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?
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.
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.
0 < T <= 10000
0 < N, T <= 1000
0 <= M <= 1000
M,T <= N
Sample Input and Output
4 2 1
The probability is 1⁄2. So output is 500000004.
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