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).