| # chsparr |
|
|
| ## Problem Description |
| Chef has a an array A consisting of N elements. He wants to add some elements into the array as per the below mentioned process. |
| After each minute, Chef iterates over the array in order from left to right, and takes every two neighbouring pair of elements, say x and y, he adds a new element x + y in the middle of elements x and y. |
| For example, if initial array A = {1, 6, 9}. |
|
|
| After first minute, the array A will be equal to {1, 7, 6, 15, 9}. Please note that the elements shown in the bold font are the newly added elements during first minute. As you can observe that 7 = 1 + 6, and 15 = 6 + 9. |
| After second minute, the array will be {1, 8, 7, 13, 6, 21, 15, 24, 9}. Once again, elements added during the second minute, are shown in bold. |
|
|
| Chef wants to know the sum of elements between x^th and y^th positions in the array A (i.e. Ax + Ax + 1 + ... + Ay) after m minutes. As the answer could be large, output it modulo 10^9+7 (1000000007). Please note that we use 1 based indexing in the problem. |
|
|
| Input |
|
|
| The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows. |
| The first line of each test case contains four space-separated integers N, m, x, y denoting the number of elements in the array A in the beginning, amount of minutes and range for finding sum. |
| The second line contains N space-separated integers A1, A2, ..., AN denoting the array A in the beginning. |
|
|
|
|
| Output |
|
|
| For each test case, output a single line containing an integer corresponding to the sum of elements between x^th and y^th positions in the array A after m minutes modulo 10^9+7. |
|
|
|
|
| Constraints |
|
|
| 1 ≤ T ≤ 10 |
| 1 ≤ N ≤ 10^5 |
| 1 ≤ Ai ≤ 10^3 |
| 1 ≤ m ≤ 30 |
| 1 ≤ x ≤ y ≤ size of the array A (|A|) after m minutes |
|
|
|
|
| Example |
| Input:
|
| 2
|
| 3 1 1 5
|
| 1 6 9
|
| 3 2 6 7
|
| 1 6 9
|
|
|
| Output:
|
| 38
|
| 36
|
|
|
|
|
| Explanation |
| Example case 1. After the first minute A = {1, 7, 6, 15, 9} and sum of all elements will be 38. |
| Example case 2. After the second minute the array A will be {1, 8, 7, 13, 6, 21, 15, 24, 9} and sum of elements between 6^th and 7^th equals to 21 + 15 = 36. |
|
|
| ## Contest Information |
| - **Contest ID**: 0 |
| - **Problem Index**: |
| - **Points**: 0.0 |
| - **Rating**: 0 |
| - **Tags**: None |
| - **Time Limit**: None seconds |
| - **Memory Limit**: 0 bytes |
|
|
| ## Task |
| Solve this competitive programming problem. Provide a complete solution that handles all the given constraints and edge cases. |
