Question

Lazy Student
Problem Description
There is a test of Algorithms. Teacher provides a question bank consisting of N questions and guarantees all the questions in the test will be from this question bank. Due to lack of time and his laziness, Codu could only practice M questions. There are T questions in a question paper selected randomly. Passing criteria is solving at least 1 of the T problems. Codu can't solve the question he didn't practice. What is the probability that Codu will pass the test?

Constraints
0 < T <= 10000

0 < N, T <= 1000

0 <= M <= 1000

M,T <= N

Input Format
First line contains single integer T denoting the number of test cases.

First line of each test case contains 3 integers separated by space denoting N, T, and M.

Output
For each test case, print a single integer.

If probability is p/q where p & q are co-prime, print (p*mulInv(q)) modulo 1000000007, where mulInv(x) is multiplicative inverse of x under modulo 1000000007.

Test Case

Explanation
Example 1

Input

1

4 2 1

Output

500000004

Explanation

The probability is ½. So output is 500000004.

Answer 1

Language used: Python 3.0

Program:

import math

n=int(input())

for i in range(n):

   N,T,M = map(int,input().split(' '))

   probability=(1-(math.factorial(N-M))/(math.factorial(T)*math.factorial(N-M)))

   #taking in the values of p,q from probability as of p/q

   p,q=probability.as_integer_ratio()

   #creating the multiple inverse of q

   print(pow(q,1000000007-2,1000000007))

Input:

1

4 2 1

Output:

500000004

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