You are given three integers \(Z, O, K\).

Your task is to determine the number of distinct sequences of length \(Z + O\) that contains exactly \(Z\) zeroes and \(O\) ones. Also, the length of longest non-decreasing subsequence in the sequence is of length \(\ge K\).

Note

Two sequences are said to be distinct if there exists at least one index where the value of element present is different in both sequences.
A non-decreasing subsequence of \(a\) is a sequence of integers \(a_{p_1}, a_{p_2}, ... , a_{p_k}\) where \(p_1 < p_2 < .. < p_k\) and \(a_{p_1} \le a_{p_2} \le ... \le a_{p_k}\).

Input format

The first line contains an integer \(T\) that denotes the number of test cases.
For each test case:
- The first line contains three space-separated integers \(Z , O , K\).

Output format

For each test case, print the number of distinct sequences that satisfy the provided conditions.

Note: The result can be a large value, print the output in modulo \(10^9 + 7\) format.

Constraints

\(1 \le T \le 10 \\ 1 \le K \le 10^2 \\ 1 \le Z, O \le 50\)