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 = s 1 s 2... s n is string s i s i + 1... s j . String x = x 1 x 2... x p is lexicographically larger than string y = y 1 y 2... y p , if there is such number r ( r p ), that x 1 = y 1, x 2 = y 2, ... , x r = y r and x r + 1 y r + 1 . The string characters are compared by their ASCII codes.

输入描述:

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.

输出描述:

Print a single number — the answer to the problem modulo 1000000007(109 + 7).