409416: GYM103535 D Link with Balls

There were a lot of balls in the factory of Ball Illusion Technology(BIT). Link, a boy, went there to get some balls, but suddenly, he found that there were too many ways to get balls.

There are $$$2n$$$ buckets in the factory. Link may get $$$kx$$$ balls from the $$$2x-1^{th}$$$ bucket, where $$$k$$$ is a non-negtive integer. He may also get at most $$$x$$$ balls from the $$$2x^{th}$$$ bucket.

Link wanted to get $$$m$$$ balls, and he wondered how many ways there were to take out exactly $$$m$$$ balls. While Link is calculating the answer, he wants you to calculate it as well, and you should output the answer modulo $$$10^9+7$$$.

The input consists of multiple test cases.

The first line contains an integer $$$T$$$ ($$$1 \leq T \leq 10^5$$$) – the number of test cases.

Each test case contains two integers $$$n$$$ and $$$m$$$($$$1 \leq n,m \leq 10^6$$$).

For each test case, print the answer modulo $$$10^9+7$$$ in a single line.

4
1 1
2 2
3 3
1000000 1000000

2
6
20
192151600