CodeForces 785D Anton and School - 2

#include <cstdio>
#include <cmath>
#include <cstring>
#include <map>
#include <algorithm>
using namespace std;
typedef long long LL; 

char s[200010];
long long L[200010],R[200010];
LL fac[200010];
long long mod = 1e9+7;

void init()    
{    
    int i;    
    fac[0] =1;    
    for(i =1; i <= 200000; i++)    
        fac[i] = fac[i-1]*i%mod;    
}    
LL pow(LL a, LL b)    
{    
    LL tmp = a % mod, ans =1;    
    while(b)    
    {    
        if(b &1)  ans = ans * tmp % mod;    
        tmp = tmp*tmp % mod;    
        b >>=1;    
    }    
    return  ans;    
}    
LL C(LL n, LL m)    
{    
    if(m>n||m<0)return 0;    
    return  fac[n]*pow(fac[m]*fac[n-m],mod-2)%mod;    
}   

int main()
{	
	init();
	scanf("%s",s);
	int len = strlen(s);

	for(int i=1;i<=len;i++)
	{
		L[i] = L[i-1];
		if(s[i-1]==‘(‘) L[i]++;
	}

	for(int i=len;i>=1;i--)
	{
		R[i] = R[i+1];
		if(s[i-1]==‘)‘) R[i]++;
	}

	long long ans = 0;

	for(int i=1;i<=len;i++)
	{
		if(s[i-1]==‘(‘) continue;
		if(L[i]==0) continue;

		long long m,k1,k2;

		m = min(L[i],R[i]);
		if(m==0) k1=1;
		else k1 = C(L[i]+R[i],m);

		m = min(L[i],R[i]-1);
		if(m==0) k2=1;
		else k2 = C(L[i]+R[i]-1,m);
		
		long long k = (k1-k2+mod)%mod;
		ans = ( ans + k ) %mod;
	}

	printf("%lld\n",ans);

	return 0;
}