A DNA-analysis tool scans a string s of n lowercase letters using a sliding window of fixed length k (1 ≤ k ≤ n). It looks at all n - k + 1 contiguous windows of length k. Two windows are considered the same class if they contain exactly the same multiset of characters (the same letters with the same counts — order does not matter; that is, one window is a rearrangement of the other).
Count the number of distinct classes among all the windows.
Input format
Line 1: two space-separated integers n and k.
Line 2: the string s, of length n, consisting of lowercase English letters.
Output format
A single integer: the number of distinct character-multiset classes among all n - k + 1 windows of length k.
Constraints
- 1 ≤ k ≤ n ≤ 2000
sconsists only of lowercase English letters.