Levko and Strings

1000ms

262144K

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... s_n is string s_is_{i + 1}... s_j.

String x = x₁x₂... x_p is lexicographically larger than string y = y₁y₂... y_p, if there is such number r (r < p), that x₁ = y₁, x₂ = y₂, ... , x_r = y_r and x_{r + 1} > y_{r + 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).

Sample Input:

2 2
yz

Sample Output:

Sample Input:

2 3
yx

Sample Output:

Sample Input:

4 7
abcd

Sample Output:

Informação

Provedor Codeforces

Código CF360C