Arrange-II

import functools
class Solution:
    # @param A : string
    # @param B : integer
    # @return an integer
    @functools.lru_cache(None)
    def dfs(self,i,d,A) :
        n=len(A)
        if d==1:
            w,b=0,0
            for idx in range(i,n):
                w+=A[idx]=='W'
            b = n-i-w
            return w*b

        res,w,b= float('inf'), 0,0
        for j in range(i,n):
            w+=A[j]=='W'
            b+=A[j]=='B'
            res = min(res,w*b+self.dfs(j+1,d-1,A))
        return res

    def arrange(self, A, B):
        n = len(A)
        if n < B:
            return -1
        return self.dfs(0,B,A)