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