CERI2018I - Check factorization

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Your friend build a fantastic factoring algorithm, and challenge you to check his results.

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 $N \pmod m$.

Input

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

Each test is on 2 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 $N \pmod m$.

Example

Input:
3
0 1000
17,1
2 100
2,1 5,1 7,2
1 1000
3,1 1000000007,1
Output:
17
90
21

Explanation

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

For the second test case, $N = 2^1 \times 5^1 \times 7^2 = 490$, and $N \pmod {100} = 90$.

For the third test case, $N = 3^1\times 1000000007^1 = 3000000021$, and $N \pmod {1000} = 21$.


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[Rampage] Blue.Mary: 2018-05-08 08:35:25

Please check the input file. At least one test case (including sample given above) doesn't satiesfy "the second line contains 2(k+1) integers".
=(Francky)=> Done, many thanks for your catch.

Last edit: 2018-05-08 10:57:54

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