## BLUEEQ2 - Help Blue Mary Please! (Act II)

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Today Mary's math homework is to solve an equation. She knows all ki and pi, and 1<=xi<=M. All xi must be integers. She must work out the number of different solutions of this equation this day.Can you give her a hand?

### Input

There is a single integer T in the very first line of the input denoted the number of tests.T blocks follow.

For each test case:

The first line contains a single integer n(n<=6).The second line contains a single integer m(m<=150).n lines follow,each contains two space-separated integers ki and pi, i=1,2,...,n. All pi are positive. ### Output

For each test case output a single line ,which contains a single integer - the answer.You may assume this number is less than 2^31.

### Example

```Input:
1
3
150
1 2
-1 2
1 2

Output:
178
```

Warning: The time limit is very strict for this problem.

hide comments fire_heart: 2016-08-20 14:30:01 p is not larger than 31 :)

 Added by: Fudan University Problem Setters Date: 2007-04-01 Time limit: 1s Source limit: 50000B Memory limit: 1536MB Cluster: Cube (Intel G860) Languages: All except: C99 ERL GOSU JS-RHINO Resource: Chinese National Olympiad in Informatics 2001,Day 2; translated by Blue Mary