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.

Solution in Python#

#!/bin/python3

import os
import sys


def facdiv(m,n):
    p = 1
    for i in range(m+1,n+1):
        p*=i
    return p

def solve(n, m):
    m-=1
    nums=[n,m]
    nums.sort()
    n,m = nums
    answer = facdiv(m,m+n) //facdiv(0,n)
    return int(answer%(10**9+7))

for _ in range(int(input())):
    n,m = list(map(int,input().split()))
    print(solve(n,m))