- Time limit: 1.00 s
- Memory limit: 512 MB
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
- $1 \le k \le n \le 10^6$
Input:
6
(()
Output:
2
Explanation: There are two possible sequences:
(())()
and (()())
.