Bracket Sequences II

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Your task is to calculate the number of valid bracket sequences of length n when a prefix of the sequence is given. Input The first input line has an integer n. The second line has a string of k characters: the prefix of the sequence. Output Print the number of sequences modulo 10^9+7. Constraints - 1 \le k \le n \le 10^6 Example Input: 6 (() Output: 2 Explanation: There are two possi

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