516787, 842157965, 758540540, 899195004, 192866260, 298251198, 911024998, 281642491, 366305018, 93321393, 933652497, 187369244, 994763065, 974563094, 286465012, 6876626, 123240400, 899041496, 891524093, 587219766, 510648609, 886400812, 717605711, 832639454, 456586840, 890305724, 374322663, 476948864, 714521798, 806081834, 154913863, 184507204, 565017645, 359360942, 226227207, 943805354, 879713891, 28300463, 844046586, 706503012, 15031623, 602891221, 449994011, 429292701, 899847770, 909535767, 865536546, 622078150, 66601641, 567722822, 828035432, 935175598, 935782124, 325407749, 463188457, 353894608, 749505837, 158440462, 702923608, 420501860, 989087570, 503460816, 271912181, 921980537, 87500768, 227684280, 351077163, 128327765, 836013349, 82461624, 295456421, 386637263, 600156233, 502322651, 645144639, 332803155, 139250169, 724016152, 740528942, 216488748, 298324999, 69466573, 838604549, 119698605, 835581445, 559518287, 77580012, 109155046, 609068539, 679255046, 782439433, 16960034, 914500321, 188266170, 959524768, 375096550, 3094361, 818577996, 88376119, 295387788, 937771268, 241726717, 19483933, 801713227, 38845511, 909129618, 320998733, 947880729, 274312683, 583042620, 327502151, 392250695, 938063247, 433806210, 320013106, 247561395, 304723446, 611800364, 577060365, 518782308, 952367951, 819385379, 203754331, 711291907, 290605789, 749869057, 733529888, 633003904, 594843571, 192144646, 342115005, 412233315, 924583709, 97759251, 432096176, 406625474, 60904078, 950288812, 720563991, 986529732, 27726928, 826628963, 330110044, 680618414, 750432866, 704987127, 349851229, 957446793, 994106082, 964714593, 339325676, 568810410, 185071587, 902279601, 913974357, 494139547, 446348148, 709195114, 953091402, 56379663, 367959861, 281772441, 175196907, 193158275, 591846189, 893584006, 900705808, 703748452, 924796691, 955182610, 886452586, 65435036, 635566900, 28855687, 443491459, 690061446, 556798193, 9778386, 460625734, 646822056, 716713751, 730066421, 477579974, 146209395, 847190339, 176173546, 40613475, 50420939, 551346875, 271525429, 643454834, 986743868, 370646383, 665033659, 924577549, 546684285, 938981083, 624381953, 527738628, 542018238, 2038188, 145725045, 237290896, 997676911, 450178420, 912688277, 118435639, 11486528, 705900202, 202431677, 192518381, 671602045, 524597190, 472156307, 798191456, 191013884, 934641081, 489337562, 383463593, 768395147, 229903967, 631270075, 540498309, 16900237, 929809699, 373270149, 248241931, 748287763, 377585869, 171386530, 720126208, 398399552, 746424329, 780422708, 263989991, 144150331, 345958011, 184078779, 849716529, 276430122, 605908393, 326539204, 130170106, 563687452, 588859714, 674283665, 773268553, 140985367, 442740209, 932840764, 803692213, 776248623, 102992327, 419190881, 323989045, 553359913, 451617740, 599999359, 949584992, 352146874, 8417860, 650074816, 636395179, 768103782, 682960839, 553435832, 98017018, 806524428, 153285580, 876112460, 709111592, 603725337, 82707016, 864503674, 532395304, 763740367, 320428443, 379729145, 206378202, 680903181, 310883041, 445254189, 126149027, 273461883, 790776573, 376515829, 490534546, 318491172, 588756105, 312761075, 842506060, 139182834, 951966515, 79500949, 316087467, 752278281, 351106473, 348364212, 649911847, 858572035, 849559195, 766230357, 961896111, 988444396, 300011676, 612853334, 455255122, 140179071, 619331365, 954812054, 800697415, 514517471, 699778998, 758837919, 55278400, 516027398, 350535328, 781676228, 478056366, 349769427, 915507737, 376695263, 736494145, 149726433, 410799331, 311719233, 336582226, 464149486, 521637541, 192169181, 442290372, 652236634, 479169732, 155712251, 721111414, 680393351, 420535896, 798964537, 514829309, 988764062, 666186499, 853508305, 280825326, 656624234, 907253455, 430487118, 326331827, 545746561, 827210170, 373350456, 880494766, 936340106, 709879081, 671019740, 615892470, 443164028, 123400371, 326315738, 95200497, 627134840, 991822544, 437718122, 592920007, 904605167, 905083519, 726598280, 597140825, 42194731, 232502620, 230014486, 395654696, 673026577, 34860748, 8399639, 487126339, 602543803, 183266410, 486233582, 622113033, 226354871, 513926678, 57608157, 838319130, 70955021, 858358992, 905682627, 353579736, 735788126, 273412180, 793891862, 724650768, 237352722, 220878161, 286383119, 873889021, 448770918, 571576457, 457064700, 808457106, 917436360, 98816323, 6170200, 728387901, 363854644, 252591279, 274048961, 7956286, 637650320, 256711099, 945972172, 579818106, 78260003, 827183598, 478105170, 515727903, 782298425, 683020935, 286579514, 456793959, 241673300, 940919299, 151633926, 479483506, 783637880, 744563278, 194826046, 681909654, 39401860, 871867480, 657387639, 352880111, 58648378, 558020170, 617722759, 318251790, 170015800, 162945446, 572250893, 609284472, 479951416, 334825495, 697419076, 222518413, 396625552, 215892174, 435841502, 979726838, 498656066, 50438781, 402675120, 904655923, 954618407, 995106918, 976073668, 274170531, 452417665, 494657303, 48000351, 623413256, 489764874, 705184329, 54333014, 147217316, 380916964, 982762341, 347752784, 840431395, 512502012, 827240979, 827374545, 988905570, 6691096, 505607621, 851226644, 941414337, 139757636, 189794485, 636226035, 544814232, 838057823, 246615043, 857037689, 429695095, 563521819, 700350061, 314791528, 759275308, 106136809, 863215350, 890722174, 513201198, 169588058, 18407361, 244698626, 849811136, 523102482, 988046602, 937782887, 198214237, 614732875, 630068637, 776909733, 423614087, 954107868, 971491122, 626364901, 782341807, 205066338, 211662798, 79759682, 771776143, 296281276, 54867662, 182304810, 456507748, 875738804, 38934346, 513924246, 67624364, 441174614, 592597203, 887963047, 671412907, 81132428, 371466099, 369507194, 791536706, 405337304, 86703244, 176293055, 999075953, 745554972, 204186361, 893201172, 902183545, 232118291, 783284181, 583351046, 462807027, 880136338, 397240388, 429481088, 935167180, 94816457, 835991466, 140864722, 480726275, 578198429, 856901163, 610851517, 525053793, 56521769, 819030192, 953111395, 380870582, 979283515, 451835306, 177019966, 106203176, 40984474, 458810736, 35062861, 94798699, 410892526, 757973576, 760225808, 144301397, 438487129, 458087910, 617841306, 53862063, 881474555, 648725032, 625850869, 106846793, 59103321, 130287170, 55858190, 106256979, 467609062, 733529465, 921660093, 42651837, 287224135, 331009045, 739351487, 59263952, 997062136, 25975033, 185527666, 792017077, 891541964, 20833729, 813291921, 652900308, 212233283, 154043146, 364259532, 839047024, 470259066, 944742692, 41438365, 431113069, 571174040, 442001780, 573198268, 878497441, 132693610, 902642512, 23692264, 852735461, 643391819, 665958762, 221963136, 749511817, 579518106, 5509355, 630358796, 910782109, 113100991, 192061930, 597184570, 716798456, 574838673, 76997997, 479259004, 234621367, 931318381, 608674963, 29866866, 975279414, 502991113, 434655698, 407023589, 411870282, 624474665, 274221751, 99950408, 262106537, 716845021, 337077676, 609345062, 519122507, 304289114, 719951465, 176110, 954987274, 815425092, 71039173, 710080504, 81802667, 591535768, 229776424, 753255660, 366725518, 165047097, 551944877, 80392950, 640999654, 841446938, 272892163, 438868922, 559793645, 171495704, 60344413, 243984976, 764656231, 158874348, 895875300, 270565635, 304699972, 354588864, 184701914, 893713292, 933071872, 45850169, 525883529, 689305900, 242554507, 57949580, 323918702, 101033909, 627515772, 406634322, 136135600, 527436270, 112688027, 171304360, 393831291, 586183317, 275121519, 263520185, 137794446, 28125746, 620367348, 504148197, 538271959, 175747565, 185043089, 986833262, 312234376, 319599038, 734318940, 351400556, 216417579, 990681532, 112333277, 41996147, 774213456, 300932224, 453811385, 266081497, 61674859, 585868369, 171763549, 673828718, 473270348, 702710701, 637874468, 464683132, 582244949, 806149756, 764639168, 513696848, 338291917, 456000069, 627643430, 298904242, 251893994, 293059545, 954290084, 295451152, 760257821, 72194535, 771892440, 100458621, 168583877, 843097152, 759290206, 725400684, 566933715, 967502404, 176293142, 994525645, 325106871, 783667701, 924375833, 483334099, 290840983, 442401896, 404387225, 470441542, 781870448, 699909558, 856628449, 138270830, 15404944, 265728940, 544184140, 233968399, 444536340, 993221223, 451426594, 503397701, 360556046, 323610031, 298766218, 964482359, 63537228, 869661946, 558806744, 818817797, 915391262, 482475944, 503546583, 390943121, 633746812, 279591874, 924859066, 208413322, 879899082, 317222003, 513817540, 606889261, 799186780, 730547604, 322327396, 431469975, 793382208, 173561212, 786905107, 380400206, 373707612, 880782649, 963531696, 667116659, 190112770, 993269622, 964146561, 767628943, 804378147, 599274498, 303043090, 963770167, 699452920, 407487594, 524024414, 121796924, 209262746, 754647745, 669101433, 579471, 513069676, 737185823, 418631796, 695520704, 234254946, 773037087, 559865799, 481101916, 342912787, 283825443, 562977445, 340069583, 155078035, 980182810, 488659457, 202466600, 803091352, 936976299, 297769593, 949965738, 957792076, 298368043, 711194837, 597086919, 95857692, 664946225, 271093470, 34373913, 328645400, 563232451, 548159833, 370578326, 341724629, 970549012, 591472013, 847365157, 114268571, 722927905, 502447327, 255313162, 385122142, 927473524, 979135073, 591906203, 39050727, 510464489, 614585705, 622637922, 420776640, 509461937, 161789328, 792251179, 776709370, 567866941, 785129893, 490536534, 921640074, 900064689, 134379550, 564983414, 178914109, 114331868, 994623611, 898404498, 561919861, 576618887, 627898067, 580860331, 20603532, 769682024, 199635178, 575226037, 279515065, 803439446, 424828341, 261990628, 23433182, 733710688, 139333207, 767734981, 433105596, 660640752, 278130782, 109192457, 839583446, 447875256, 998085433, 846337512, 117751281, 617136025, 723718152, 419778792, 955213217, 619319990, 44924395, 816057871, 743856842, 984688650, 417707366, 535204575, 932319570, 499027506, 757931450, 405807634, 198275254, 980132060, 396039667, 773943660, 926781176, 402287440, 629006096, 538452985, 404137215, 136426050, 741093962, 753989209, 257877342, 572462575, 540950406, 344324171, 70391687, 778181364, 955321310, 587315315, 701178046, 840234656, 225094713, 308147716, 838792576, 577487562, 428502981, 653074512, 590610055, 22598444, 21969844, 242033708, 200611577, 913875283, 21876486, 864542873, 466860493, 25129619, 25861233, 497900922, 348987843, 146526320, 542646176, 435079770, 372207157, 417808697, 177347109, 664264967, 731449192, 270112119, 619416470, 501592599, 945285293, 775436697, 64684103, 881390905, 891804122, 292170167, 118540739, 809761542, 342847561, 45686286, 17746520, 222267418, 530720762, 79757126, 253665319, 52359476, 973757830, 343395681, 349734517, 779132365, 633288479, 428790068, 735405769, 936327, 233381154, 235513417, 230466169, 729889208, 642147090, 264047853, 357577935, 396460793, 17007473, 905811528, 651024950, 770437648, 31356370, 949893395, 452004702, 607769622, 253388505, 928791893, 483206806, 15949365, 70764511, 337582256, 799890148, 50790079, 800223418, 421005375, 833478899, 602288424, 994690921, 844945588, 727969738, 58278989, 478667095, 377425093, 219545894, 432428602, 999338857, 678478121, 179889098, 623037361, 575912807, 90750292, 523987250, 774673273, 2931546, 399612618, 797302772, 8047395, 421356798, 196796557, 825496749, 591440418, 577121907, 618773777, 363632593, 213617612, 853018562, 180469239, 961617719, 310023263, 742673092, 655797100, 861038177, 797995633, 465619274, 854917557, 123935363, 443643673, 394051857, 90279500, 490194570, 83428862, 430037524, 610041888, 311163423, 520620262, 169446134, 808117550, 632459432, 381251382, 346320498, 161215196, 704184307, 688824397, 514266523, 66767622, 586999323, 306657051, 753063585, 74564118, 993075793, 872789450, 906304100, 218396656, 577982969, 610374013, 702670844, 256984048, 872185032, 208700944, 565405050, 209770397, 111430212, 145382655, 141132443, 952829628, 915578955, 875330929, 674809968, 891091669, 467382882, 402830535, 105814930, 381274054, 84882080, 555155219, 71716099, 81058288, 113633678, 429414773, 643478179, 282900296, 180887696, 101813286, 582886359, 926302011, 127830490, 974561999, 678979957, 675810563, 375230659, 251575431, 800128462, 589823166, 573359566, 708197522, 912006365, 251823052, 490901285, 813346737, 487054442, 588098708, 160981422, 590826962, 167504460, 136972197, 824608063, 475195129, 889909517, 110895714, 160321121, 552603184, 920553189, 125616, 137676272, 396242954, 130709706, 531011987, 114316378, 577851397, 885029833, 108135122, 152740409, 739150447, 100715168, 411667132, 402176397, 703079243, 545106065, 978705614, 126221092, 650389554, 313746178, 264361702, 412538332, 34271410, 820810110, 797295926, 180883545, 703461511, 539699710, 458898889, 15423689, 394876600, 756894171, 204056690, 692078708, 42292733, 25739014, 131211609, 674999466, 75862537, 503311196, 357686483, 760240237, 237647953, 535155316, 242230925, 326263516, 754612079, 586766296, 843895003, 651214819, 285752803, 931658651, 191339174, 203873908, 733326685, 872130605, 25673318, 971861256, 555079522, 84129738, 573747161, 355027765, 954081720, 418893878, 833372449, 720089116, 363921348, 925613852, 452403950, 284839614, 602996529, 974354701, 904221851, 218635168, 203196222, 71410642, 196847096, 172839711, 894622134, 709570724, 732459572, 832165085, 943571413, 760445692, 763530951, 217170005, 501593706, 198934970, 224464895, 179615431, 737325133, 652926420, 658044632, 829284550, 407788216, 928500387, 846501560, 832629424, 730184349, 748959037, 993263004, 483341165, 760577570, 766246230, 185966985, 899426837, 430861015, 412592063, 221554189, 592046348, 370745595, 147080153, 429956703, 204342011, 534758139, 477671890, 383591193, 649229183, 803175346, 543054612, 983774914, 755405964, 851439346, 475030812, 960070022, 347640738, 366119567, 81137461, 287914088, 637020556, 696062279, 600184316, 597550213, 307991163, 627140047, 33844861, 741156415, 174973638, 574924861, 502004294, 491152708, 371933489, 438599924, 587503204, 193675146, 867012871, 274780783, 941157221, 449928147, 747475818, 288524351, 90529330, 290172614, 70302635, 82436581, 199034166, 780273590, 637808001, 477744689, 700640330, 972326100, 644125193, 552632007, 96183701, 678074581, 325174055, 945207565, 301517157, 888945905, 81566506, 337123444, 83307725, 604189118, 408153267, 10114851, 892666301, 430660969, 282910377, 645991093, 975760701, 922491341, 563114517, 413834577, 608867809, 702678873, 93860474, 240074889, 287619413, 687601022, 587446313, 190697662, 66710624, 674239863, 23759387, 77500791, 306766612, 409398851, 627519898, 892641270, 346119516, 284466612, 336799609, 782919190, 91984401, 341136087, 668652196, 264866524, 894091373, 910411446, 305660546, 850604912, 368603531, 564185476, 756115901, 581148958, 596575932, 723098293, 810811689, 913143023, 151599645, 854619381, 889156821, 529687085, 198061242, 364390766, 284844314, 996488966, 836507816, 377375165, 487047340, 85104984, 342239169, 531699480, 920465303, 597966992, 890413931, 54449645, 405975404, 344339940, 539846152, 470593371, 982871602, 999770783, 687080452, 333132915, 995794614, 700662458, 657704829, 458172140, 852366457, 892033037, 16098443, 403744750, 153717031, 271167945, 319392064, 978886419, 807618453, 276595107, 210811421, 786015306, 723887375, 473100165, 703954414, 919750518, 559613824, 730762418, 464465081, 172686743, 797703304, 81655104, 24445208, 141972075, 727565736, 346267315, 704764241, 282371565, 566660583, 765413571, 302560684, 855886849, 327446857, 268072995, 848079230, 642483112, 240138770, 63004413, 420838215, 428052926, 689971987, 17735377, 40056281, 542960992, 240791257, 938461643, 875019804, 704770908, 500797649, 847535470, 24200970, 869316303, 164334954, 635671329, 436468370, 292969748, 756640174, 417497368, 945587124, 949382707, 366282432, 613919734, 589840291, 448881684, 800194301, 556634614, 330028859, 401982489, 411682499, 221062819, 919817980, 781624956, 491813524, 503434815, 8759396, 44031875, 20864087, 661420038, 441518512, 370031045, 146092060, 708630917, 526594381, 875883167, 799549479, 649041100, 270405497, 214632309, 512954334, 651999541, 241597439, 981291010, 5848525, 666523910, 123504938, 443285828, 634468868, 436414601, 510406000, 801551761, 531835613, 348954373, 585619485, 521498960, 679477350, 930221422, 799957751, 189755282, 1457352, 415701017, 724751331, 4222728, 397645388, 782331041, 870241151, 716445163, 165413954, 328116809, 940753698, 398122521, 157281967, 841068974, 369059355, 899260451, 600164635, 618898110, 132983072, 652704045, 597401296, 743971057, 378882954, 545752642, 144543907, 779751315, 902491077, 64784838, 361065245, 237387461, 972159779, 981493685, 772257605, 7872904, 173966631, 829401986, 217882632, 185883021, 385536532, 199384449, 77521529, 104413257, 504844988, 9386376, 136063584, 25580340, 800622837, 580449079, 197138693, 810700347, 763720982, 710241975, 415333057, 856117621, 440012626, 114874418, 883151394, 988916521, 803164096, 250309293, 17129655, 347825922, 110647442, 483309937, 637003058, 386259388, 802673236, 83851532, 386284368, 603113310, 287899051, 314487419, 357672055, 132138283, 153757680, 643352680, 620940764, 729354284, 120444471, 317296061, 244079872, 837361835, 328559334, 20753296, 607766336, 275380364, 474104964, 304815072, 554859931, 702578849, 299080134, 359335896, 273841164, 425700489, 391169404, 737455720, 174690882, 348945851, 539790326, 123939376, 91293241, 646955702, 910041041, 546962165, 698330961, 950246518, 491395984, 873356226, 525474239, 363683933, 797599340, 457775551, 655032397, 255530066, 387557965, 331626276, 174616901, 631235849, 301788375, 176275910, 471394126, 804523931, 188267973, 111549293, 762548196, 656012815, 773597299, 925800788, 742909561, 698169694, 284889618, 507442591, 535598797, 986885029, 956922608, 360737463, 181535042, 412633748, 415334195, 996174643, 123053682, 260358171, 581047315, 134878294, 838183063, 302086397, 504235848, 500593555, 286601363, 97145024, 374340006, 644823136, 942490885, 444650363, 975303189, 90817293, 815477264, 624435770, 655205631, 122735593, 974382955, 310837117, 888064814, 865550878, 912960868, 769355029, 291185785, 826544564, 174428626, 304974552, 95866444, 987313881, 820023723, 967368714, 74762275, 926055517, 383165581, 419141944, 977896516, 513039177, 337388264, 170779735, 716724714, 756025030, 408834521, 306287555, 743885292, 426085681, 909637787, 387178645, 280140144, 91051996, 982026219, 483325865, 20848431, 872255607, 840925747, 479195087, 227339302, 179221391, 218557659, 459990279, 582485153, 318270090, 814083344, 162040399, 914181390, 169539254, 727379327, 384270613, 733185434, 506372503, 372506400, 839079012, 502848401, 288666702, 307741746, 308806047, 113220437, 486000339, 359901345, 232543336, 452962805, 775755558, 494592194, 403968024, 299804084, 652727332, 712368182, 401426835, 22803499, 59321479, 828497152, 487330172, 851301692, 749979448, 570884023, 240776933, 680251868, 789206582, 928290712, 524972703, 984929998, 399739037, 105898794, 782263936, 705272165, 744183733, 263769041, 73042386, 305403469, 182852066, 898637099, 403636833, 577839025, 382244008, 700411289, 427050689, 299408758, 57799366, 540377616, 314427536, 335922353, 678469802, 416008735, 238007752, 803793488, 369580307, 233746272, 62634076, 907724679, 149464782, 682476550, 275541128, 530586550, 632813157, 400233055, 733622268, 40415373, 648246963, 526588515, 63744929, 392975655, 471355883, 482216171, 270893265, 259914148, 763215609, 280441023, 354647789, 303590337, 573200363, 514364054, 195579685, 122440561, 273551019, 829526533, 452504895, 122859094, 835608487, 421139542, 69814697, 658438382, 394112913, 944889133, 78509925, 992671430, 691182454, 695950249, 759893060, 405924113, 234170727, 773956275, 162153016, 287942660, 73294111, 566679839, 894485073, 289269385, 289244823, 320653827, 433078264, 919780754, 867145535, 996622318, 707182271, 718742226, 893027897, 236205907, 434486781, 814512281, 224605077, 955837111, 875209639, 190787491, 372003612, 52574486, 942782287, 969564442, 254820388, 916114610, 679392192, 64306857, 765030639, 417169671, 530084215, 343565573, 233487673, 780160623, 507440434, 197036761, 171241425, 863155419, 350747029, 296274814, 476582563, 243377294, 83771912, 84289201, 242627975, 434498222, 180509420, 88337802, 185962172, 617812012, 689597309, 163826560, 879974789, 418932665, 788363400, 649435529, 313121009, 441247062, 804318444, 359354768, 16826418, 173443669, 690525261, 762296764, 701860841, 524413693, 506157616, 198111318, 343513656, 867236064, 427051449, 272919536, 770516746, 956084158, 84357991, 362770002, 543111591, 6570065, 759336084, 83210205, 464997011, 419204961, 655827446, 822604194, 424985875, 500292197, 464214774, 668355495, 191803752, 26604015, 130184027, 989627202, 811824158, 715379195, 314529946, 467392798, 719861441, 781605620, 866657347, 911687487, 204736972, 442675495, 688044889, 39555227, 885934716, 891401652, 538033089, 74522073, 458231477, 553377229, 863054851, 857388030, 571332261, 747981575, 758683549, 519140828, 154459506, 194488988, 301982461, 604978022, 868006553, 724188988, 164119254, 195299280, 626396112, 670359125, 716573762, 817495378, 723227450, 294748272, 539658078, 432647463, 850138223, 281278771, 467448083, 276647092, 829422390, 774123976, 107540797, 450361185, 654203837, 921742552, 837815216, 645729845, 567468688, 327854146, 991014820, 278670012, 705473149, 82490442, 307224677, 326174317, 340256878, 388069071, 334141078, 182695636, 549986981, 199293461, 40613842, 901920648, 383466863, 988407925, 830700785, 746709104, 760238366, 93479607, 788611170, 782637518, 294902754, 176853359, 681818848, 292104163, 390786442, 217312947, 727921253, 222861294, 580816464, 264604036, 467493624, 76113899, 424199101, 560298496, 477306126, 605602552, 762949075, 449547410, 504834483, 829741001, 41108046, 997569313, 732403339, 844256007, 699010282, 603681822, 156479606, 743981007, 758352726, 205084796, 975860997, 475132554, 994227225, 571362817, 321557828, 156850919, 418589535, 295176407, 156253492, 530911542, 814793153, 416053097, 974803241, 600568189, 891672873, 540255959, 594091194, 54205458, 702587399, 574414878, 294014328, 198722730, 627471403, 156221301, 382378914, 847163951, 17890733, 792085531, 643856183, 793920644, 910551783, 105588522, 208099438, 595811946, 940982753, 5536712, 497075722, 520374060, 666516091, 792872826, 262574794, 142495788, 259182803, 713513118, 918485955, 894362175, 641330324, 642854117, 212883516, 337874956, 913610201, 519256267, 617189990, 979845590, 63258922, 803629268, 903376767, 741564646, 109689142, 928663428, 26304111, 464039784, 410381781, 458037366, 153065117, 229454854, 573531528, 22025851, 751323774, 172569541, 420485529, 662898764, 97952645, 682156554, 964219953, 164396834, 196608774, 550941761, 939096635, 5595671, 945819150, 601219060, 120895320, 220433737, 582245488, 373112511, 930899441, 796692406, 388050432, 468529597, 581321720, 970821313, 782364856, 504663116, 121797561, 738682416, 692912336, 100115111, 952427749, 971436316, 492916765, 32770663, 732855395, 686561832, 157073175, 589552039, 845092955, 715461328, 612053455, 470563790, 94230660, 609908077, 900831433, 481053795, 681448784, 276359455, 47099521, 528093896, 727568067, 396437597, 877656698, 140024573, 896926670, 88006388, 666298201, 151838532, 2033748, 973324745, 110800056, 556600124, 645760244, 267441251, 422538960, 537711253, 957675873, 349779706, 798698292, 584433957, 156465950, 738708536, 550165857, 873940927, 118694024, 973012534, 256205146, 427547417, 887471560, 341036540, 9208558, 288934787, 333404585, 98357914, 118442527, 727299405, 846528301, 630314507, 98050244, 760308536, 967371008, 317970053, 836470719, 394194162, 662605384, 243892023, 503884319, 134918108, 203217364, 809675514, 66601684, 97114772, 670707391, 851093923, 445306183, 157007255, 137706639, 51874766, 9809288, 836573986, 336147778, 909833791, 522625770, 838020734, 467934858, 377725922, 745883066, 131239622, 757752772, 922920780, 193307292, 517953129, 801318804, 226474747, 269116853, 736749125, 441583472, 712146988, 685049199, 78119779, 164730875, 36005626, 305438515, 526928065, 945133075, 546176363, 943268166, 265829440, 679987812, 967023789, 292593413, 609171096, 502200795, 665814214, 877986797, 589801753, 333795858, 223793822, 235448435, 775197237, 915495777, 723189118, 161171842, 284458039, 756369167, 244348660, 122961602, 77066766, 431018476, 751710128, 93539935, 449093294, 993242411, 257619570, 418869751, 254725444, 825550535, 951282500, 222153520, 627202437, 875136225, 484941958, 606180924, 541677836, 539919200, 144890482, 543473800, 872283146, 672339343, 741884423, 532207743, 205957539, 101238918, 206822200, 206632778, 37217643, 593170436, 930477122, 822987279, 296056734, 883517457, 894679798, 217587536, 418943025, 316432521, 197388955, 910994248, 35491135, 817526725, 616506906, 282153566, 282280791, 149859963, 920344477, 169520238, 392541959, 459318395, 165725395, 489155428, 824192995, 594134078, 621206309, 524794560, 458113747, 816858049, 693641553, 764559560, 9431971, 955789856, 235586888, 409390605, 593408282, 888938179, 199200181, 786567341, 16168104, 518033012, 654953780, 391266117, 73514264, 253014739, 869306528, 10510685, 698656125, 65052317, 145576308, 196278790, 682487181, 771434702, 189870854, 407975577, 560486089, 413436509, 450397455, 460244393, 337998650, 332755560, 168200870, 347410448, 575146860, 346155195, 498568497, 620525262, 654249163, 981733908, 715020440, 161822169, 266879256, 301822116, 963810867, 201446273, 746620437, 608509347, 112438487, 820848191, 342520165, 237476236, 54951198, 821673979, 91876169, 52474540, 156321410, 302102009, 401354676, 865493891, 200927574, 114156900, 885637563, 534388200, 929428249, 136876894, 138575823, 878638396, 662501500, 618481625, 409405863, 405671081, 999189126, 936786431, 870497169, 107619032, 816050077, 940488768, 658333857, 965928108, 919875319, 649693911, 557885370, 505364267, 337609574, 24054125, 427882916, 235671981, 753538156, 96897412, 403111963, 62648200, 307827137, 260416097, 359700360, 353915650, 403412080, 903996490, 190394454, 117016851, 416552970, 555384808, 981423960, 179648810, 900219112, 855489246, 438029458, 304423879, 819282344, 814153105, 806928920, 503320427, 962934195, 714169196, 971770969, 919932591, 901019470, 427236479, 725070563, 886136187, 100873028, 938076539, 378221931, 965294338, 676286922, 179460046, 809548938, 84116570, 571957521, 505328100, 575991326, 938761141, 739617991, 32116666, 339449102, 755562453, 536477136, 428955686, 285029089, 608820846, 601632137, 585123334, 734265820, 275686238, 599819255, 177423985, 570998061, 843022682, 46197596, 751938049, 558791334, 401257299, 732591099, 620431785, 422106706, 940569562, 907639482, 31918973, 684976168, 919769499, 906832728, 629706579, 5997595, 558421320, 354740192, 846629863, 279217733, 904927141, 721592106, 480642131, 864266943, 10363155, 92889442, 888533585, 132239001, 359963054, 936595993, 805479966, 558933530, 171439484, 328379250, 216351890, 262227900, 669060313, 760898455, 216656030, 199691858, 807478091, 829257860, 576112661, 581201850, 847703443, 542764930, 163633088, 886922893, 521650120, 559782044, 896631854, 653997783, 247697422, 441578618, 698773048, 655025152, 89209255, 762715264, 792242005, 461633275, 527815311, 903630576, 647806830, 580480762, 867917277, 248389159, 621043481, 10280582, 15205142, 171378898, 579730760, 808231349, 821974455, 285993711, 829643233, 550141721, 469875199, 282498818, 678635126, 409538803, 608697256, 761061975, 275920, 151529951, 835714924, 637341464, 941908749, 932741412, 874815790, 291156686, 823515369, 662740572, 642989393, 234643365, 771932630, 209507701, 95551246, 392531924, 378897692, 963870317, 771717701, 560572965, 539365844, 57495080, 424541204, 1387998, 757659636, 161022548, 135539696, 603921405, 321438152, 518033910, 407329945, 860449205, 548810091, 517350564, 348160599, 939355261, 568696443, 797090710, 86182254, 214652160, 155388732, 530768237, 780186328, 988131572, 240600933, 213993042, 649001169, 74006774, 163822237, 538446340, 172837764, 996299010, 219609558, 513383176, 207339863, 657566528, 821005453, 798157684, 492787788, 35910368, 673828729, 152397120, 809715620, 924249074, 895451593, 497922846, 601730919, 523493322, 981316619, 688187212, 297344226, 313504134, 642505665, 757240812, 246782730, 961185890, 377787235, 972116499, 323673564, 577160537, 691007405, 865987875, 126391307, 43578183, 152613914, 29904767, 196543498, 985184084, 79718155, 387601429, 659136098, 607955437, 623590482, 871824502, 433540188, 289370567, 758267797, 534176456, 469460523, 581379132, 218856341, 6014557, 715612596, 166356319, 207590615, 51010290, 876276788, 360195180, 493755702, 768620145, 526075515, 988212109, 142726848, 497074768, 645637277, 973752686, 812506307, 151225277, 23675143, 633391966, 517068035, 46441398, 485634209, 441194298, 18800507, 861260214, 828895960, 333128812, 994424408, 473955171, 820017131, 432481509, 901739721, 689324600, 842986424, 802190135, 41447207, 59573252, 478217273, 846052567, 761976075, 218942333, 511105652, 142407174, 774646236, 637614523, 567480767, 497466427, 750729873, 540603479, 530437559, 584988874, 660103741, 54402571, 666039128, 816876089, 776739440, 317934038, 740793766, 789212107, 214733437, 687019066, 558878137, 855190716, 939200870, 684194903, 890025384, 116443472, 413137034, 851155627, 470948631, 573641262, 678761998, 241440140, 656359724, 294333156, 830424185, 853120203, 298105605, 939921781, 265531098, 23261188, 589689140, 696819440, 805351308, 810115053, 571556129, 549052546, 131385622, 449344866, 142678118, 54874669, 640037201, 215237806, 687638983, 603448636, 849615256, 686651923, 362917935, 813083314, 696494932, 658447348, 602576869, 117130957, 403640422, 238515790, 388807260, 148608790, 520525435, 593176871, 75585276, 563471824, 935397756, 900252782, 385952433, 273199043, 576278613, 834030346, 761976397, 364271165, 233910377, 649887106, 242802337, 510365782, 567292527, 974802654, 645992901, 918698423, 554554102, 185921804, 875850432, 321758812, 845410025, 173081883, 290270340, 955087799, 915214995, 883653151, 541719090, 465931216, 677385356, 230394276, 691454722, 541976669, 498909634, 969729317, 439973921, 908645556, 502113407, 783538314, 837494078, 309298839, 682397433, 441549997, 657530622, 839152811, 220499618, 139132741, 303832054, 483475412, 421549441, 541456843, 32556178, 384615327, 878831984, 487451696, 475697578, 783738654, 29882584, 849888506, 503913852, 798176312, 460050124, 642040796, 741899064, 368924735, 462641121, 11618581, 924308383, 786162408, 916427386, 450615234, 263080252, 732241820, 817550435, 540271628, 855309529, 368197354, 554525522, 658529597, 42743878, 880381714, 709207460, 820503126, 952737217, 994504528, 631526188, 924178415, 603978253, 907182509, 742516580, 9029989, 273210494, 57439265, 805701560, 460993834, 351672013, 183726833, 112797993, 147801124, 762554217, 683347526, 884048629, 902257288, 973159532, 725663790, 251232490, 579136773, 516612720, 661113235, 244220398, 200272805, 975925524, 495914531, 340209729, 290956268, 320347736, 427677733, 371315730, 706073974, 545021887, 196056365, 474617462, 381639767, 96958229, 805088621, 807198576, 300812239, 712538117, 826406837, 895589803, 797330133, 757972312, 524591877, 683951452, 351620379, 24965350, 962598, 870415403, 683863210, 522549079, 647397798, 67007187, 41352218, 186646074, 748563677, 206726951, 523757764, 111074272, 65517548, 100158056, 643015822, 748193878, 633078752, 131081096, 464316264, 191117430, 136804573, 130986316, 971229855, 638702394, 43887481, 427718754, 394398226, 955302646, 387252441, 526448692, 391872952, 732410214, 316337474, 760952251, 645405845, 633272948, 792546167, 264213722, 756363182, 724187245, 885830931, 170113188, 53479349, 588648703, 805129454, 153508046, 828025794, 605384453, 654857809, 49417258, 236308173, 162955022, 304937522, 797076919, 102322468, 443616652, 380946515, 913833011, 969259147, 16708547, 290635451, 489509990, 398703227, 933914002, 841431430, 151748760, 880897105, 405406233, 556285632, 12267923, 970664465, 416344822, 898070938, 353715705, 945894982, 300153580, 694507988, 10453644, 315942391, 437787218, 742395886, 479478984, 527607013, 756909401, 198530290, 866816354, 582383588, 481742002, 684420702, 561734360, 119140816, 77017878, 499943245, 953742300, 351354811, 416038421, 616083789, 435977331, 504262974, 565992779, 885876351, 919226024, 648769794, 71299482, 727912800, 689154533, 398971303, 649659910, 264870556, 938525313, 195028568, 317334537, 129113273, 291781852, 982764086, 260387291, 605784385, 786185674, 389708391, 32672301, 656037190, 632554104, 543238401, 293213932, 439325180, 646925131, 556078501, 5561402, 128555892, 314305561, 723907023, 425300405, 974612848, 583643465, 521145312, 806009129, 749797261, 686679576, 234855367, 982125126, 975307757, 611932369, 300997373, 110764665, 728474870, 52336390, 444665417, 709248549, 446953566, 786778156, 970383052, 186462569, 558112723, 519416166, 166466801, 885155827, 932109855, 51487355, 888887016, 418734039, 169651166, 858593753, 111622765, 58959651, 931413005, 437758200, 629419307, 519756640, 28621617, 589407215, 599281480, 941776902, 680072433, 562932108, 314507313, 816412373, 220953021, 439274884, 921341336, 300685323, 733382228, 909225422, 396303245, 45839793, 632057455, 961034942, 156697552, 719679307, 510940913, 56766032, 934400480, 130648860, 106124743, 505831032, 451729348, 59126825, 545594718, 939934495, 586970702, 214153924, 20804755, 440685261, 17789113, 21131656, 556073805, 126662665, 459475290, 742884887, 378653964, 610907683, 405210829, 40502148, 597987047, 442510065, 815441256, 492634522, 506692099, 775029365, 352272950, 296706824, 92038611, 798222032, 133573095, 454851374, 385886384, 580962629, 701013246, 179767459, 737054025, 146695011, 951491595, 351042545, 659560312, 433197950, 18767192, 653919448, 327768093, 556803382, 851126809, 897678750, 908969532, 113499832, 626023122, 381399481, 501711159, 298748806, 138231317, 817172165, 268910549, 337474783, 296624989, 812730139, 516760569, 290601586, 543565835, 161895936, 908705814, 227639620, 713047521, 750203765, 787335531, 157002566, 6417999, 864138854, 361351847, 299946194, 911581860, 203452657, 30861727, 628305270, 292723356, 857300755, 39990453, 760661953, 330547842, 887412036, 259801924, 42621544, 491737166, 437507721, 507694245, 850492602, 933645722, 337472147, 698301554, 727056641, 902798440, 386608475, 931874766, 318914320, 760069997, 918031191, 966272422, 556513246, 360225478, 857683102, 788864254, 575263723, 741096649, 736897155, 659118931, 903898527, 787322936, 894071064, 647174057, 463869941, 298373311, 400670612, 637696221, 964245186, 566837456, 27088404, 537852709, 188322921, 862233868, 195870616, 411627685, 241122315, 847372820, 623928678, 632129777, 133254032, 987906617, 958080238, 745293008, 673136545, 284682397, 400816552, 510879933, 584465553, 740802605, 412547323, 226269308, 823725662, 838936354, 30537476, 521849380, 266364177, 12645448, 344034892, 545687669, 689719921, 75123494, 307792318, 308853401, 524695167, 565988455, 937061022, 504034063, 410644571, 667429533, 319315809, 996162584, 230463138, 464376606, 692963156, 44771726, 845711275, 725573233, 40181327, 78763771, 274306497, 86547752, 52399331, 345558444, 783826968, 210412844, 568202428, 158843826, 608005318, 997663917, 268468142, 93842257, 441069692, 772380500, 273343456, 115714082, 378615492, 158841606, 334636018, 124736971, 836744154, 441395996, 268162148, 285477457, 225648839, 505520480, 714189279, 467771909, 987156303, 984940270, 465803572, 217718522, 590166370, 236940417, 574615618, 341130858, 905979747, 905699524, 304792846, 627432587, 180590247, 451837849, 54025721, 546452878, 134763626, 127133785, 816292396, 392450706, 601823961, 669869849, 912759319, 297595465, 260998469, 992091816, 809283320, 957476781, 424430589, 225339918, 522894387, 360698913, 961802806, 514868961, 727904424, 689750967, 82444652, 156602344, 245182824, 279532925, 191484541, 21657008, 541236305, 345173802, 532158773, 484792280, 735202865, 916636267, 916888952, 570403162, 836299017, 347938925, 947077612, 971054767, 396527853, 596142044, 191078159, 601925918, 738903631, 195984375, 966252007, 205656381, 801230, 641691806, 723534631, 357542719, 745365190, 98257773, 34336460, 997925459, 778202911, 593251680, 763553724, 279037279, 245900534, 308631579, 911711768, 341547786, 676510334, 385789837, 918896711, 177833062, 273576076, 878904284, 659137, 262247959, 527620050, 469609053, 515225568, 419394002, 700231218, 307599147, 93274196, 287039819, 628863771, 265297540, 953684183, 572513505, 810487710, 332868508, 818436744, 738858700, 408624833, 509891763, 415006155, 79222974, 299881167, 546307136, 678885689, 883247179, 172047658, 794565242, 279755761, 579397063, 329339282, 609038628, 567637238, 726457460, 826262450, 586466331, 574326336, 485575947, 78586381, 762731324, 866201786, 911092087, 365654262, 915364905, 879507056, 974697768, 435200699, 292066445, 430776970, 442367424, 23886550, 192206354, 463268041, 622452650, 719562152, 693738179, 557824113, 964036575, 825791753, 886542257, 53229884, 988149998, 361891653, 646343269, 100664835, 81461975, 447083539, 288419881, 705696647, 79217207, 542609316, 345563502, 664120464, 3883985, 439104768, 108706417, 481011208, 823632994, 643666644, 649122244, 132639301, 746735840, 420044476, 705186385, 89440790, 550629950, 860139332, 389790568, 371498534, 366315200, 451746564, 753069279, 97506919, 674656864, 48226130, 850780428, 643955640, 293265066, 180724502, 902569099, 706253897, 455037993, 664299863, 840518315, 716091614, 201841450, 629802917, 198178038, 81322293, 33865085, 747340193, 285637992, 117139759, 503814148, 554278823, 658793038, 600544411, 993681669, 150418054, 410427823, 80786427, 766186401, 62507504, 341063294, 249905300, 201357604, 546432728, 386639577, 586456774, 916411440, 996134562, 703870039, 407293409, 399957252, 859703390, 123306609, 865204276, 903901318, 207589780, 519569110, 215283195, 768862021, 707076805, 169141721, 214623806, 395960458, 300992670, 155181373, 826279857, 507113183, 771992784, 189535929, 9916586, 644240470, 149284505, 118143064, 585174853, 105715351, 912023848, 301105600, 352183707, 378289793, 445575039, 500762058, 101266553, 846822969, 655878955, 773778827, 887026832, 565957794, 386225898, 2331083, 701859101, 35416175, 173186280, 410749885, 801648957, 597437582, 265732827, 525336491, 316989267, 895329874, 672564930, 716821399, 634931361, 625596251, 738557839, 778931380, 494533644, 804108209, 366332334, 898023129, 493158748, 412397924, 642124934, 840278414, 253537524, 858348810, 835644389, 54986449, 94246971, 152215539, 7663164, 540537794, 542203928, 956884846, 681179506, 415704609, 940400249, 54842343, 623978651, 563514227, 13612854, 731019300, 566469799, 70834831, 146360942, 694108326, 515503915, 44376329, 352734173, 999738545, 629625322, 923629931, 411588392, 11917090, 10752218, 183412159, 332040002, 610802199, 186111417, 990191318, 580568812, 182974997, 941114547, 415251128, 155066410, 958675559, 374381730, 578155119, 289445470, 774667044, 971907319, 436340818, 947079211, 536199987, 685193976, 874528104, 305872803, 682594289, 154656831, 265054863, 103804138, 469451427, 143457579, 474774706, 540328283, 366715792, 719638880, 816688517, 588322811, 299052291, 203321282, 376004399, 803899840, 854592047, 940919246, 17572884, 340415078, 292861903, 905200792, 513470363, 698475580, 48540262, 258510771, 658133119, 530961780, 948774796, 827674122, 404162277, 599899408, 949396266, 351910733, 762725197, 323872672, 223625686, 526998994, 562132608, 799229741, 204434863, 524485484, 817868374, 465647025, 6247875, 255761765, 300850179, 374914190, 382009576, 428212841, 650180164, 269480173, 304107449, 886090329, 245491912, 167885754, 575134235, 912916654, 811929733, 951185954, 945641399, 648631970, 320767003, 558761892, 15317359, 404167296, 389063028, 522516940, 704562206, 885210028, 57619261, 283859795, 285301829, 235529066, 998270992, 114142564, 188133814, 859621854, 138128007, 986850946, 748936945, 202000371, 476469096, 181899344, 176779129, 385255251, 47970810, 164643418, 617506619, 115002505, 439962620, 938600906, 866934835, 156319153, 234528332, 526203453, 45291204, 463922277, 389396289, 824332251, 329791786, 369675826, 360790897, 35575497, 219357774, 312988193, 392803407, 417930237, 890064119, 393382880, 651885356, 715113970, 538965312, 631775057, 59428495, 545411269, 880957865, 891209720, 810650441, 925665767, 540594601, 326975687, 619963617, 503339974, 38357883, 24079497, 426246154, 183378019, 342883939, 898000358, 131194239, 249284990, 893893112, 404510820, 993328312, 234102472, 67750954, 841523619, 104884926, 218908630, 120209741, 760630199, 226817304, 13645098, 134882215, 772551551, 278969047, 472286166, 250670733, 986660304, 753546876, 190733201, 129394933, 777423369, 645813843, 580812170, 410426737, 948972591, 976434012, 124370506, 456645911, 850321238, 979636435, 695266885, 202533350, 42884773, 308868456, 347524352, 653738223, 220974887, 897532349, 754795629, 424761866, 956469914, 561139949, 316694867, 964973308, 896418436, 720105265, 371982458, 924839957, 527546258, 275222901, 494648241, 302474041, 137454014, 378735962, 927803194, 437625025, 785726726, 461507491, 723275773, 43068606, 190267177, 555376908, 637621740, 965727382, 199887494, 236955737, 422993932, 766812134, 159378588, 375944953, 407159445, 22991471, 265142038, 453921242, 245686098, 41722911, 882236545, 824552627, 387438312, 679034344, 697476589, 105101381, 578114181, 949267357, 201816077, 944578484, 533484081, 465201769, 896690611, 981105102, 971353440, 609743020, 931656021, 289710352, 905818837, 449674955, 355035676, 421871456, 61224445, 303315013, 143615232, 672924056, 235435142, 398149415, 53245814, 422246160, 713857394, 870241258, 331183866, 754109162, 109105974, 148637582, 791197291, 542076813, 460410898, 294093918, 208172214, 717318022, 780723940, 493027452, 176761528, 848954727, 597029086, 253607102, 888168655, 300230384, 357267752, 779210006, 843552203, 283071296, 192719520, 514757860, 65289483, 836088077, 680455139, 565494088, 107780077, 817880538, 708918465, 990294312, 998873193, 404366797, 920235729, 378887906, 323400115, 345644993, 639797650, 741051613, 952385960, 326073757, 105031001, 500836356, 82200536, 650990931, 804921412, 231794670, 249325796, 264543292, 14388989, 278354703, 815307437, 869223550, 432427346, 325991754, 333466863, 37228004, 816843977, 12945244, 494577615, 143648789, 763966138, 19627283, 728899617, 557780186, 54304618, 452551707, 231223757, 967672154, 821392482, 97920516, 56090157, 717910228, 222022724, 211281631, 552477333, 207377171, 937913519, 251763729, 52366399, 673908293, 320487489, 216727732, 396418046, 426267969, 432640184, 2653271, 15622630, 317012899, 573292140, 640392901, 340158485, 646232214, 56169021, 191771318, 623948080, 123896681, 694340870, 527328212, 116436312, 338670524, 680085690, 809505663, 282525935, 166375412, 774462809, 305690822, 926420608, 441520060, 229045194, 974545382, 24754030, 5224758, 129569187, 653434184, 580338969, 235218380, 228109433, 549146922, 815909941, 39072646, 212108939, 305484362, 400498410, 893478847, 77331557, 917031080, 17861031, 437650913, 889283705, 242212157, 126865088, 394464363, 203959967, 996593148, 834751994, 961652965, 690185030, 176114979, 359647849, 372879915, 499899610, 394971580, 271247343, 589941048, 949344656, 388169748, 818940472, 667545311, 668387866, 362042505, 653052205, 571731369, 959216509, 703264043, 967115605, 801752219, 661219914, 788728790, 889471410, 805579621, 711600635, 112556637, 820730050, 6267835, 954441351, 45071213, 82600005, 905145879, 425438110, 711137835, 82256155, 863965498, 218752920, 912555617, 492663173, 871990329, 713454536, 88988358, 221811623, 99539997, 759327150, 841678612, 452055332, 821650753, 535433354, 15609773, 127046468, 795323792, 130903729, 615621437, 927510082, 239149592, 877156066, 908856644, 877647273, 677671370, 815568130, 251466715, 800103858, 46795987, 153700688, 973586120, 715210728, 597548553, 412893283, 516218263, 746419285, 456012880, 22656739, 590596557, 798004071, 414492704, 826578212, 186170190, 651664295, 628063901, 413073374, 231340400, 644416003, 265576400, 219588600, 876210301, 617295161, 768704927, 747429840, 730354735, 698173479, 906935605, 825792321, 331942397, 564838587, 806409661, 859766013, 672910281, 682938632, 602788765, 503452415, 789778494, 810352414, 978335243, 888112450, 335478283, 400354949, 645815400, 164952373, 2571968, 350598854, 59326517, 382974582, 396895910, 801000606, 155516904, 993368470, 239682451, 599795583, 707112273, 108139698, 492102311, 71724967, 364245053, 920447503, 464759298, 742529312, 247982024, 662700348, 977117305, 400024210, 240620387, 233315284, 882613941, 644081882, 264344307, 716359201, 103765765, 854966207, 549994102, 542455236, 315566580, 187125059, 985853595, 166207850, 231428570, 635652625, 616229356, 385631727, 256990283, 942380173, 122119949, 98623276, 320343404, 156301386, 317567265, 398580214, 963735281, 850082950, 332282160, 804217200, 569292813, 603922127, 347295105, 999538708, 945024747, 517852971, 157597507, 688598862, 315327193, 699111545, 574239651, 670975359, 29988105, 854618360, 787043605, 171045982, 929524721, 462479791, 672556829, 129251745, 90524612, 345799674, 239976186, 946962485, 161690469, 357337667, 881707641, 796067517, 260985324, 361024691, 950541493, 327787180, 550501995, 238705492, 244822756, 170310991, 859732864, 847826085, 715343470, 650399173, 904574277, 861392497, 882643173, 988214029, 783748386, 763013069, 605363053, 18967937, 384405007, 574882188, 8860347, 80499174, 345223928, 733229358, 904778779, 120532910, 952481426, 642332744, 966062019, 101142106, 108559951, 778813728, 57941180, 798431188, 474110326, 77622833, 129451783, 563886929, 808694598, 802643396, 806476964, 408572770, 39717027, 102484704, 995337279, 799901792, 3092692, 46545971, 766147289, 45417025, 277214187, 939866332, 374288109, 585739201, 232432658, 885463702, 356051247, 816457458, 233664219, 56689412, 856920195, 205447800, 783991597, 969668490, 261979113, 599510116, 101943354, 517711310, 973984718, 789923479, 454799856, 783786584, 62397238, 941697530, 648441467, 192004448, 301429793, 407386075, 181495950, 264286795, 686963820, 776017512, 476391572, 916554106, 188686516, 202385142, 821376867, 920477329, 427599182, 815365673, 268371039, 323371494, 720212651, 314083316, 996896832, 52626469, 721845785, 693639981, 613797579, 367528838, 741866779, 780134562, 226559816, 633635811, 339699753, 908718352, 160438962, 150608957, 215533449, 557260448, 664743480, 48018347, 814252170, 957683678, 574116074, 158671302, 170865757, 633424640, 512779982, 509267255, 364359804, 989071842, 800460097, 851606352, 112827609, 329445167, 157827272, 359478064, 725648047, 305209188, 396547342, 970847299, 996871439, 76638207, 500387434, 33923947, 287536042, 830556757, 823159140, 996968606, 558866830, 64311354, 707555301, 276565626, 434796575, 769449179, 641811708, 204163050, 119302994, 923012622, 512515490, 866948868, 687291924, 496262418, 975115316, 680502282, 475707894, 784478850, 412999801, 250774295, 850709128, 789363108, 816112923, 658711368, 444594349, 588539094, 860162463, 260573369, 91711942, 604200697, 594721932, 738875563, 100947810, 395270511, 78631999, 75451850, 326362590, 334525755, 764922430, 761549662, 925457720, 247208724, 507970946, 365156187, 265959220, 705180584, 27795404, 181582548, 17863210, 805091580, 138504137, 527123307, 733404215, 331430165, 472485462, 474389200, 10423622, 817378233, 476341743, 401877017, 73133871, 682221893, 62842211, 527932421, 79071841, 248442225, 934661340, 761555222, 394608623, 630807701, 641475931, 332836804, 444445179, 112287607, 244468199, 659380189, 467249972, 708287552, 793925919, 948948521, 743088537, 747277728, 93305465, 38043285, 640098260, 129103908, 55920126, 26389492, 114563377, 476824684, 741384233, 662101199, 239612311, 214222064, 135253043, 525170312, 123862203, 814575804, 582435000, 954101234, 52701603, 486049485, 11001233, 334563191, 872446331, 180290544, 103391935, 47748363, 761506310, 728338232, 165364139, 292675948, 670813918, 221265899, 961511229, 576788276, 590121062, 339024118, 61541115, 909007252, 827588583, 681543023, 68120380, 925169984, 859583599, 697561211, 915879384, 196153172, 671408779, 155677789, 498069886, 367237965, 239158505, 692983284, 255116178, 180310209, 528558814, 464310167, 903926430, 670102579, 864080485, 34873848, 913485056, 134225604, 96844918, 499895023, 639957410, 990277178, 998384442, 953368080, 849432453, 783512480, 532323231, 940408639, 68213667, 578688444, 694816398, 144828793, 795192202, 445140350, 701620092, 595620297, 541733034, 81504989, 458608696, 766796389, 483215342, 126851327, 120646329, 715464952, 441402650, 65528015, 147509525, 699937747, 853204687, 437275977, 280117981, 160327337, 529470387, 25329278, 75439052, 288183883, 302776284, 287285621, 103419506, 349527721, 774655525, 756453403, 307720117, 9888220, 223962457, 822022684, 972040796, 788025077, 498497933, 86141063, 212829098, 114978072, 746631830, 670947230, 743091193, 464393998, 666483577, 376269674, 9310072, 665288795, 387705442, 876096417, 311315291, 822389481, 918973584, 622972535, 160382364, 802388142, 694974229, 461681494, 792409633, 545547505, 271288272, 772465586, 879279785, 583607680, 945504156, 430245811, 128460867, 640027682, 727619104, 938958103, 470273780, 232700631, 139269472, 34768139, 44757395, 770560175, 657032322, 278088081, 799399765, 17935408, 967352203, 481644816, 909586473, 648534525, 700914668, 269107792, 101417720, 484126550, 124624771, 401205571, 501103821, 139012402, 352480046, 375294413, 77495817, 874225305, 238668546, 514629284, 842691237, 864058537, 831979388, 745611032, 778222789, 991292334, 773838258, 622541173, 67562755, 929105207, 354751176, 644521248, 706940094, 914249641, 506762456, 981360284, 868822515, 65207406, 443820808, 343234524, 720482144, 159224811, 215845299, 471128011, 651344093, 158501917, 406199307, 703452409, 282061084, 175914983, 561326571, 343890361, 656677094, 516764153, 414569026, 352329876, 715584331, 517742834, 464312039, 38607916, 243827233, 639465228, 984083317, 759043595, 5946183, 926814233, 725465495, 637855659, 903287880, 686097736, 796375449, 819815108, 604996598, 338188859, 621069803, 586911049, 478967110, 803668524, 767377777, 332992652, 390361677, 101568530, 113998580, 424136307, 821662924, 463398704, 717063511, 925018824, 434148133, 525590222, 424933256, 120972523, 666072751, 459475572, 522246252, 367641555, 791528949, 898640422, 768184380, 436987269, 451640885, 991405264, 489547808, 696298834, 586537371, 884409029, 106017153, 683460575, 34878000, 232326793, 876280554, 744861020, 3985791, 258290133, 556759814, 764985232, 58506583, 44372724, 618718367, 598223440, 685130146, 289526212, 987049197, 616107649, 29690263, 980815206, 649409812, 796515012, 124602251, 491919341, 793399028, 438929508, 42945574, 121671526, 624872110, 132477325, 775135746, 55092805, 504671452, 716066845, 439281340, 742485317, 897090697, 218382695, 562493582, 995009326, 480414093, 644788518, 174912391, 520439214, 759439499, 143624332, 774605795, 759242801, 100794661, 390240645, 393755211, 453545887, 938964280, 509277755, 58210391, 818115084, 680321081, 653901968, 143580477, 423851115, 235539669, 27850330, 679790133, 794043704, 83640223, 249363479, 278723681, 386093447, 742793870, 437968782, 770533571, 970896170, 255010090, 197469818, 255262296, 563116183, 592601057, 440110211, 845100221, 414546249, 301357122, 361489770, 330736944, 907485447, 461643609, 773648663, 240390158, 320343361, 505216086, 623472075, 213903487, 135576473, 40064991, 411788655, 1840920, 141988426, 239184305, 32171950, 877582261, 693569957, 574812381, 747702512, 162004029, 513801210, 281481536, 984163443, 376646581, 716292304, 830209373, 560190838, 60201774, 293996917, 939046840, 595429467, 609323560, 27889427, 687591204, 327332319, 213290287, 968566753, 766037849, 738180048, 346781069, 714937594, 537035054, 49190817, 60776400, 320484106, 671452356, 377600580, 712151507, 905379591, 492788347, 31573529, 119034970, 47416382, 499986805, 997092057, 883218518, 986707384, 20544527, 297214768, 377905509, 605798079, 330328375, 587761498, 855147112, 802527385, 866188078, 603342272, 261590046, 451189930, 920718896, 389941613, 47978595, 930365485, 278274609, 727367952, 362972705, 434532496, 975139096, 819440494, 851939091, 520902423, 740993011, 268447267, 16572673, 92568091, 523657350, 712628477, 343327702, 63763484, 526644663, 609642160, 623247421, 986505224, 44859868, 617748735, 543155181, 290540618, 158569856, 138097237, 983851632, 323254860, 800180817, 265306314, 654193962, 777340464, 525953159, 391292030, 132562161, 158724389, 766151825, 912593671, 596524675, 220560875, 457076674, 136839981, 587610652, 744121821, 610841916, 698847196, 688641873, 908167489, 232087827, 760766069, 692780101, 796199665, 389839498, 122994260, 64583394, 374287718, 474570840, 604062880, 915040253, 101737723, 507387950, 360394224, 698270905, 543050867, 819159047, 203147654, 493870317, 748913588, 599930227, 372712669, 522948573, 720506937, 730338447, 251188613, 571088941, 336083838, 997563751, 350012953, 102967365, 607677745, 772418688, 599355590, 747049199, 147254690, 23398461, 708085425, 39726296, 666981245, 916182700, 554978629, 589921092, 623043532, 701823916, 828669212, 298697593, 430564600, 804270238, 180549926, 339796670, 317333108, 727816220, 658214179, 704460522, 873274802, 573195641, 279685352, 228609784, 284540614, 24794261, 220871590, 318165848, 43923040, 131765909, 790692182, 119420782, 256259197, 176291728, 936750992, 275777831, 586153463, 177356492, 618480833, 496064602, 309159897, 712958258, 220447198, 815906771, 276485881, 201112005, 379984956, 964653969, 436953670, 573736887, 956698655, 515241013, 23598280, 974957640, 396585973, 245951847, 162885129, 119813119, 871832009, 848877978, 770089916, 412222790, 248759344, 260135954, 771341080, 65770711, 202333739, 818832646, 500934545, 865556165, 904574689, 566045979, 723961023, 697983691, 424231845, 522542529, 908799095, 388926147, 422767056, 420288606, 645543548, 529698396, 441934947, 188390918, 814388254, 571322036, 719072867, 532954014, 136178789, 316508755, 107025088, 206235333, 346187147, 721577569, 149384247, 746371584, 366990611, 634343881, 336777425, 806792587, 277637295, 445753852, 749130066, 542437897, 372775183, 588813946, 696425666, 712930085, 401006790, 849858720, 16741050, 159346677, 715804592, 459654301, 652721672, 866832161, 899987651, 994362497, 939296900, 614055810, 518436286, 562235685, 490644635, 425839736, 133165913, 269527754, 538656181, 153453535, 199257143, 904907592, 198076157, 325513885, 233634466, 838949124, 330433635, 401876385, 433476665, 485457076, 815449173, 294230227, 971868852, 881093963, 879257292, 906308177, 16868812, 583203212, 621878430, 919168097, 4171572, 278484289, 76005862, 598710051, 604738363, 467428534, 905420374, 138571148, 648426182, 565451868, 898042014, 900155151, 436258856, 733440131, 647360130, 516509261, 844041547, 964858698, 115966133, 723782806, 203219400, 324265305, 834193866, 3753234, 44567009, 591958194, 40855317, 140470340, 611674389, 547493519, 458966953, 863530455, 957239824, 166816802, 717833013, 695488197, 538519075, 939638212, 46985762, 217138490, 994426032, 573027255, 199240003, 219521587, 491404946, 795965051, 647739785, 593484406, 645774475, 998861399, 316603956, 334015970, 156199065, 277881785, 367343564, 322759866, 536888885, 484449998, 512859659, 449267770, 414937317, 572548284, 932492888, 119750936, 87402336, 460108315, 98358516, 329787285, 872810014, 39548256, 928455132, 669531029, 296563472, 388158807, 497357565, 247981374, 855784929, 124109759, 448979424, 92063689, 818576108, 726976171, 302380837, 587855237, 150338427, 494610526, 676629107, 116445892, 149880076, 941071333, 140138890, 660891586, 692993529, 855232946, 724205835, 228833801, 717426666, 625756850, 725235400, 761917260, 985087981, 832005982, 249626997, 404386898, 766900415, 695809069, 173072397, 238674466, 966300197, 74778372, 586824489, 52134791, 444683370, 68701770, 518987833, 442179004, 489260191, 295751636, 400186764, 436436748, 922116400, 279199037, 37350129, 476283466, 677019002, 840465529, 317710899, 364679938, 609561085, 934781644, 180927013, 478325528, 1518195, 354925266, 157804922, 967881002, 110404971, 978283605, 504583276, 788884194, 352409587, 439874432, 86108595, 894858182, 831555984, 633262196, 361608458, 603787844, 894401864, 67588347, 955282098, 321232596, 831961803, 811739214, 822291342, 235189709, 355571521, 774167165, 110554900, 634495756, 441048726, 683852900, 467536908, 757820551, 450364546, 359943670, 541292725, 616730170, 364215171, 194950245, 905539426, 32467052, 974753387, 173867455, 680770155, 538710134, 336165126, 691180968, 532497703, 851480805, 45552032, 660243735, 262173003, 852367623, 820411122, 247064282, 226022657, 468945962, 957224612, 911234628, 833445905, 583465831, 803315496, 933144749, 63963348, 482357191, 901245675, 142302739, 78936835, 10282609, 949064088, 697598818, 948059324, 447894080, 130103384, 190515121, 357342639, 796622031, 903531182, 263271238, 139605615, 8975606, 370197896, 214190428, 309856587, 739768377, 560994496, 840530545, 450318864, 403497898, 683678295, 500122575, 830513135, 16906061, 792583592, 282385304, 732124527, 790791423, 780286521, 67811702, 424617995, 41699355, 340241987, 549401840, 977558284, 140092780, 664009357, 649349092, 296244631, 980925766, 4507653, 325119630, 579717303, 16442617, 356659753, 678360892, 434144571, 869330975, 739834043, 15984418, 710733955, 965542634, 234127305, 978021652, 791785593, 323371510, 828211232, 239850107, 657997213, 999955106, 233794004, 362023631, 492544452, 92993003, 839241655, 159559090, 630738083, 657448605, 163147658, 612116259, 953518362, 505609295, 240673666, 917551, 156779495, 699301213, 557163852, 303347976, 609314130, 799264734, 535404560, 70436457, 104014611, 339085468, 834223318, 152417817, 515908724, 905142610, 157245258, 364290395, 113683839, 602228989, 47108946, 287901710, 260578798, 198370257, 36941070, 786264236, 125698838, 622882204, 918232106, 156631231, 288060772, 337527565, 130180166, 298889466, 15526979, 94608468, 914744510, 554422860, 667677542, 964945962, 794759785, 913242365, 148174576, 705412895, 7469369, 349004594, 503101429, 673630858, 271386839, 66634622, 760954883, 831793829, 399926876, 120005257, 41584947, 550115943, 780432201, 509670095, 682938837, 276156646, 123189029, 722304837, 258990834, 367334992, 7809574, 769182511, 802162627, 835323110, 963319302, 9536898, 963191189, 934708460, 66366999, 674289951, 43334554, 331249112, 791847234, 882819144, 407526595, 709617560, 682465646, 61906845, 533053742, 645217138, 940058194, 701580798, 116861062, 931802628, 548177941, 512037742, 447740029, 23120555, 656664651, 503212915, 80708922, 594503441, 753650372, 892828694, 78637642, 690532243, 315608658, 852051723, 790981844, 251796526, 44015398, 936785177, 737818343, 142810275, 599858505, 173834924, 865953771, 22860977, 743030618, 846066600, 205241179, 486878240, 765925414, 177020716, 97769569, 388644524, 172022383, 405411417, 172779253, 314674339, 988150960, 95342994, 601863105, 813551331, 563602503, 313915571, 971067927, 964474094, 703291048, 249803535, 471813462, 766968689, 189545469, 577903652, 792433140, 571398208, 757398464, 230016505, 181228708, 336750987, 383514763, 975664416, 731319303, 361210060, 623363688, 816329962, 312049955, 764936676, 440212440, 798866617, 876280366, 589528732, 49259251, 599395189, 388823444, 84937098, 331574513, 763715993, 341547656, 226998564, 636359056, 245482826, 567673362, 406168126, 611268057, 707476641, 152751992, 799798111, 153745931, 47931840, 665262714, 297991184, 451203387, 25739880, 967458497, 441282375, 817078939, 176602863, 61032732, 966123974, 643193415, 473346963, 663064272, 269356877, 16264986, 712721472, 189423555, 741395021, 345536170, 556341549, 213250633, 168887751, 625915700, 531098881, 597953140, 396592901, 114263738, 17603131, 125718555, 823387910, 879650370, 773644914, 301485393, 9255607, 267844422, 924540687, 758964745, 136745738, 460960341, 280907009, 364725039, 550542214, 300625915, 614786911, 21864651, 141138137, 199889826, 327036908, 946316711, 602837947, 612045339, 894883655, 430681861, 961056738, 176838223, 813208160, 568948954, 555118245, 367823104, 816901031, 151750003, 432291188, 996760941, 876712217, 170167389, 305787121, 484379667, 31203598, 389197464, 834246950, 635627380, 883768169, 176287609, 960208862, 836850880, 802307066, 318798308, 765181229, 694087892, 727581990, 436205868, 716519107, 811919628, 211009811, 994395838, 940320236, 900061348, 226062442, 135144726, 481425955, 500770664, 797581090, 624060705, 728925509, 293753323, 530564638, 460259890, 247801027, 468449272, 94555702, 670051292, 394570720, 627483323, 926972208, 537153924, 167938980, 356381102, 43020379, 212787393, 509625299, 88004907, 684819221, 125995679, 389294933, 659084922, 863185842, 311081699, 355530842, 571398790, 939225259, 102835229, 342198592, 211798715, 963926783, 486126396, 657612504, 974424231, 891219130, 132450478, 891889762, 229254918, 401064160, 927342323, 626089605, 33672693, 122795846, 123017501, 227343229, 746153554, 14691446, 614721354, 629619102, 73736575, 746881672, 540698963, 240739736, 361740480, 130496714, 896380772, 405951301, 497450401, 733900756, 916069404, 607541405, 135190654, 955258701, 988310199, 304200761, 561922221, 954205796, 14589448, 193982789, 316678428, 817157497, 113149294, 785778732, 63006515, 712975977, 129239741, 155378047, 136274311, 401595275, 877464406, 79188634, 417703405, 200962664, 429290488, 217431189, 599223542, 196357188, 824617184, 56016053, 735173634, 822378671, 363675394, 73943985, 982088714, 887477663, 793720830, 252910209, 351829095, 257583443, 432778492, 168047138, 516911784, 242643183, 322610230, 560830925, 286837463, 753895107, 601381501, 403315308, 575927677, 158808236, 959297723, 337469814, 584870237, 97375506, 871254657, 203099646, 229377847, 37503469, 248579459, 664934909, 76372313, 26266727, 554086901, 211050772, 874997163, 738982657, 528661525, 212409332, 683114083, 30075946, 922275571, 937389792, 304239250, 518009237, 486552091, 654790295, 139261818, 651194208, 946069977, 549874863, 791281080, 104539570, 493866648, 86886377, 631311987, 433480457, 78337724, 137913852, 770257433, 447216236, 528068994, 866287991, 946627154, 793872290, 911816135, 785613854, 548735092, 732204616, 257626418, 954284101, 660379743, 981753142, 291626088, 491361573, 137584635, 996874037, 562080907, 655509140, 765790272, 542990370, 752481068, 959427753, 71429333, 856484891, 697743668, 951641032, 923595919, 372191575, 61193218, 949450805, 349344555, 982358099, 233871679, 528214939, 278880838, 935615313, 866972277, 819626310, 824571952, 187060639, 323811002, 359304041, 962144767, 591619810, 525770940, 56782568, 562521658, 766010183, 945101001, 3105574, 448144283, 168205974, 671452312, 243617941, 91010033, 871622698, 961028825, 699310254, 117214327, 255112656, 338727512, 70939057, 982342803, 363773571, 826893518, 851029416, 812095542, 617915439, 343283119, 446557594, 239537801, 663605454, 937539164, 32386612, 40489029, 42359935, 783260727, 416378698, 439983523, 325651296, 897193724, 723241247, 340874773, 126683829, 990991720, 80575175, 369276313, 134838803, 875993561, 348205566, 789298596, 608944316, 75963077, 914472982, 990354423, 429164543, 995928990, 806552268, 886459879, 989765902, 519830138, 517914654, 401859944, 995122110, 192217950, 931601391, 766297398, 17415710, 544700302, 998939883, 307767652, 491752022, 46452668, 72130753, 419432348, 778682122, 402985843, 921668700, 610848334, 633693961, 724118613, 45128055, 141188815, 950906411, 434595489, 126462542, 242240845, 796306039, 191738063, 124158342, 654686099, 132117609, 503500865, 484236541, 690573439, 649362674, 664985262, 198900202, 410232902, 16602332, 61752711, 340826712, 538675354, 888598561, 949947703, 959626481, 355320143, 87882594, 51968756, 616953324, 671905395, 69664352, 918901303, 915892455, 779473729, 787640228, 517456106, 374062765, 3973408, 571611894, 355411599, 229663280, 474707955, 804569187, 281658393, 163479671, 486825489, 457435052, 108763306, 999081945, 905573109, 57304786, 783441733, 61119711, 206470905, 61069370, 276534535, 332936764, 701988125, 987468924, 292327689, 541819726, 291659987, 201967426, 591821046, 54882261, 741730089, 719505095, 442102332, 131677792, 302682221, 44393504, 846381341, 829048839, 91731486, 947652617, 400352444, 624135589, 497452928, 336611373, 472680380, 6684090, 743645320, 14733718, 817001123, 179771299, 315948267, 537244051, 350582584, 379135433, 789078578, 37934467, 156733318, 136687934, 535746813, 282532590, 460513783, 11476664, 142834166, 758776889, 94274345, 483321682, 527157344, 912625437, 852369692, 157756480, 710812809, 556900405, 403099718, 866247828, 580852893, 231393537, 86643448, 292669082, 2204641, 939341007, 78011798, 348279340, 966862695, 974363417, 39611459, 126881678, 483561187, 828232988, 353047694, 600004479, 839082077, 14089812, 330327702, 82748855, 523564242, 395905186, 475123222, 804046972, 618836125, 647394688, 640251357, 542373591, 300476409, 100209169, 541348340, 357127864, 517162573, 461135812, 72820014, 381051787, 984155377, 964956747, 490389744, 864379793, 171892821, 715112494, 484836022, 397525841, 995383445, 543822151, 651695076, 836473629, 680383703, 144024885, 538879337, 542453554, 218592807, 480364913, 204919736, 18259777, 694125666, 857197825, 457668159, 211971700, 69967338, 637134983, 124128403, 196908319, 841238014, 658857655, 205175343, 226198970, 162770913, 706672349, 413741800, 118221375, 653893549, 72262490, 695247839, 343686447, 105088779, 107570769, 89601816, 501111576, 314319100, 380203093, 952540620, 485119682, 345483428, 76486395, 542624915, 729832951, 627251279, 649812672, 184370589, 157053730, 709243610, 382090244, 696180866, 369477824, 382886148, 102492061, 684707506, 224913340, 602411116, 75992739, 849710585, 420698557, 652410285, 531858883, 261754753, 99495572, 133925223, 323837033, 391164673, 525930473, 777121047, 333823768, 511726624, 196385938, 784197560, 113853560, 998640600, 829992063, 199930036, 774425380, 444723793, 951526354, 776389321, 535659766, 412105722, 10524815, 402792253, 32285143, 794067740, 192615598, 661290154, 986010545, 106345723, 559998806, 529041703, 16153211, 991771996, 546224422, 183546967, 631989071, 76728391, 329752254, 190922075, 724278510, 825539964, 157868048, 968537778, 399460434, 316119901, 7589001, 705524500, 665617375, 312358276, 4167642, 581343980, 985559612, 251936668, 596547703, 391237975, 819270468, 715628313, 20182694, 180497846, 129038628, 364873380, 118786773, 909982801, 45181090, 243557936, 554794750, 101652853, 757743797, 136751408, 38267970, 732787105, 405970048, 889514555, 849105395, 270925089, 317452428, 89450415, 687042506, 233277425, 880223040, 569755351, 749486077, 933694476, 301382664, 454115458, 728346916, 451703011, 556172336, 19877651, 316093171, 587432460, 133324154, 657523655, 42688361, 360546394, 449393501, 613995171, 571196314, 901614861, 639573878, 77349289, 495337193, 969649037, 202513603, 672157887, 830099718, 380877704, 866906967, 331917420, 792346620, 587938437, 971813366, 464190622, 411836621, 661063597, 41664394, 396145135, 623571044, 360190628, 288298808, 788615365, 415987607, 991387253, 764089727, 870838261, 957499768, 458466670, 886243004, 23236655, 235070105, 993474782, 716608890, 332312335, 47651154, 627739550, 196630730, 34357483, 437090054, 920400352, 209916681, 83692890, 915373880, 155293625, 701717274, 791079666, 125958123, 678841659, 129260492, 614710260, 683132155, 272453037, 87009237, 161053234, 673997536, 115263950, 696899241, 229399978, 519110957, 354494851, 928401183, 574646716, 405928257, 197522126, 152280690, 422911488, 722556945, 978071399, 223153711, 734911760, 855317065, 850806494, 653450782, 703387385, 179859401, 218285815, 975935480, 51699246, 972643318, 448171217, 524737602, 187446572, 643095967, 822893444, 3244738, 788736682, 296195666, 433751741, 749621964, 36578255, 102009509, 102346075, 608365056, 462817120, 797361667, 385120949, 866249428, 996470158, 464128233, 488550741, 38139929, 775973454, 951007359, 526667395, 84936915, 228089589, 913522884, 164419458, 89998516, 757331758, 780496655, 726369225, 522542858, 929716216, 145233876, 97580852, 615651945, 759103745, 549058746, 521193922, 80474726, 461761898, 423577581, 924830988, 722505011, 617983077, 352012729, 931925399, 947491719, 810683705, 398087889, 284729079, 596565119, 822816347, 169477434, 261069012, 925081604, 812554257, 4614103, 212781604, 899416497, 692841837, 138502477, 367831317, 466585230, 146488177, 549418549, 414837974, 193506514, 264078270, 497821924, 284952964, 896458706, 240588129, 649012523, 908525619, 235193810, 662645371, 346671281, 386310029, 10333935, 92783829, 603793292, 612187174, 590585231, 691354870, 227682782, 727278232, 96404369, 23108196, 401442155, 924309554, 832107815, 695518370, 530760390, 558513341, 626752508, 497566921, 734338102, 391654633, 82025233, 443282496, 746351896, 927125511, 887621946, 7099976, 317388026, 534047917, 854907790, 242091601, 77518062, 484874570, 96650354, 728051850, 571023907, 137283793, 49894467, 307397289, 284784507, 843563931, 131308276, 480377644, 991765825, 858942207, 414143483, 236283915, 189656577, 469626924, 702210312, 769495460, 365246419, 687314635, 3919326, 184754913, 757548221, 974531310, 645913701, 166576380, 551539449, 280665093, 714501947, 959193732, 827033456, 349423638, 491470314, 695714582, 91682111, 761809699, 893074731, 732336626, 353244705, 447939405, 891427051, 653759919, 926311454, 165398748, 318839593, 295160414, 237473949, 334247876, 3368693, 537592643, 37290747, 178414447, 932380862, 356431196, 995307450, 187116104, 647215667, 896452907, 26634283, 137129499, 117646126, 501886784, 646217101, 336915030, 287664328, 434013680, 652480234, 432514153, 124735038, 411235136, 411602102, 84339813, 344963800, 618361110, 784957910, 456296136, 164846888, 408109854, 610709998, 824138484, 404395936, 505960314, 308662256, 178058161, 530381402, 782256076, 834051825, 70511527, 124993337, 201016071, 261978168, 127505817, 164207813, 930843312, 8864805, 610668302, 650768076, 826655106, 534240522, 413827035, 193505040, 791756432, 683244039, 633489186, 729781021, 73969679, 748475854, 134587847, 373792415, 203902324, 714402797, 162745388, 667972331, 57677526, 527205477, 962720077, 49910284, 547404260, 590063411, 601449358, 348392510, 283993933, 482340092, 644816747, 205307872, 620182667, 82612071, 484982344, 465315110, 698674786, 191001272, 172332872, 946119198, 719883941, 954679383, 914089206, 621924391, 987992178, 952114660, 592922360, 847896893, 485755689, 292189976, 884357307, 449996710, 686277904, 222445846, 544466060, 697154170, 485618885, 506673506, 349005510, 280475048, 907002449, 733685565, 598711818, 689703065, 992194908, 800946863, 478816066, 275228496, 444963614, 387971074, 874601363, 693564572, 643615233, 978734140, 968542187, 800341368, 814136933, 881565014, 478692964, 690699046, 806122553, 143508475, 679207852, 749650333, 304818034, 448882871, 777974081, 19579243, 264876486, 920578942, 950309754, 935341997, 676844542, 461225682, 41039166, 238261992, 597633564, 834674170, 358676548, 959055401, 732568276, 654542242, 20886576, 519496588, 117791267, 519724196, 874417221, 153153161, 393284013, 335225632, 566479586, 898443012, 206119413, 382629689, 62018018, 814637685, 40642256, 838745092, 757079974, 410594683, 127843591, 747528947, 501601498, 323842962, 202118376, 859901510, 995140075, 70878082, 569089244, 647497519, 709827653, 160841915, 380767638, 209585268, 426407437, 996960854, 293342964, 986859880, 388975931, 640288197, 558981273, 785279935, 663065809, 425242604, 795857052, 817885230, 292326438, 439421781, 858767853, 359024043, 563315405, 881886041, 301706441, 665668137, 940406452, 859341175, 610272442, 988650038, 467674564, 595733307, 224670151, 546273675, 26855759, 293117550, 755855066, 659210578, 677409260, 365752139, 809881287, 269353758, 286784911, 94065130, 493661609, 329558920, 349492429, 575328637, 813189738, 446960085, 745811114, 911348686, 304420614, 883891146, 459884635, 717520353, 157581584, 893771752, 251763802, 569248030, 64560590, 841536292, 744184394, 214586398, 546578262, 388198097, 587950015, 533409866, 832476678, 732092697, 345651724, 934405230, 700869871, 227490145, 351601293, 220154561, 355146024, 638611050, 332163544, 598086612, 805555069, 308733286, 151212896, 724226706, 332307750, 632979741, 842031676, 826395351, 503014816, 689491256, 427548429, 517796805, 626740601, 549773314, 657144462, 776728514, 764310372, 86473424, 537220599, 494007367, 952922867, 300207480, 769883832, 594495319, 165371850, 582182364, 50817791, 83306084, 262064341, 657041262, 403164028, 667547153, 296843495, 989872619, 195911261, 822427183, 966387374, 86068283, 685952323, 122923837, 722238175, 207943805, 289831281, 468111011, 934563545, 294361498, 540496994, 300966420, 56863071, 249927961, 942472782, 585938403, 7550201, 998829925, 358705423, 502385911, 106008357, 133251927, 836416589, 760120313, 206600065, 233229888, 671063507, 260482150, 560711250, 552127083, 575309032, 28873685, 993475875, 939597352, 848547442, 668233622, 790236833, 426699271, 214699599, 311868287, 974771997, 610414580, 983426633, 520768249, 295929332, 96489795, 781174831, 834902819, 127769013, 420478876, 515093905, 102108112, 747268945, 471146833, 501871135, 109054646, 229514168, 680680818, 53742012, 330075762, 458391294, 109300480, 136097253, 82363800, 596361267, 716975875, 792709599, 284220338, 876492052, 562320674, 375011490, 975550889, 445421180, 570337013, 447942541, 916875439, 623408060, 967009496, 125973745, 904021417, 101400346, 41086313, 47760826, 384081405, 668409662, 636733251, 824394392, 886393798, 598016813, 634779868, 312226553, 599717101, 701938853, 286039907, 255040303, 897272683, 523021538, 478540489, 143133073, 198588456, 136458618, 565492037, 950177248, 879068675, 846816074, 814365134, 759629505, 489661196, 935337346, 739541683, 217104154, 304422600, 330846519, 404897768, 124788629, 438335780, 372733946, 622362010, 395722696, 277100056, 908389256, 587561364, 9120751, 390929465, 385976108, 354010431, 944067176, 457015217, 855407385, 79851074, 881296732, 32616096, 629278910, 178662048, 576920680, 826079949, 470894116, 307504127, 893470540, 681329870, 907129424, 958307123, 425586214, 90016476, 287448101, 378762820, 103881578, 850744220, 414306572, 844415325, 993662674, 761368124, 426984726, 572143243, 549591193, 318531571, 732320949, 2550383, 604623267, 695921080, 272584175, 796846803, 167103546, 808785349, 272854035, 435066421, 273936919, 841230246, 380707346, 905040170, 68986745, 937094675, 696789447, 61670119, 729952644, 804280480, 151087797, 44834415, 314140645, 83933423, 871617204, 494749763, 484033978, 408035606, 645739075, 200185583, 878339273, 893449765, 943642483, 141808578, 550737281, 536644345, 495556184, 717343906, 626744374, 12873616, 133256100, 905167126, 584401550, 226617881, 403354227, 495162591, 202373221, 765960397, 646064048, 511682168, 813590852, 354720084, 502385164, 975681217, 36809955, 690333094, 775216187, 93976746, 440092607, 659446562, 409522990, 808426515, 711555858, 690028556, 301523309, 606509329, 880370827, 264064729, 638588496, 561106769, 539539705, 68273130, 561642729, 204204146, 342532754, 881873860, 45494865, 803713598, 824282473, 109062202, 48901013, 350413683, 519689542, 27230520, 885157499, 740267704, 440003074, 178568044, 649203155, 568132633, 776749234, 311489380, 988771246, 295944279, 881001290, 243548761, 961360298, 513082165, 463834896, 47343951, 947723658, 732081244, 410180203, 453750081, 207668803, 396718734, 186576408, 793940987, 545761893, 701746466, 422081927, 696284557, 919060774, 769676310, 203780016, 964554065, 303003429, 907651319, 386023160, 328757097, 258018694, 590624301, 986883448, 357939197, 108094554, 870218120, 950293969, 641049262, 319228397, 556217524, 452151101, 179377562, 624214720, 810736880, 557190247, 961863974, 291938490, 551923228, 959582628, 953015935, 881058724, 168471452, 34308296, 951451402, 240488108, 780874430, 672763304, 423475882, 815369973, 608616037, 434612635, 470469841, 559528420, 719190777, 569827245, 3093322, 138693159, 568075277, 333456204, 536005810, 666811610, 524145355, 723600196, 863088555, 809297265, 406650672, 533372275, 565168285, 143005290, 269012459, 326934265, 650641532, 948825463, 556401059, 792020380, 933092247, 117536478, 317599907, 741081791, 727165800, 839107842, 364438638, 829863287, 178330998, 675672730, 572780192, 232485594, 929274198, 456335362, 726893119, 648087573, 320322869, 681637551, 214349514, 472740291, 368217359, 845009454, 81824153, 44802543, 565280555, 895820097, 99224231, 444333746, 17019458, 268946923, 306356391, 36885376, 164839576, 422870420, 970738560, 289910913, 583938862, 31105828, 314499091, 448169787, 639773253, 655091467, 363430765, 508577760, 840370578, 200837514, 757601657, 905220815, 411142994, 817760242, 653318826, 589525873, 608418728, 351278933, 660987020, 201948623, 663565659, 636424702, 925676477, 107852100, 428590574, 103432586, 142886970, 975697402, 721371312, 306056268, 956463846, 973137093, 429260356, 400504401, 466788511, 449935707, 736416123, 937302262, 740939118, 351101897, 442814562, 871336807, 223454476, 522289154, 288575316, 491856821, 116716045, 690450781, 710265214, 805555057, 30695099, 327118577, 946790109, 23801545, 516939602, 289053761, 315952644, 579924388, 507451226, 485271375, 381160949, 125085623, 366845689, 367961032, 314286400, 710639442, 772332801, 156424426, 196563861, 217078283, 835411446, 305768609, 479720936, 910052636, 386955650, 578881846, 579975167, 447364654, 779181628, 564858733, 309766278, 485744376, 421078332, 521987945, 615156887, 781026289, 92429730, 138574141, 449658112, 447782815, 410325473, 449454747, 410542993, 721606781, 386286463, 138891979, 963589377, 67798348, 200785858, 450096149, 481571739, 997440884, 616763473, 605170678, 536271435, 364434420, 730277887, 423681603, 575760961, 316533524, 471777021, 819379953, 230399789, 602243365, 35168062, 857552405, 498741578, 849831630, 285094141, 453611263, 517662171, 104553693, 112848628, 763510840, 69700215, 796583614, 496401580, 738570522, 111281736, 666663244, 966107780, 529799487, 836614864, 991460244, 448160557, 673186247, 188117604, 579200066, 898988180, 182799197, 705021899, 374829172, 862397411, 508941550, 33057913, 379365272, 629300732, 214852830, 861531346, 234320376, 495332656, 908699004, 865425404, 487576686, 351557153, 975078062, 296833432, 317315575, 911334946, 381866544, 189994260, 225730768, 819815457, 538192089, 120165512, 906265237, 321498216, 543420486, 265800709, 425558313, 136248317, 510914129, 655789575, 960311333, 115842068, 146826991, 639007988, 682959798, 456704563, 534923945, 164467396, 888478019, 560263635, 185088361, 332296898, 907662766, 886416673, 369288158, 929574506, 813777697, 143197094, 952097362, 948794342, 901334215, 769180508, 185221305, 190282909, 315911023, 264706841, 399405196, 820887064, 463835797, 97957513, 994508459, 899349581, 164236578, 487480966, 368224623, 28195118, 710330739, 782320160, 950825070, 581524481, 373604699, 873274205, 933246634, 675540482, 260334961, 147118615, 654212760, 767466312, 809154662, 641838354, 595367271, 95043372, 49415084, 434090342, 326791678, 68888478, 802943805, 651114374, 971653756, 567166855, 287884429, 974974010, 251224807, 67113001, 396407606, 571146518, 361484193, 328539510, 839027653, 845177145, 8332719, 838894910, 932115662, 690130443, 434934833, 319468133, 14579893, 925892121, 387319695, 607300412, 433967443, 813974270, 434708273, 923666831, 582254836, 926459825, 109220202, 77279955, 59015171, 522417252, 600919074, 435881944, 808178255, 200613516, 871192494, 643897012, 740673518, 96925861, 703474867, 659939285, 471741859, 970469309, 838907402, 578462505, 148046674, 365406397, 186942896, 316067127, 995138640, 583710600, 91331578, 682346031, 764937409, 921964627, 999803777, 549901181, 598970434, 952477033, 846752769, 342865707, 227543503, 75104690, 516266858, 330043862, 200661826, 950026861, 254515287, 889662386, 131919565, 140252660, 793616894, 673318794, 830575032, 802585082, 89263333, 931150230, 716298391, 913299131, 672998708, 252121437, 720163236, 715365533, 134552863, 566747588, 465280837, 97160520, 286664879, 50885957, 93255921, 829652026, 922808483, 71762040, 771192630, 950485243, 620473233, 820488000, 410318915, 726910497, 171236219, 335735227, 369329752, 795083476, 233879096, 783926937, 787809538, 570394899, 35803497, 281661937, 393644357, 704641735, 899552446, 641603036, 329993282, 34395715, 302436143, 313785598, 900708697, 238214231, 341015835, 656634284, 272841938, 986527187, 679651864, 743802200, 522399802, 649526359, 778746782, 711901280, 358135339, 835216708, 595644307, 643972110, 256724220, 629755932, 439403386, 849244372, 935014405, 595362979, 681101458, 348032087, 412151156, 476197860, 941418198, 480527561, 732798488, 411596139, 569377035, 316526543, 430484122, 31458121, 982521790, 257979111, 650626085, 125631046, 45259174, 791819035, 688105733, 43186172, 879520579, 745437709, 49344707, 535310755, 128374497, 750165313, 989471934, 763655658, 963502965, 365239995, 659668974, 432744401, 219004256, 43236286, 256031574, 81825185, 965878819, 953914867, 919192735, 307812706, 270374152, 836693242, 273132579, 476428619, 161527230, 884745904, 216548943, 301671825, 313454843, 865239510, 529421372, 585951615, 293698417, 930256360, 851314588, 863413307, 286404893, 2195353, 406707616, 438492860, 241408057, 673194214, 477470020, 97492770, 53160464, 105741053, 286728737, 209400637, 650587391, 493200524, 310904043, 738031373, 648494613, 292539673, 879949298, 803609009, 647990295, 874918943, 425921595, 828327756, 905057456, 888898003, 118638112, 386843617, 13560673, 369022955, 194597462, 413863356, 339987505, 506063175, 869674636, 563703689, 467989264, 648664898, 389494728, 184216693, 74673977, 247886161, 391154808, 800354188, 516700975, 538857298, 97633066, 248701197, 289601955, 35251393, 974685921, 207159971, 501582870, 61807787, 566157909, 432800064, 448307408, 139361647, 752172671, 260454641, 702127328, 181766908, 344793957, 406440404, 524778184, 807160011, 487815169, 360173465, 316750904, 246989913, 543431742, 437548979, 152239743, 142456595, 200081211, 147156887, 716577358, 543820724, 543995554, 628148362, 446477120, 893161310, 908942070, 411620182, 43379379, 588034715, 477681310, 579464194, 854716748, 385113602, 409362063, 923031946, 218933921, 469735073, 670024505, 816737592, 326193181, 190524165, 863149, 117144540, 111901126, 557720020, 617224125, 271355123, 984505640, 801074305, 428333343, 996365498, 163736019, 895202464, 606872499, 937100559, 817006480, 168105221, 137539855, 249072398, 876760488, 868254596, 220377526, 301538193, 696807489, 466351245, 88966740, 789894853, 113510571, 304534003, 659538364, 189074911, 828161504, 275137812, 158894257, 14870659, 516670153, 494237227, 548735363, 804981085, 751808980, 700022914, 194823141, 481679169, 580229680, 609577186, 93390946, 753139005, 483368685, 456310706, 967857121, 990786111, 947189681, 173608133, 920043537, 596128894, 339457160, 385426189, 812705344, 56821674, 584027226, 48672937, 751117248, 378031097, 275978775, 548607537, 710101458, 807517477, 433576063, 515380877, 401507827, 460679472, 516482149, 481994007, 676503591, 573678202, 12833184, 515325902, 243665496, 770918772, 273502283, 907047066, 872170911, 997988283, 218847474, 549585759, 241992357, 394586036, 437115919, 298060111, 952332026, 772648171, 755049140, 470031581, 400064459, 485462874, 820936561, 441247717, 331877710, 8600657, 429446960, 921527735, 953879151, 598622070, 436810402, 497814807, 193307898, 6960779, 398875528, 194976754, 375487213, 851622051, 527781725, 925175918, 73188435, 264346529, 905885440, 514638895, 655842709, 385602498, 713956651, 687527141, 766167365, 100342716, 817571941, 284508702, 452855414, 267739299, 562938360, 370791624, 982965789, 517477936, 455461382, 668890931, 731815597, 653744437, 103174471, 207483581, 223785494, 620512886, 883714826, 607533706, 458598890, 447153731, 578770851, 991082816, 409825844, 947313072, 611863680, 641619051, 915527944, 219868687, 884844371, 320282756, 935910090, 723334054, 866420765, 432661210, 858640720, 399012870, 274594490, 619427457, 287114183, 526113103, 117079936, 953176940, 348204958, 330039038, 96649300, 964255651, 76396483, 560049300, 171742833, 753359230, 955409568, 701138205, 106394086, 283109605, 659966034, 203469473, 322067923, 705270679, 527955533, 644508649, 453243061, 334781304, 67161693, 740239736, 845276576, 606254028, 968633413, 270153230, 15609874, 556896113, 473048001, 952026023, 155024247, 8998372, 808878561, 90299280, 256184723, 528969810, 135127449, 294752131, 519091287, 597347636, 484178318, 983115861, 986523245, 982391115, 211087471, 718673428, 280193826, 961685921, 478746454, 622959905, 488452369, 215431500, 475298644, 672808055, 812220649, 129881590, 938263230, 225324862, 551452162, 642621178, 252563814, 343155482, 718791305, 150998375, 522990841, 987476746, 973450520, 13780350, 536636163, 566202945, 469358025, 269010485, 590742601, 490368447, 398268500, 754484287, 680270667, 738144905, 546979769, 891441127, 839618226, 676486701, 534327077, 18410771, 712745100, 439665032, 973998715, 251758473, 107240016, 369514425, 898227701, 913356569, 49993499, 863673055, 102964880, 500497333, 932180724, 739260615, 851220709, 516718684, 884688895, 881837804, 864898721, 898198439, 157092668, 149569962, 84749678, 299212506, 628166833, 347804602, 77971286, 947183907, 954511938, 705491353, 702275009, 245800435, 131769945, 843468954, 286112306, 474536317, 759420360, 506838542, 904281379, 36147631, 48374304, 590613169, 4567540, 846581514, 4218417, 866975656, 227946538, 285289124, 802272596, 569796677, 599551926, 551648808, 401867835, 123877689, 437131181, 756819363, 978030744, 680406928, 439707356, 256161616, 933029007, 460897678, 302662979, 993174909, 752302344, 892740959, 140295730, 259872679, 372022669, 294737191, 379296980, 914479296, 699616799, 678879908, 735798660, 282637198, 892675904, 586857450, 159511658, 259683720, 828864364, 836588071, 915672883, 916968245, 989264680, 383917973, 97063267, 284314145, 777674784, 158017025, 835459049, 377613286, 639961404, 455844893, 367144039, 196173019, 237302493, 797545388, 250759510, 743579771, 686599720, 667024929, 981399332, 60613076, 508281481, 87331087, 322048384, 388881812, 150142705, 903371857, 483270733, 350856070, 276655865, 884448113, 118717917, 556313968, 31167998, 537573530, 181298663, 632802073, 864915106, 67724929, 596666269, 475598371, 623835548, 44787751, 157746260, 223777373, 164632886, 609599525, 341031194, 85033113, 580474066, 13208933, 965498017, 130163801, 647994691, 292203283, 925434943, 102702379, 946728937, 39826707, 574698030, 658433269, 397800637, 704419188, 931450316, 411767838, 366351065, 646336687, 176344362, 191679281, 75556938, 58973368, 3218152, 618316253, 250821515, 313406860, 532623839, 841011772, 223309583, 556155174, 870059877, 243933433, 175211890, 934707688, 780761246, 11359400, 371564365, 673150414, 351175999, 291115749, 38891848, 301962843, 411486232, 516877756, 723851104, 73965722, 974497020, 492180986, 342706112, 753093367, 158220204, 979586405, 577233074, 194508705, 806173734, 748368, 520958330, 244197405, 330882986, 298730479, 661182063, 888944717, 143437490, 967367041, 364803711, 455190360, 690696999, 737051690, 573843117, 358260951, 142176931, 559743527, 318271254, 237800975, 215724646, 857838583, 746012189, 137791770, 458472384, 649699269, 622531836, 406789211, 201621307, 253319713, 275520458, 279276021, 271704284, 125048181, 609944319, 953334436, 195441216, 793939906, 772366633, 28840526, 829116352, 510321088, 64670846, 879689322, 987774, 433238720, 774260444, 425137601, 339840412, 189797030, 729406428, 270570642, 592171879, 804379631, 52413932, 165881688, 617957463, 646944415, 568341675, 108071671, 611919703, 93147523, 451987707, 1607942, 992413706, 655301052, 453804636, 213026408, 118394261, 567118201, 457240833, 222928598, 238578817, 93228069, 421164362, 237482704, 878961040, 41261614, 600236901, 992672382, 611345648, 242618495, 307349352, 597451722, 91873110, 878404944, 615331857, 252748995, 658530937, 412382651, 335465809, 158197678, 877133891, 419957196, 264480433, 529121317, 532657139, 757662623, 658296384, 130633535, 620318965, 758820720, 543594273, 910068187, 133603693, 689223716, 47935942, 103805811, 364895168, 7562600, 326456562, 307799389, 762806623, 101400368, 401428519, 33138792, 295226394, 905759641, 718353656, 976602785, 442118145, 196667033, 873226571, 317904901, 375909392, 893472771, 480996636, 321989373, 531861785, 875300465, 426070983, 547884832, 877846695, 176508789, 865774296, 865649775, 322445565, 648870647, 367921534, 612629197, 589614120, 345054597, 422925088, 651649273, 330361455, 64133505, 174957910, 685448984, 693065435, 80483864, 976471519, 887069055, 994721324, 863001281, 447365519, 771713149, 711921631, 877279512, 22100553, 314695277, 251097133, 169331996, 364409454, 764751124, 250763534, 516226905, 143962397, 624828994, 822801528, 693915417, 478568026, 928241645, 610057491, 141124962, 264059137, 256758089, 101794811, 579419161, 539358054, 345440035, 477733296, 821100707, 638936437, 253148016, 601578049, 394307354, 151651720, 582916995, 393777146, 13646419, 432700597, 993428107, 875316212, 806514254, 936213550, 905679371, 940320401, 829245842, 932730924, 362980932, 618279821, 82340475, 561171162, 22141237, 830173107, 392075026, 941214025, 440381232, 52377502, 119904829, 157354681, 689822577, 849699016, 661567741, 257137000, 923981802, 454285513, 38927215, 181680345, 454437758, 87713768, 280150329, 970107625, 831695693, 484159362, 463304544, 496944089, 123472960, 831604000, 71739042, 153229273, 106297005, 37142690, 963662759, 247071638, 632700227, 966905844, 457127990, 485852764, 113476979, 318276105, 355236508, 76451547, 704898948, 575087092, 163128955, 107548452, 234744201, 243555040, 903182697, 846150516, 483788672, 662660595, 397736851, 49347019, 470250498, 75727487, 182554961, 806928334, 943238213, 285518270, 481445966, 318078051, 950980460, 718422139, 140108202, 794006176, 245252443, 465136378, 680181836, 477929664, 316579067, 854371076, 321414839, 17700762, 16408800, 691948880, 412827872, 224778154, 474907217, 271227144, 839429554, 166326684, 318904342, 607894826, 128918784, 504844822, 263628223, 798306374, 982777833, 544934058, 109100343, 308419483, 65305083, 747110157, 241876360, 138328203, 64527473, 996606751, 466036867, 105341835, 607336865, 610397061, 536506380, 916148715, 712623038, 317971675, 66178585, 975227262, 971884423, 260482022, 929041781, 172666494, 128979462, 952743659, 546369495, 968666262, 190772628, 592305700, 36608007, 252862205, 403710188, 830991188, 247670400, 540238133, 478799614, 121339973, 487504370, 853917198, 33756563, 361211150, 955317848, 982057642, 929985389, 719821202, 966852668, 854518984, 44072911, 113099323, 489122972, 564888685, 782228354, 316941843, 967587793, 176094958, 972061015, 286448925, 878827714, 601165015, 79012603, 608884782, 568444368, 370316526, 403886558, 47473938, 233041528, 290603434, 884774420, 190565495, 891557315, 18294026, 324295655, 717088952, 145845242, 184190531, 258272085, 518258612, 665321656, 505198860, 789908896, 725918546, 831706171, 49662920, 332359094, 399589219, 995901752, 400797353, 279087721, 736899154, 242414293, 188850743, 967181857, 3566564, 869418591, 385828372, 559465968, 384074028, 217187641, 754213738, 301996045, 901926994, 368159305, 86644611, 481383651, 545833600, 634039019, 165021260, 680472418, 823426663, 804756391, 483951822, 883605273, 671903498, 406103228, 340279543, 291165199, 328358375, 730959671, 981669752, 783065460, 835459869, 625918879, 451260650, 560399166, 978114792, 96547748, 397797194, 336190163, 692959665, 432027731, 135333392, 369624994, 219280228, 781754273, 300980847, 327819310, 386250264, 349925829, 397786077, 23595725, 214821763, 930579782, 961827542, 417158549, 757115662, 475619185, 66143066, 223493609, 820039299, 229484430, 863784690, 280923827, 162130527, 905033864, 422369748, 644068477, 785057358, 885379637, 646477182, 418656779, 505056782, 727053873, 259226312, 972453671, 117645710, 382508016, 771973663, 968666011, 847467700, 913904976, 183329339, 450162823, 46566130, 699623814, 332717611, 429775125, 534492651, 962391879, 443231580, 258986803, 381592242, 425043963, 380220176, 767203673, 538467676, 586131243, 697520864, 7568165, 229823841, 902381948, 101302039, 685515168, 473475665, 201713009, 254193721, 123586217, 41439893, 965066407, 899403604, 996800382, 109383056, 158585220, 813868937, 65000896, 764458233, 197973089, 893565574, 370933566, 644033819, 853856107, 204819348, 676506848, 811855744, 194554913, 446421233, 842016569, 568974301, 72574602, 853763096, 785951003, 145650361, 128736890, 929902038, 957090421, 558068622, 606498352, 56944947, 16347504, 641463994, 623693696, 764936442, 206148511, 712168923, 57965818, 51072578, 30702425, 576003802, 889902327, 604780073, 662487020, 983447369, 743171873, 759313901, 50280522, 801558525, 947491471, 981984837, 241357782, 963287805, 435647602, 458131266, 373349702, 610583246, 699352491, 491475352, 417383272, 804799465, 236137423, 452141692, 969126621, 502606981, 584458011, 694353581, 329123065, 413968878, 370580720, 266740800, 688378977, 290283256, 901799705, 861701845, 609179885, 312462770, 150499657, 41495472, 681706504, 998810702, 960418947, 630022640, 204907115, 262648082, 959257353, 613662887, 272117135, 415292654, 41904193, 822169368, 273788879, 723468938, 756079640, 681147777, 909467445, 55303267, 566432645, 301657081, 890620444, 852725669, 272074481, 898442665, 358730533, 632984774, 669655580, 437799276, 442864874, 724657594, 81642203, 295212280, 704714265, 528250379, 468658748, 319485637, 289109633, 420826795, 802571131, 333089160, 9105168, 121804180, 277349377, 809611190, 637825551, 810155749, 781244279, 708121069, 74844781, 85845403, 174947523, 813995491, 554729, 487724406, 969261886, 910070813, 315810447, 575859816, 259540544, 339189421, 794153639, 725332850, 741959802, 874531680, 625018533, 807923706, 1016939, 814599856, 662249010, 422331290, 388845287, 45597134, 318055390, 520227459, 375860611, 279796235, 148019281, 954531613, 186203250, 154620612, 731086901, 331526642, 40212927, 517139381, 313868984, 622852872, 301699838, 959898776, 81775147, 716305797, 91445233, 231891111, 437569795, 650094342, 25865053, 252697830, 279844433, 865882161, 305677417, 972107840, 839714624, 756774902, 663867140, 236186007, 513125379, 813287956, 909221992, 996396975, 458162908, 478669916, 944980147, 229426540, 338406906, 116339799, 932287331, 598131187, 739367745, 998051224, 159257502, 197887194, 930433391, 250109854, 300534137, 387781246, 172780670, 995506495, 194850789, 13966488, 653151101, 529299935, 785822554, 376967092, 983891666, 910987948, 37473641, 750585466, 719968498, 952315449, 30248919, 915945047, 79331976, 6918658, 524430326, 307608427, 40322164, 828284607, 410477063, 491469487, 575433063, 901918558, 866377867, 694128078, 398492071, 662052770, 61475445, 13518324, 234815923, 936267218, 383138505, 472898789, 345311002, 474441895, 299912571, 298349142, 459152484, 798739868, 74894701, 601682776, 48847280, 262229010, 626968119, 280091036, 888899825, 848751558, 947289800, 493773485, 103011530, 193019276, 273733572, 211990864, 152009458, 895425003, 629915013, 848564795, 41479083, 595616871, 75526163, 127211841, 991549626, 136486090, 783914822, 19212538, 334961074, 389126353, 739634777, 286679433, 221771713, 353811064, 538694278, 349012859, 601934822, 319401303, 872350995, 948077345, 780690008, 63767061, 687514777, 262571454, 540191404, 427269317, 407805, 521770570, 238985751, 632981337, 191894833, 954183090, 626556382, 612561129, 486447371, 325705168, 211887440, 161272634, 863360122, 925808813, 907724102, 664364632, 621258355, 689738325, 970390749, 289107741, 968907607, 386664108, 324407786, 189214202, 94612769, 593540865, 818396722, 254777408, 66691030, 834792830, 966296331, 173098037, 303149574, 561165641, 661186855, 841073977, 667171481, 781289985, 299363357, 51022632, 202052501, 26016979, 578175746, 145430618, 652713007, 471261297, 772450324, 784999729, 577988244, 67890273, 741389201, 118465541, 6050095, 342625702, 919884813, 253709131, 406017492, 845663064, 642741056, 657956728, 163205371, 959937828, 700319548, 851518414, 600022558, 59707662, 900916714, 304155974, 186408548, 447687211, 38917455, 667434628, 827202270, 394995313, 887970090, 496729829, 913606802, 774537916, 243516441, 288139983, 648316709, 874569150, 12359921, 258576758, 10470075, 142644236, 751349131, 789374808, 583619371, 28855486, 755680848, 482495919, 858044358, 965621204, 463665465, 160139927, 254576513, 3137613, 682370755, 863651484, 254083707, 606659902, 124617064, 526697937, 415206917, 927615905, 345783120, 406155363, 88667915, 564652937, 452668074, 178281423, 648198353, 43755348, 619453515, 52059752, 597836585, 769189848, 612453815, 598885316, 225595299, 432050619, 86706456, 156089499, 780935774, 735331951, 464717825, 235545049, 904783686, 712028198, 260692842, 98425338, 708548297, 539306974, 183093098, 876238134, 273623239, 268052704, 402230585, 295585367, 136393737, 159430223, 838742875, 66136179, 865967320, 128902827, 393184743, 271261920, 847771598, 422915902, 309622271, 823500218, 750431417, 555225771, 535173550, 187718294, 540873787, 36188775, 627630638, 698226492, 771685991, 180591225, 253185367, 663333008, 934005090, 989720905, 397568532, 332281166, 323438160, 590369488, 701385518, 125043879, 100763482, 740685005, 174968061, 193406147, 782576920, 425146376, 57774011, 801434431, 259065302, 998444973, 531249774, 79513070, 460945026, 386023741, 308675594, 624033198, 288844530, 223862878, 767285952, 775848095, 760544423, 149206424, 653926693, 806088, 973654478, 356310954, 310683711, 552031652, 657320302, 502172167, 317078379, 912043267, 426454236, 1525211, 972505356, 123243739, 305733203, 302837337, 112216714, 478046820, 811350688, 346440555, 880333732, 88600295, 214354380, 752630263, 476239915, 369268847, 109018340, 937609199, 216510085, 70779970, 912585285, 555923233, 244378232, 580137846, 428237395, 131250989, 542770151, 528765499, 257549549, 279480697, 361350456, 569874965, 778742353, 131198130, 220391377, 890988791, 266179110, 757366602, 894525444, 632264883, 976996481, 34168160, 770666346, 14913825, 699198648, 145539675, 347831319, 387549936, 360171497, 704466824, 369032493, 525472286, 655311528, 13831945, 477525173, 72688342, 430823182, 399852477, 151427728, 90651225, 237114877, 738051275, 339214329, 882866547, 260578702, 52265072, 438937738, 465177540, 476887776, 685094257, 209749737, 597179396, 588413973, 151115073, 571344897, 193458025, 740492759, 982231666, 598757068, 335058294, 875262949, 972568489, 357178756, 909058372, 998165642, 95450196, 954093196, 507210548, 826485751, 507555160, 882023761, 946059965, 335671275, 57747441, 679491626, 260964931, 619028054, 765488126, 793672520, 265282067, 211080148, 228306876, 855969708, 97210537, 628871705, 458519333, 446815272, 940666410, 530840423, 275928775, 861687702, 516814285, 532619015, 176372071, 31622202, 69014999, 494778071, 518374110, 818922717, 335125010, 324754357, 249928610, 397269981, 957760055, 59590883, 980538640, 169766809, 478549851, 742793553, 272172360, 817652701, 378450331, 314452383, 212632586, 370032194, 862925085, 839775596, 401038312, 765882590, 25165547, 409081185, 758717854, 29323144, 802113406, 619335348, 670187597, 432992764, 842300893, 451190819, 543777190, 955899663, 167468838, 911305454, 943898810, 429047069, 870305674, 108945073, 375917020, 157236084, 269449257, 509246236, 623982958, 152174729, 214323077, 326196592, 160257757, 347196106, 427685579, 101980047, 148361038, 162482083, 397455571, 656528552, 337869993, 332644833, 951987822, 159756238, 911309883, 445389380, 53561727, 389885080, 892891025, 615089903, 397677586, 826739378, 597832725, 820872628, 92304719, 974260177, 188145987, 496908853, 652170816, 442522275, 135927893, 78123716, 184120078, 184137826, 933891864, 154815712, 976529142, 996029324, 364254469, 439608844, 813275602, 402508956, 93046189, 398679305, 185801436, 212295926, 439035545, 347505648, 983238079, 531951038, 891923807, 374326942, 15383427, 269669111, 253280873, 743917086, 24854336, 937583156, 413136149, 605154802, 676774715, 234441052, 377327301, 116490810, 324311745, 274836385, 459002617, 642516882, 551396111, 999882622, 68450921, 1175391, 993786840, 466454106, 632627337, 677853710, 46385419, 766606653, 554175716, 195409438, 800676227, 998397981, 603943619, 455388781, 796053487, 74531244, 750692148, 527969567, 15571312, 675420846, 547105516, 614303552, 867181126, 118961158, 254387999, 997958504, 141355567, 792788923, 195849658, 139015753, 186702814, 917327862, 657267424, 957504120, 791970733, 391916529, 104634974, 21408071, 882177415, 639306152, 85771927, 145946594, 502658797, 84541966, 6037049, 607214057, 892819474, 381942649, 567045503, 982239196, 536589177, 413343240, 646834247, 952516105, 815609737, 73110969, 32844520, 690559674, 485839152, 270935012, 837605968, 930228322, 648048461, 262494, 59563011, 155651427, 602871424, 271981151, 341302491, 393093646, 347279617, 780965491, 407384524, 371554884, 98929662, 461255312, 978259876, 480744698, 224461704, 435067194, 887615803, 567271624, 803306762, 665097394, 673323885, 836951559, 680647204, 682723396, 558406523, 947807862, 950256734, 674056879, 279729097, 839146595, 98739001, 556215231, 481665717, 693320682, 756390517, 243299690, 657060868, 884378811, 524717438, 452407484, 58830953, 300892817, 237906350, 195229497, 803119766, 655150059, 941488260, 358730238, 371764031, 832355827, 23839303, 207738227, 16373697, 182385232, 380362034, 512306434, 894095701, 567218130, 192638973, 197385856, 242273426, 422060930, 927336265, 882999313, 85163850, 90610765, 33516238, 776923674, 671945613, 767518373, 860734720, 513009892, 472622396, 819011033, 211774526, 855935661, 421296735, 54833051, 1416094, 509163150, 50750086, 339376333, 365461760, 591744996, 442439639, 587598543, 160213172, 34913210, 249568549, 914294680, 894468449, 837470852, 494512780, 560807828, 276349974, 260858355, 544586482, 624530253, 849676050, 35894795, 427983737, 634172670, 273198955, 461621948, 113624766, 205576139, 782246301, 757272230, 842899237, 905693435, 700009439, 591057257, 189436606, 641184817, 587002957, 463527400, 403404023, 402230310, 38604363, 262577276, 405489435, 357904488, 993262554, 865360593, 491408058, 876957195, 311669384, 136847160, 574403364, 180979520, 987273841, 222568585, 699944150, 21794238, 895981287, 680683489, 488202442, 136390356, 536222139, 65700491, 78705970, 554264708, 800700778, 877949733, 936619470, 591954633, 79930816, 232205499, 37931336, 179217025, 305784357, 196364163, 935032428, 552372894, 509841874, 711591431, 996630040, 642916, 198447071, 915387142, 385230643, 426677354, 179661606, 666228106, 281381972, 21429528, 2191402, 295070217, 607871566, 521848641, 275787847, 653311201, 648284498, 967871972, 903775523, 105354847, 569100761, 822251904, 275538852, 817375763, 572291096, 118333166, 608263793, 498534249, 919601492, 471522834, 259782980, 334129544, 456851834, 516704059, 471048481, 126884638, 30081818, 558935040, 583999555, 61163733, 951959983, 878291251, 499057382, 343314917, 994473755, 764749508, 83074152, 255800380, 838086053, 778110962, 998662202, 417771902, 827436248, 445301100, 271108584, 958805228, 913987415, 249598684, 555368814, 126805845, 311277480, 73260345, 925419810, 165617237, 667438706, 773770039, 337277232, 831108292, 454416114, 874855177, 441074449, 906486196, 782284609, 295082215, 190072540, 121569484, 496608056, 642677391, 512247467, 873809389, 786633911, 102873144, 741263564, 769060751, 627628656, 139637891, 741475920, 426381493, 762813552, 394760846, 593805238, 691291458, 513182619, 327390967, 816275818, 462583724, 421047168, 4215878, 21775094, 532928014, 349426192, 970410167, 188617352, 817169677, 688570103, 718024792, 282214936, 317892068, 114773345, 583410508, 739470781, 94259673, 222912358, 738351720, 539132037, 39110660, 313825975, 111631432, 930240694, 799716896, 37829409, 90700055, 765040251, 202940178, 31774394, 843145447, 53574577, 613865045, 170916701, 740673169, 66242574, 447994721, 154332620, 241825115, 221628267, 42426927, 295021729, 187970787, 199337830, 511017251, 609990874, 187911787, 584799814, 306857594, 18098904, 642531198, 779530001, 122663809, 945498313, 358155409, 388933963, 280750065, 453524674, 361745865, 311474775, 21450966, 400540171, 945495115, 466756739, 334373940, 12551322, 831392833, 766253952, 69538398, 858018825, 449528783, 947166417, 49062715, 957112193, 428920544, 723426839, 505318870, 836263110, 861684657, 34751022, 548529387, 108983646, 251654221, 497438877, 378555567, 599603889, 686154590, 201411534, 273011910, 38224192, 778627463, 782893383, 661223512, 246845715, 621158987, 120250031, 38693343, 418418530, 265971666, 734449581, 465850256, 429076292, 552575684, 747114073, 655379359, 978748955, 344425978, 641850087, 878812392, 460399252, 504818791, 939041896, 530873458, 571966528, 947544044, 397643361, 889040140, 827855632, 107802721, 137555469, 375116253, 226267054, 361691180, 630946265, 295389486, 875708036, 321513361, 616054935, 161133240, 61648419, 725988549, 813232915, 652535669, 365046239, 897259434, 959336119, 328361321, 396973885, 71397766, 581117480, 489869662, 460992716, 917971209, 51184201, 690159198, 940767627, 973124740, 265477103, 56609201, 469731120, 967549345, 977409499, 30294318, 796423675, 70708268, 104452036, 121343816, 940465673, 625350932, 797652177, 109187462, 746373726, 705459831, 80487522, 855767497, 942139863, 568910441, 895048574, 700590502, 415404273, 252217289, 94055450, 874235040, 122183486, 968016460, 968614878, 828691592, 254812248, 523490646, 130727131, 459286199, 309967067, 833390190, 220402695, 511094645, 220300093, 268174725, 215845968, 488623676, 389256368, 138136913, 836426446, 275077522, 264633042, 858862295, 915566835, 214320683, 349513725, 86088675, 526247205, 1700558, 893993001, 841981939, 715256704, 140563385, 631019443, 698068815, 231899014, 111686518, 199655514, 540424465, 531214798, 267882778, 784866455, 799347117, 353588410, 971786551, 156430187, 565553809, 881876002, 331880225, 874832854, 511205301, 562763196, 923845265, 330271805, 60322815, 62502709, 122414205, 632820266, 405262634, 425725055, 896024188, 348400951, 470749323, 976671021, 824936190, 939001425, 701367300, 112163366, 933483820, 971535286, 283400354, 233196847, 403610942, 219204911, 71500414, 848345305, 352782827, 898523232, 91443117, 889609617, 565883503, 448977602, 118249615, 808569208, 625833554, 127672920, 784729794, 644993716, 810757642, 512950813, 519619492, 8568259, 887384931, 231353434, 922985111, 747386311, 809094756, 911512113, 759298643, 46077263, 929973819, 499857545, 691351502, 678348757, 536348909, 491359820, 351274326, 789957387, 409753268, 844615730, 91931982, 838875162, 257831421, 386366850, 494492965, 883904471, 388612395, 828568935, 521117244, 434355759, 78218608, 98904475, 91001285, 163101649, 774830410, 825536780, 473268970, 886616187, 44585408, 672761234, 531154845, 971312894, 42201937, 374104877, 217729653, 130610711, 781051513, 637073473, 164601516, 976702498, 79686152, 296832558, 510366757, 927991689, 385958478, 371563135, 786213492, 711428392, 210238491, 13745017, 217103950, 820921427, 217787485, 380017179, 347828973, 439541232, 503462259, 456307830, 416940005, 426211136, 326200475, 177568034, 967198783, 114296696, 957169224, 293349105, 747394558, 154211810, 62410548, 806143565, 52332520, 377130911, 977261652, 435871599, 407508034, 73674120, 139382365, 148706460, 879606220, 797879289, 156369444, 339462214, 523028992, 324632342, 464689503, 197567132, 58905185, 421193436, 796330951, 982358570, 310473646, 265066471, 287988234, 291864971, 315960951, 366067801, 506497255, 547385666, 971493023, 338560962, 122370536, 959160777, 357941253, 9434272, 830153306, 859341283, 937973251, 49370531, 521893201, 903786626, 790399646, 894276400, 903222513, 685799357, 358065184, 181291136, 774917506, 885888507, 224879640, 627205562, 825355570, 293006912, 360617824, 423386310, 722949994, 474239002, 587027227, 73018378, 527152439, 2364845, 300887166, 763586731, 539088422, 915295637, 778943620, 211892412, 261581172, 780254877, 73258932, 833103048, 807528799, 788659340, 745015038, 175249943, 567118538, 848857792, 15861337, 872461336, 554173529, 60780917, 903022017, 730173290, 911355463, 369478815, 135315569, 913642887, 561167237, 414861934, 838117083, 558130852, 888336283, 964857226, 670688658, 603097383, 822444638, 730055488, 890136457, 321344697, 594520233, 614676708, 684584794, 450172507, 759647440, 795300852, 496345923, 23434402, 171265437, 696471192, 484926459, 130474058, 886921116, 978962903, 75304233, 83144210, 632235419, 91052314, 750626304, 305613920, 552055828, 844058303, 638360532, 844024437, 725493496, 152620754, 388529120, 379227534, 537023216, 881387373, 51382411, 179635836, 213610630, 544049700, 986548874, 373327268, 740298135, 487360185, 356946053, 973810594, 575704981, 372815408, 837954179, 888163710, 859437700, 439957356, 379186882, 425572734, 17151186, 471190295, 807741660, 878693668, 530412915, 321590759, 568236824, 250190458, 955609897, 611008215, 92361195, 164029717, 73685446, 66523665, 506137498, 402586347, 818453749, 513730788, 425844930, 581093945, 186626107, 881906527, 572206979, 953820917, 218623244, 667593159, 730230499, 82022003, 276863138, 259288238, 871562639, 309774004, 901574227, 272803967, 986094813, 313719478, 563782200, 550321319, 974926430, 51565918, 680528207, 598928758, 954879289, 454367651, 89217175, 426272620, 528609468, 356339537, 882946011, 541155220, 910403347, 679182531, 789987651, 769268709, 545586281, 260932373, 953901399, 614243501, 265665124, 522158120, 93508886, 217809415, 373690731, 59394985, 322524431, 218070480, 348413551, 190872799, 795741345, 18304232, 30981280, 161186209, 93764158, 742293354, 231016397, 660996306, 879905982, 295603817, 803417050, 800257962, 645705994, 51662926, 489770883, 348800998, 162219632, 306283154, 993959005, 458172277, 292681888, 621100450, 55953959, 277770324, 768080358, 388918303, 508635529, 147204371, 653757323, 608212216, 488155246, 905442431, 269819737, 348135643, 802721705, 727538620, 838869694, 768846325, 72705567, 2917271, 156586064, 558767351, 46099501, 73129814, 201208153, 319867050, 668413395, 149807342, 167762847, 580923731, 51579738, 483011118, 729358604, 878049390, 35995329, 633140146, 961892000, 557871030, 178741044, 700471875, 679023190, 484157946, 698010337, 900991985, 109342881, 874920003, 238435832, 851197205, 315562463, 618815599, 107603440, 916956036, 740141927, 114643909, 568596525, 134475127, 449056364, 382120449, 979201285, 150289259, 170928417, 459364641, 385272422, 176618349, 901332432, 251464096, 606114608, 78948602, 675737703, 586291298, 318184509, 201557694, 627171010, 981175079, 942875884, 79112814, 11126652, 220746187, 860661751, 535105527, 285652218, 924014055, 886913577, 651521984, 487467879, 860854605, 208189453, 514330753, 282248253, 346498262, 899115750, 964797665, 80112349, 56718332, 241434680, 390615064, 15992928, 768775700, 771453997, 730314942, 187806076, 127859046, 579982129, 999035537, 284408078, 486947377, 265189729, 245302679, 582234386, 152215567, 93626834, 20140945, 253066060, 781417035, 722912618, 510676540, 700434291, 265335267, 80019467, 138137745, 786921628, 855442313, 545371378, 966986296, 43926316, 965220069, 834131258, 694586307, 955270213, 64571830, 428858967, 714250637, 875937365, 721103773, 743266500, 410974686, 841738982, 721718392, 192532226, 281722487, 980628386, 308122101, 346455837, 974901010, 871585719, 403486615, 288011484, 602675127, 502159124, 428156069, 161132354, 281841246, 108137019, 799048156, 181804317, 56058428, 760466481, 863672379, 570422177, 535651742, 940764013, 73742745, 46691152, 767431245, 75782565, 580992610, 235798661, 528362502, 361433951, 810916148, 503718636, 147124920, 784609103, 250773233, 358579612, 136893555, 290762904, 539894506, 356827242, 468478938, 234308605, 764451582, 414990687, 359103975, 607817419, 828868724, 625332183, 746125268, 847896215, 249649446, 738693481, 307223826, 900080935, 371915368, 19934399, 459081657, 122924506, 981916796, 779833178, 972858689, 666949399, 358396149, 985306500, 642696770, 702670415, 159745706, 907509139, 773432631, 38103458, 239809570, 851530440, 405843614, 251018626, 661928953, 926050372, 957056330, 959840395, 323285397, 924207971, 992726456, 138495836, 452156222, 67332393, 765743835, 111967099, 342543530, 40394068, 441185389, 838389071, 818485865, 627680886, 30537274, 955600892, 916053492, 27102407, 823045200, 826881383, 774023529, 250054422, 494135371, 695497413, 275728531, 222546046, 423641123, 422697817, 870331817, 129090800, 710165049, 314261885, 85657099, 278457417, 631018571, 527536213, 167710262, 297061627, 595658186, 906356203, 996739817, 774718967, 569092555, 917124190, 985872029, 37854163, 597885816, 76105975, 425232593, 114620617, 496361983, 845543834, 213834730, 772362164, 940157357, 457095306, 875201413, 949362426, 619157958, 983650259, 918155649, 414114875, 446099734, 229926358, 618805821, 681785499, 680434040, 303063948, 518379601, 23957944, 935436813, 400803950, 727262787, 855642325, 426244346, 244149962, 899581461, 416922029, 15130327, 954137168, 196215227, 216069713, 285011004, 716815089, 759246963, 141993273, 603497766, 689237214, 198417373, 630592492, 709464828, 387786543, 373690973, 388099666, 601225061, 242444525, 79697603, 850145602, 919992347, 473272416, 129208382, 669091583, 199905613, 165914039, 950787160, 456444556, 298768092, 891239943, 871414129, 873923941, 217453204, 934666286, 730565127, 748390764, 904593166, 671477325, 751173496, 31455102, 913359282, 563702548, 763312441, 636497600, 443242973, 407868989, 801959305, 357268029, 785182063, 776929735, 245163613, 53463168, 729059770, 844784893, 982897964, 916042548, 684234056, 750295903, 454213989, 958557996, 704123155, 124773408, 747789678, 624361752, 203383649, 266160873, 532074552, 866449339, 196304148, 695132716, 877603942, 125601734, 349087002, 164475724, 738651033, 673671540, 146685989, 336102161, 817918988, 759423881, 898490938, 267782873, 349207092, 409959242, 174903716, 875233705, 644587668, 107258446, 807970494, 575098468, 567864876, 814860164, 812145023, 73361276, 128302090, 582760503, 64362997, 293161538, 420446532, 753739370, 749024856, 440921868, 695372138, 530355028, 137157144, 299698708, 304762186, 266852379, 259997081, 335960596, 295651483, 75748580, 813995633, 624583780, 458780768, 704058007, 967918318, 976948501, 345235104, 580762717, 887268490, 621596015, 910128015, 501969879, 334591172, 56951730, 486417821, 879739185, 228912463, 507461977, 268337507, 822948650, 88344354, 292151959, 579711582, 645640875, 522205658, 69453717, 842341659, 839432720, 858159750, 962943188, 658785855, 791738287, 460820562, 442121645, 833144297, 915682199, 157243110, 698488400, 757297069, 969228484, 634692983, 662470068, 766095008, 99762503, 568209873, 873156079, 966679164, 274972511, 999935604, 421388279, 284330122, 364007550, 148652805, 690492643, 84045000, 393911307, 147335081, 55893709, 779866591, 513227205, 802840675, 345469386, 849948576, 67455147, 793223988, 440569200, 414141978, 192138225, 694196607, 809634686, 226721255, 6937929, 477953755, 320585254, 584216582, 381489894, 504128766, 142182045, 293374683, 75852730, 765165325, 173790671, 24148504, 381907510, 738301828, 77301592, 263544094, 600167459, 441423330, 472756510, 438669301, 700297566, 332243535, 838404631, 605435919, 297760252, 871143030, 760575336, 749352903, 283154789, 530354052, 597474318, 768482466, 457816017, 785962416, 512252352, 739598308, 761673790, 211464485, 364803929, 659785789, 216530272, 308039663, 72328488, 656539167, 515927222, 275505151, 476315414, 438508579, 262836591, 889507418, 21718498, 170484470, 422706660, 234801896, 252382185, 509700794, 56092078, 783411558, 471942916, 488673025, 306752017, 495392329, 933541945, 995722700, 81166867, 94300972, 416010790, 491799027, 486566568, 333195311, 788569734, 213384988, 628689339, 362965631, 209614483, 736342462, 61918932, 42407847, 387070428, 684670516, 708537529, 691427860, 972576235, 460882302, 135671169, 678579303, 526400524, 82332336, 228285408, 421089488, 530519348, 35126611, 799392197, 385903608, 165481988, 347953446, 923532436, 433558842, 37265955, 945262965, 587945162, 543777200, 384142225, 214670210, 234138698, 260372135, 11357265, 675280704, 888239589, 146709428, 727397867, 356139670, 296787824, 432853592, 214221713, 581773141, 689508395, 882785628, 897365028, 965669867, 618288713, 784103326, 987054639, 691301706, 280974678, 467670, 567202589, 657835403, 225668959, 231794114, 470934033, 463418767, 892930146, 488101996, 113206014, 532335697, 330093615, 833839900, 117267457, 140035313, 680525048, 668786912, 357856772, 713191217, 889032634, 715732963, 646389460, 776160849, 169670459, 991672330, 700603581, 608333509, 233284725, 322146922, 983995544, 856789200, 227702190, 170691724, 470785192, 56302081, 956479399, 695575446, 523382368, 161377338, 78306686, 384039744, 76977749, 876297715, 11932850, 643114007, 702849735, 260061758, 573509928, 283021639, 369423428, 153846276, 882015393, 109476902, 700993311, 428018306, 874542293, 945778675, 912017653, 471026903, 28636787, 711856860, 488240871, 303220911, 251221550, 819756752, 236214049, 326478346, 281787335, 203751404, 18215784, 778628237, 181827839, 833223129, 686511336, 889260557, 729991206, 594757393, 442206721, 273864083, 384515331, 498547703, 43893904, 369354027, 276435734, 638831430, 925423903, 169244447, 713571854, 299793714, 983123116, 6137572, 309244051, 947922421, 524362359, 937839278, 575359983, 232557369, 549173814, 605540478, 717738697, 573000968, 278461952, 779167530, 908713614, 254373222, 69042323, 446070331, 152604039, 211148618, 756713835, 225057605, 805558514, 384757371, 144290779, 130318371, 265027278, 455143480, 45266602, 775642009, 963732204, 654266367, 970497697, 115382794, 696780322, 398234479, 717278431, 39511188, 605472602, 383930491, 251295223, 953190711, 224443665, 129139683, 789728038, 34551920, 181054167, 440385937, 504523438, 110423967, 70296556, 560697036, 153648088, 63465732, 276720061, 561743072, 783292620, 433499438, 813231545, 217668702, 222015669, 799037663, 532469458, 67418169, 112908703, 979712956, 498170560, 889325879, 586355132, 545873908, 923848961, 41556268, 16719790, 765934070, 481138422, 302165970, 907445460, 433241265, 361828344, 848113380, 10725932, 135348035, 300143467, 977403649, 211486864, 996581724, 857308411, 30799664, 592384025, 118291046, 862606361, 813197625, 154198508, 521000208, 63418145, 316042241, 905265785, 615144761, 399982377, 221692047, 146591014, 996230327, 140733252, 669617502, 436236718, 85439385, 264640272, 294214873, 473522066, 349159543, 978310929, 587017871, 157116111, 244805985, 713087973, 604138936, 917408935, 767545133, 735962944, 501309183, 869698117, 374047213, 284729114, 274950670, 184467706, 632518228, 921051614, 908329701, 127291830, 744000609, 783609542, 317289750, 563583281, 247110221, 506899775, 91856877, 968426730, 254507513, 874871206, 575635127, 57435169, 746994297, 270199279, 586078303, 534321245, 89231316, 243409389, 984872695, 602875687, 967193641, 504410790, 324320432, 304800220, 10521796, 884694599, 676495875, 586838365, 509790815, 157561197, 774167141, 491513562, 792482408, 394148935, 48076889, 275628373, 379638863, 135909169, 872322060, 56542370, 793881914, 479648044, 882974572, 936470318, 698841280, 679338441, 280697003, 242669991, 51860054, 19311647, 544563396, 645639294, 817836345, 291739587, 137774091, 664759485, 207205472, 785646140, 472371166, 814061619, 738607318, 798721454, 562874834, 90637655, 482896215, 180230722, 670725360, 825790750, 750162303, 76458241, 212563156, 81578370, 730833567, 154525275, 710887944, 783760398, 135609983, 822847829, 959137681, 896091487, 285429755, 878941490, 991946966, 939828831, 675059043, 240827909, 797730460, 491094367, 484390208, 586788685, 519797221, 803029456, 120049921, 331729630, 397300202, 468600471, 828310349, 638126999, 512407676, 735815049, 127262936, 360343240, 7214375, 473778287, 235353321, 701002453, 715479638, 498559607, 269250768, 17435562, 251019353, 426105364, 347104312, 240219577, 628274267, 757358261, 597600425, 296858682, 666252098, 695389094, 293106674, 415656122, 665800058, 743289643, 382080907, 184920043, 232781552, 28659416, 279425793, 751073673, 272752149, 113606357, 464422580, 332790942, 769105564, 66227382, 655754767, 653635143, 883077510, 279612181, 332563529, 347448883, 297285810, 726023510, 843570161, 298154159, 470796295, 327308944, 113299238, 420094140, 621563499, 732594414, 527424672, 189955811, 88601537, 626969880, 269283967, 740152930, 353906394, 57253165, 944317805, 620598263, 683428048, 36852308, 871862030, 678348288, 310407690, 953562020, 227682529, 572993318, 82430002, 969777815, 554836885, 4873418, 683126130, 194441563, 745216479, 960711940, 693571409, 64208011, 945689679, 299701949, 697680525, 213296897, 893596671, 400586138, 41173684, 922268205, 958418171, 488821749, 36529135, 540106555, 163305597, 888193507, 72802106, 40085557, 257306459, 965204803, 18789935, 39650900, 818242382, 206953651, 505422039, 828151969, 938142662, 290115927, 673156181, 41602560, 470608759, 826550194, 478289274, 231916019, 375935944, 464624252, 203862981, 654765651, 475202611, 357143587, 703460680, 922164684, 797317963, 798629850, 657656608, 216063806, 953940252, 785202388, 609890670, 6070761, 590037797, 261732383, 728031156, 241277287, 320810213, 46201245, 182836601, 754966506, 912477679, 712052485, 718347636, 402664349, 280061965, 390476070, 112291771, 409647473, 681680536, 571240716, 488320887, 330501527, 423725809, 307436782, 667885754, 875599826, 868342507, 739163591, 867478879, 377571395, 462261459, 910035125, 340881623, 821972217, 973002933, 587897458, 95223618, 213731211, 625519532, 702748071, 763165112, 117498976, 280741451, 911555769, 291782621, 678441732, 78414036, 218754310, 503291170, 181903682, 527431509, 341541936, 824366369, 24087331, 403096850, 835643270, 356380095, 137038296, 379940473, 641028920, 267463118, 159922152, 580147292, 245576907, 985289324, 825503700, 75333101, 324344277, 107539347, 735471268, 983095077, 633527988, 459403618, 681886098, 119994641, 442437245, 39091298, 953624636, 422982958, 708465168, 78935680, 314924579, 277911085, 923660822, 22714294, 611620744, 963727647, 476973023, 330324835, 478335574, 72355991, 544175411, 964656943, 716739422, 552686247, 592826379, 808023158, 259666800, 347002052, 984521898, 814791516, 344934666, 719828517, 469381415, 884908741, 200180287, 423779896, 41633238, 339758222, 560420792, 859462956, 336479717, 433063522, 442090958, 204755917, 822941177, 840693411, 978598224, 639366865, 977983683, 925515878, 678739322, 75207901, 309177706, 830157283, 92747617, 246131952, 451185842, 670662922, 285923176, 947753495, 654538696, 40335675, 159488505, 523544064, 977203358, 192587577, 265007352, 779596339, 320103439, 961678983, 541360377, 597394538, 54730152, 591734791, 217078181, 996935610, 814574403, 924288531, 298744802, 711774921, 28039273, 280372620, 820034597, 980882203, 773310834, 136014992, 171449411, 41741132, 730813893, 481589193, 570447133, 991236757, 692966948, 65460580, 184658084, 171501287, 815773176, 825117500, 931547129, 387941744, 908458727, 487557708, 76385657, 827276764, 205478515, 414272069, 645950877, 876208898, 569961692, 757503587, 877666335, 884968386, 245737184, 323677992, 317195208, 889574872, 384145786, 930587285, 530919159, 813408878, 927773635, 895141725, 277900575, 264735404, 933186467, 57780251, 80114404, 659834834, 13855452, 794169414, 123524600, 105237100, 497059383, 119462424, 141899200, 96046910, 677566679, 482489122, 917795144, 55577609, 558261741, 942262253, 669596670, 5533979, 231193661, 938720988, 125715452, 330012465, 561431792, 602849400, 29398540, 88364399, 916987529, 988017263, 595622798, 663106284, 717020886, 946344088, 401886877, 91464655, 491778803, 585268694, 767167093, 352231945, 793528015, 700821486, 168737843, 728863788, 351355858, 642892016, 934782279, 780056996, 189398410, 640479396, 275680174, 44959867, 402603064, 939592466, 484707834, 720999673, 484138750, 311007072, 650497665, 477425697, 279917251, 793053232, 347000982, 459462237, 624383496, 840732695, 829981890, 812798015, 834549047, 904859071, 861079068, 349014573, 728195373, 940381353, 161509916, 98629444, 65919379, 931746946, 860873110, 51745688, 392710988, 767153449, 376345771, 780480140, 341017321, 631497010, 426799303, 316555344, 935706066, 740367913, 878456862, 290369023, 341149647, 108018899, 704391065, 946613030, 888698675, 625735641, 705230057, 682993926, 917724882, 267857696, 533789043, 854033932, 902228283, 961793006, 388168134, 408216414, 320802404, 624710290, 625665173, 115125988, 86937866, 422682070, 133614559, 108947940, 59509483, 672451663, 846420237, 68051314, 494655172, 524261551, 371199610, 819169902, 947108113, 313958922, 604803634, 471389148, 427535663, 895367576, 320165536, 78619523, 699553733, 523981013, 468048896, 806425190, 178042814, 820486486, 655703874, 511308259, 267289904, 530097822, 4752455, 633073694, 893995653, 255335811, 23733245, 234557039])) + + +-- Grouping test cases +tests :: Test +tests = TestList [TestLabel "Test1" test1, TestLabel "Test2" test2, TestLabel "Test3" test3, TestLabel "Test4" test4, TestLabel "Test5" test5, TestLabel "Test6" test6, TestLabel "Test7" test7] + +-- Running the tests +main :: IO Counts +main = runTestTT tests