| # 360_C. Levko and Strings |
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| ## Problem Description |
| Levko loves strings of length n, consisting of lowercase English letters, very much. He has one such string s. For each string t of length n, Levko defines its beauty relative to s as the number of pairs of indexes i, j (1 ≤ i ≤ j ≤ n), such that substring t[i..j] is lexicographically larger than substring s[i..j]. |
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| The boy wondered how many strings t are there, such that their beauty relative to s equals exactly k. Help him, find the remainder after division this number by 1000000007 (109 + 7). |
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| A substring s[i..j] of string s = s1s2... sn is string sisi + 1... sj. |
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| String x = x1x2... xp is lexicographically larger than string y = y1y2... yp, if there is such number r (r < p), that x1 = y1, x2 = y2, ... , xr = yr and xr + 1 > yr + 1. The string characters are compared by their ASCII codes. |
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| Input |
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| The first line contains two integers n and k (1 ≤ n ≤ 2000, 0 ≤ k ≤ 2000). |
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| The second line contains a non-empty string s of length n. String s consists only of lowercase English letters. |
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| Output |
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| Print a single number — the answer to the problem modulo 1000000007 (109 + 7). |
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| Examples |
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| Input |
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| 2 2 |
| yz |
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| Output |
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| 26 |
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| Input |
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| 2 3 |
| yx |
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| Output |
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| 2 |
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| Input |
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| 4 7 |
| abcd |
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| Output |
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| 21962 |
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| ## Contest Information |
| - **Contest ID**: 360 |
| - **Problem Index**: C |
| - **Points**: 1500.0 |
| - **Rating**: 2500 |
| - **Tags**: combinatorics, dp |
| - **Time Limit**: {'seconds': 1, 'nanos': 0} seconds |
| - **Memory Limit**: 256000000 bytes |
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| ## Task |
| Solve this competitive programming problem. Provide a complete solution that handles all the given constraints and edge cases. |
