7667: [CSES Problem Set] Bracket Sequences II
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Description
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.
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
$1≤k≤n≤10^6$
Sample 1 Input
6
(()
Sample 1 Output
2
There are two possible sequences: (())() and (()()).