B'A sequence of brackets is called balanced if one can turn it into a valid math expression by adding characters '+ ' and '1 '. For example, sequences '(())() ', '() ', and '(()(())) ' are balanced, while ')( ', '(() ', and '(()))( ' are not. A subsequence is a sequence that can be derived from the given sequence by deleting zero or more elements without changing the order of the remaining elements. You are given three integers n , m and k . Find the number of sequences consisting of n '( ' and m ') ', such that the longest balanced subsequence is of length 2 cdot k . Since the answer can be large calculate it modulo 1 ,000 ,000 ,007 ( 10^9 + 7 ). Each test contains multiple test cases. The first line contains the number of test cases t ( 1 <= t <= 3 cdot 10^3 ). Description of the test cases follows. The first line of each test case contains three integers n , m and k ( 1 <= n, m, k <= 2 cdot 10^3 ) For each test case, print one integer -- the answer to the problem. For the first test case "()()", "(())" are the 2 sequences For the second test case no sequence is possible. For the third test case ")((()", ")(()(", ")()((", "())((" are the 4 sequences. '...