## CERI2018J - Euler Totient of factorized integer

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The goal of the problem is to compute the Euler totient function $\varphi(N)$ for some integers $N$.

Assume that number $N = p_0^{e_0} \times p_1^{e_1} \times \cdots p_k^{e_k}$, where $p_i$ are prime numbers, and $e_i$ are positive intergers.

You will be given a prime factorization of $N$, you'll have to print $\varphi(N) \pmod m$.

### Input

The first line of the input consist of a single integer number $t$ which determines the number of tests.

Each test is on two separate lines.

In each test,

• on the first line, there is two integer numbers $k$, and $m$.
• on the second line, there is $2(k+1)$ integer numbers $p_i$ and $e_i$, with $p_i$ a prime number.

#### Constraints

• $0 < t \leqslant 256$ ;
• $0 \leqslant k \leqslant 1000$ ;
• $0 < m \leqslant 2\times10^9$ ;
• $1 < p_i < 2\times10^9$, a prime number ;
• $0 < e_i < 2\times10^9$.

### Output

For each test case, print $\varphi(N) \pmod m$.

### Example

Input:
3
0 1000
17,1
2 100
2,1 5,1 7,2
1 1000
3,1 1000000007,1
Output:
16
68
12


#### Explanation

For the first test case, $N = 17^1$, and $\varphi(N) \pmod {1000} = 16$.

For the second test case, $N = 2^1 \times 5^1 \times 7^2 = 490$, and $\varphi(N) \pmod {100} = 68$.

For the third test case, $N = 3^1\times 1000000007^1 = 3000000021$, and $\varphi(N) \pmod {1000} = 12$.

 Added by: Francky Date: 2018-05-08 Time limit: 1s-3s Source limit: 50000B Memory limit: 1536MB Cluster: Cube (Intel G860) Languages: All