Too Simple
Description:
Rhason Cheung had a simple problem, and asked Teacher Mai for help. But Teacher Mai thought this problem was too simple, sometimes naive. So she ask you for help.
Teacher Mai has m functions f1,f2,⋯,fm:{1,2,⋯,n}→{1,2,⋯,n}(that means for all x∈{1,2,⋯,n},f(x)∈{1,2,⋯,n}). But Rhason only knows some of these functions, and others are unknown.
She wants to know how many different function series f1,f2,⋯,fm there are that for every i(1≤i≤n),f1(f2(⋯fm(i)))=i. Two function series f1,f2,⋯,fm and g1,g2,⋯,gm are considered different if and only if there exist i(1≤i≤m),j(1≤j≤n),fi(j)≠gi(j).
Input:
For each test case, the first lines contains two numbers n,m(1≤n,m≤100).
The following are m lines. In i-th line, there is one number −1 or n space-separated numbers.
If there is only one number −1, the function fi is unknown. Otherwise the j-th number in the i-th line means fi(j).
The following are m lines. In i-th line, there is one number −1 or n space-separated numbers.
If there is only one number −1, the function fi is unknown. Otherwise the j-th number in the i-th line means fi(j).
Output:
For each test case print the answer modulo 109+7.
Sample Input:
3 3 1 2 3 -1 3 2 1
Sample Output:
1
Hint:
The order in the function series is determined. What she can do is to assign the values to the unknown functions.
Source:
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