As Famil Door’s birthday is coming, some of his friends (like Gabi) decided to buy a present for him. His friends are going to buy a string consisted of round brackets since Famil Door loves string of brackets of length *n* more than any other strings!

The sequence of round brackets is called valid if and only if: 
 1.  the total number of opening brackets is equal to the total number of closing brackets; 1.  for any prefix of the sequence, the number of opening brackets is greater or equal than the number of closing brackets. 
Gabi bought a string *s* of length *m* (*m* ≤ *n*) and want to complete it to obtain a valid sequence of brackets of length *n*. He is going to pick some strings *p* and *q* consisting of round brackets and merge them in a string *p* + *s* + *q*, that is add the string *p* at the beginning of the string *s* and string *q* at the end of the string *s*.

Now he wonders, how many pairs of strings *p* and *q* exists, such that the string *p* + *s* + *q* is a valid sequence of round brackets. As this number may be pretty large, he wants to calculate it modulo 10<sup class="upper-index">9</sup> + 7.
First line contains *n* and *m* (1 ≤ *m* ≤ *n* ≤ 100 000, *n* - *m* ≤ 2000) — the desired length of the string and the length of the string bought by Gabi, respectively.

The second line contains string *s* of length *m* consisting of characters '(' and ')' only.
In the first sample there are four different valid pairs: 
 1.  *p* = "(", *q* = "))" 1.  *p* = "()", *q* = ")" 1.  *p* = "", *q* = "())" 1.  *p* = "", *q* = ")()" 
In the second sample the only way to obtain a desired string is choose empty *p* and *q*.

In the third sample there is no way to get a valid sequence of brackets.
4 1
(
4
4 4
(())
1
4 3
(((
0
875 50
)))((())()))((()(())))))())))((((((()))))))()(((((
0
1980 464
))(()()))(((((((((()))))))(()(((()((()))()()())()))()))(()))))))(())((())))()())()((())())()())))(())()(()))(()())()((((()))())()(())))))(()()(()(((((()(()()))(((()))(())))))()())(())))))())()()((())))))))((()(())))))()()(()((()((()()))(()))(())(()))()((((())()()))))))()(())))()(()())()())(((((()))())))())())(()))()(()))())((())((((()(()(())))(((()()))))()()()))))((()())()((())())))())))()(()(()()(((((()((((()))()(())()))))()(()))(()(((((((()((()(())))(((((())
854368836
1542 282
())())()((()(()))()((())()))((())(()))))(()()))(())((()))()((()())())()))((())(((()(())((()()())((((())))((()((((()(()()))))(()(()()(())()((())())())))))()()())))(()((((()))(()(()(()(()))())((()()()()(()(()))())(((()(())()(())()()())))()))())(()))(((())()))((())()(())))))(())))()()
631927032
2 2
)(
0
2 2
))
0
def ij(s):
    i = 0
    j = 0
    for c in s:
        if c == ')':
            if j > 0:
                j -= 1
            else:
                i += 1
        else:
            j += 1
    return i, j


def ways(n, s):
    I, J = ij(s)
    f = n - len(s) - I - J
    if f < 0 or f%2:
        return 0
    E = f//2

    C = [1]
    for n in range(E):
        C.append(C[n] * 2 * (2*n + 1) // (n+2))

    iset = set()
    for ii in I, J:
        i = ii;
        while i:
            iset.add(i)
            if i%2:
                i //= 2
            else:
                i -= 1

    W = [None for i in range(max(I, J)+1)]
    W[0] = [C[e] for e in range(E+1)]
    for i in sorted(iset):
        W[i] = [None for e in range(E+1)]
        if i%2:
            j = i//2
            for e in range(E+1):
                W[i][e] = sum(W[j][k] * W[j][e-k] for k in range(e+1))
        else:
            for e in range(E+1):
                W[i][e] = sum(C[k] * W[i-1][e-k] for k in range(e+1))
            
    else:
        return sum(W[I][e] * W[J][f-e] for f in range(E+1) for e in range(f+1))


if __name__ == '__main__':
    n, m = map(int, input().split())
    s = input()
    print(ways(n, s) % (10**9 + 7))

