Codeforces Round 921 (Div. 1) |
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Finished |
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⋅k. Since the answer can be large calculate it modulo 1000000007 (109+7).
Each test contains multiple test cases. The first line contains the number of test cases t (1≤t≤3⋅103). 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⋅103)
For each test case, print one integer — the answer to the problem.
32 2 23 2 33 2 1
2 0 4
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.
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