Solve the programming task below in a Python markdown code block.
Watson asks Sherlock: 

Given a string S of N 0's and M 1's, how many unique permutations of this string start with 1?   

Help Sherlock by printing the answer modulo (10^{9}+7).   

Input Format 

First line contains T, the number of test cases. 

Each test case consists of N and M separated by a space.

Output Format 

For each test case, print the answer modulo (10^{9}+7).

Constraints 

1 ≤ T ≤ 200 

1 ≤ N,M ≤ 1000  

Sample Input   

2
1 1
2 3

Sample Output      

1
6

Explanation 

Test1: Out of all unique permutations ie. 01 and 10, only second permutation satisfies. Hence, output is 1. 

Test2: Out of all unique permutations ie. 00111 01011 01101 01110 10011 10101 10110 11001 11010 11100, only 10011 10101 10110 11001 11010 11100 satisfy. Hence, output is 6.