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

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 2Output:178

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

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 |