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  1. Prepare
  2. Mathematics
  3. Fundamentals
  4. Sherlock and Permutations

Sherlock and Permutations

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 (109+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 (109+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.