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
import sys
input=sys.stdin.readline
n,m=map(int,input().split())
d=n-m
s=list(input().rstrip())
cnt=0
min_c=0
for i in range(m):
    if s[i]=="(":
        cnt+=1
    else:
        cnt-=1
    min_c=min(min_c,cnt)
mod=10**9+7
dp=[[0]*(d+1) for i in range(d+1)]
dp[0][0]=1
for i in range(1,d+1):
    for j in range(d+1):
        if j>0:
            dp[i][j]+=dp[i-1][j-1]
        if j+1<=d:
            dp[i][j]+=dp[i-1][j+1]
        dp[i][j]%=mod
ans=0
for l in range(d+1):
    r=d-l
    for i in range(l+1):
        if i+min_c<0 or i+cnt>d:
            continue
        ans+=dp[l][i]*dp[r][i+cnt]
        ans%=mod
print(ans)