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
#include <bits/stdc++.h>
#pragma comment(linker, "/STACK:36777216")
using namespace std;
int n, m;
long long f[2005][2005], sum[2005][2005];
char ch[2005];
int main() {
  cin >> n >> m;
  scanf(" %s", ch + 1);
  f[0][0] = 1;
  for (int i = 0; i <= n; i++) sum[i][0] = 1;
  for (int i = 1; i <= n; i++)
    for (int j = 0; j <= m; j++) {
      if (i != n)
        f[i][j] += sum[i - 1][j] * (ch[i] - 'a'), f[i][j] %= 1000000007;
      if (i == n)
        f[i][j] += sum[i - 1][j] * (ch[i] - 'a' + 1), f[i][j] %= 1000000007;
      for (int k = 0; j - (n - i + 1) * (k + 1) >= 0 && i - 1 - k >= 0; k++) {
        f[i][j] += f[i - 1 - k][j - (n - i + 1) * (k + 1)] * ('z' - ch[i]);
        f[i][j] %= 1000000007;
      }
      sum[i][j] = sum[i - 1][j] + f[i][j];
      sum[i][j] %= 1000000007;
    }
  cout << f[n][m] << endl;
}
