HDU 多校1.7

Function

Time Limit: 4000/2000 MS (Java/Others)    Memory Limit: 131072/131072 K (Java/Others)
Total Submission(s): 0    Accepted Submission(s): 0

Problem Description

You are given a permutation a from 0 to n−1 and a permutation b from 0 to m−1 .

Define that the domain of function f is the set of integers from 0 to n−1 , and the range of it is the set of integers from 0 to m−1 .

Please calculate the quantity of different functions f satisfying that f(i)=bf(ai) for each i from 0 to n−1 .

Two functions are different if and only if there exists at least one integer from 0 to n−1 mapped into different integers in these two functions.

The answer may be too large, so please output it in modulo 109+7 .

 

Input

The input contains multiple test cases.

For each case:

The first line contains two numbers n, m . (1≤n≤100000,1≤m≤100000)

The second line contains n numbers, ranged from 0 to n−1 , the i -th number of which represents ai−1 .

The third line contains m numbers, ranged from 0 to m−1 , the i -th number of which represents bi−1 .

It is guaranteed that ∑n≤106, ∑m≤106 .

 

Output

For each test case, output "Case #x : y " in one line (without quotes), where x indicates the case number starting from 1 and y denotes the answer of corresponding case.

 

Sample Input

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

 

Sample Output

Case #1: 4 Case #2: 4