360_C. Levko and Strings
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].
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).
A substring s[i..j] of string s = s1s2... sn is string sisi + 1... sj.
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.
Input
The first line contains two integers n and k (1 ≤ n ≤ 2000, 0 ≤ k ≤ 2000).
The second line contains a non-empty string s of length n. String s consists only of lowercase English letters.
Output
Print a single number — the answer to the problem modulo 1000000007 (109 + 7).
Examples
Input
2 2 yz
Output
26
Input
2 3 yx
Output
2
Input
4 7 abcd
Output
21962
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
Task
Solve this competitive programming problem. Provide a complete solution that handles all the given constraints and edge cases.