Levko and Strings
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.
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.
Print a single number — the answer to the problem modulo 1000000007 (109 + 7).
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).
Samples
2 2
yz
26
2 3
yx
2
4 7
abcd
21962