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

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