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ZOJ Problem Set - 1570
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Time Limit: 2 Seconds      Memory Limit: 65536 KB

There are n! permutations for 0, 1, 2, ..., n-1. For instance n=3 we have 6 sequences 012, 021, 102, 120, 201, 210. We put the sequence in an array a. Now it's your task to tell how many of the n! sequences satisfy

(a[a[b[0]]]*b[0]+a[a[b[1]]]*b[1]+a[a[b[2]]]*b[2]+a[a[b[3]]]*b[3])%n==k


Input

There are multiple tests, terminated with end of file.

Each line contains six integers, in the order n, k, b[0], b[1], b[2], b[3].

4 <= n < 12, 0 <= k < n, 0 <= b[i] < n.


Output

One number for each test - the number of sequences that satisfies the equation.


Sample Input

4 0 3 2 1 0
5 2 1 2 3 4


Sample Output

4
40



Author: ZHANG, Zheng
Source: ZOJ Monthly, March 2003
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