As you probably know, Anton goes to school. One of the school subjects that Anton studies is Bracketology. On the Bracketology lessons students usually learn different sequences that consist of round brackets (characters "(" and ")" (without quotes)).

On the last lesson Anton learned about the regular simple bracket sequences (RSBS). A bracket sequence s of length n is an RSBS if the following conditions are met:

  * It is not empty (that is n ≠ 0). 
  * The length of the sequence is even. 
  * First <image> charactes of the sequence are equal to "(". 
  * Last <image> charactes of the sequence are equal to ")". 



For example, the sequence "((()))" is an RSBS but the sequences "((())" and "(()())" are not RSBS.

Elena Ivanovna, Anton's teacher, gave him the following task as a homework. Given a bracket sequence s. Find the number of its distinct subsequences such that they are RSBS. Note that a subsequence of s is a string that can be obtained from s by deleting some of its elements. Two subsequences are considered distinct if distinct sets of positions are deleted.

Because the answer can be very big and Anton's teacher doesn't like big numbers, she asks Anton to find the answer modulo 109 + 7.

Anton thought of this task for a very long time, but he still doesn't know how to solve it. Help Anton to solve this task and write a program that finds the answer for it!

Input

The only line of the input contains a string s — the bracket sequence given in Anton's homework. The string consists only of characters "(" and ")" (without quotes). It's guaranteed that the string is not empty and its length doesn't exceed 200 000.

Output

Output one number — the answer for the task modulo 109 + 7.

Examples

Input

)(()()


Output

6


Input

()()()


Output

7


Input

)))


Output

0

Note

In the first sample the following subsequences are possible:

  * If we delete characters at the positions 1 and 5 (numbering starts with one), we will get the subsequence "(())". 
  * If we delete characters at the positions 1, 2, 3 and 4, we will get the subsequence "()". 
  * If we delete characters at the positions 1, 2, 4 and 5, we will get the subsequence "()". 
  * If we delete characters at the positions 1, 2, 5 and 6, we will get the subsequence "()". 
  * If we delete characters at the positions 1, 3, 4 and 5, we will get the subsequence "()". 
  * If we delete characters at the positions 1, 3, 5 and 6, we will get the subsequence "()". 



The rest of the subsequnces are not RSBS. So we got 6 distinct subsequences that are RSBS, so the answer is 6.

import java.util.*;
import java.io.*;

/**
 *
 * @author umang
 */

public class ProblemF {

    public static int mod = (int) (1e9+7);
    public static InputReader in;
    public static PrintWriter out;
    public static long[] f;
    
    public static long compute(int nm,int r){
        long ans=0;
        
        ans=f[nm];
        long tmp=pow(f[r], mod-2,mod);
        tmp=(tmp*pow(f[nm-r], mod-2, mod))%mod;
        ans=(ans*tmp)%mod;
        
        return ans;
    }
    
    public static void main(String[] args) {

        in = new InputReader(System.in);
        out = new PrintWriter(System.out);

        f=new long[500000];
        f[0]=1;
        for(int i=1;i<f.length;i++){
            f[i]=i*f[i-1];
            f[i]%=mod;
        }
        
        String s=in.readString();
        int n=s.length();
        int[] o=new int[n];
        int[] c=new int[n];
        
        for(int i=0;i<n;i++){
            if(s.charAt(i)=='(') o[i]=1;
            if(i!=0) o[i]+=o[i-1];
        }
        for(int i=n-1;i>=0;i--){
            if(s.charAt(i)==')') c[i]=1;
            if(i!=n-1) c[i]+=c[i+1];
        }
        long ans=0;
        for(int i=0;i<n;i++){
            if(s.charAt(i)=='(' && c[i]>0) ans=(ans+compute(c[i]+o[i]-1,c[i]-1))%mod;
        }
        out.println(ans);
        out.close();
    }

    static class Pair implements Comparable<Pair>{

        char c;
        int x,i;
        long y;
        long k;
        Pair (char c,int x,long y){
            this.c=c;
            this.x=x;
            this.y=y;
        }

        public int compareTo(Pair o) {
                    return Long.compare(this.x,o.x);
        }

        public boolean equals(Object o) {
            if (o instanceof Pair) {
                Pair p = (Pair)o;
                return p.x == x && p.y == y && p.k==k;
            }
            return false;
        }


        @Override
        public String toString() {
            return  "("+x + " " + y +" "+k+" "+i+" )";
        }

    } 

    public static long add(long x, long y) {
	return (x + y)%mod;
    }
    
    public static long mul(long x, long y) {
	return (x*y)%mod;
    }
    
    public static boolean isPal(String s){
        for(int i=0, j=s.length()-1;i<=j;i++,j--){
                if(s.charAt(i)!=s.charAt(j)) return false;
        }
        return true;
    }
    public static String rev(String s){
            StringBuilder sb=new StringBuilder(s);
            sb.reverse();
            return sb.toString();
    }

    public static long gcd(long x,long y){
    if(x%y==0)
            return y;
    else
            return gcd(y,x%y);
    }

    public static int gcd(int x,int y){
    if(x%y==0)
            return y;
    else 
            return gcd(y,x%y);
    }

    public static long gcdExtended(long a,long b,long[] x){

        if(a==0){
            x[0]=0;
            x[1]=1;
            return b;
        }
        long[] y=new long[2];
        long gcd=gcdExtended(b%a, a, y);

        x[0]=y[1]-(b/a)*y[0];
        x[1]=y[0];

        return gcd;
    }

    public static int abs(int a,int b){
    return (int)Math.abs(a-b);
    }

    public static long abs(long a,long b){
    return (long)Math.abs(a-b);
    }

    public static int max(int a,int b){
    if(a>b)
            return a;
    else
            return b;
    }

    public static int min(int a,int b){
    if(a>b)
            return b;
    else 
            return a;
    }

    public static long max(long a,long b){
    if(a>b)
            return a;
    else
            return b;
    }

    public static long min(long a,long b){
    if(a>b)
            return b;
    else 
            return a;
    }

    public static long pow(long n,long p,long m){
     long  result = 1;
      if(p==0)
        return 1;
    if (p==1)
        return n;
    while(p!=0)
    {
        if(p%2==1)
            result *= n;
        if(result>=m)
        result%=m;
        p >>=1;
        n*=n;
        if(n>=m)
        n%=m;
    }
    return result;
    }

    public static long pow(long n,long p){
    long  result = 1;
      if(p==0)
        return 1;
    if (p==1)
        return n;
    while(p!=0)
    {
        if(p%2==1)
            result *= n;	    
        p >>=1;
        n*=n;	    
    }
    return result;
    }
     public static void debug(Object... o) {
            System.out.println(Arrays.deepToString(o));
    }

    static class InputReader {

            private final InputStream stream;
            private final byte[] buf = new byte[8192];
            private int curChar, snumChars;
            private SpaceCharFilter filter;

            public InputReader(InputStream stream) {
                    this.stream = stream;
            }

            public int snext() {
                    if (snumChars == -1)
                            throw new InputMismatchException();
                    if (curChar >= snumChars) {
                            curChar = 0;
                            try {
                                    snumChars = stream.read(buf);
                            } catch (IOException e) {
                                    throw new InputMismatchException();
                            }
                            if (snumChars <= 0)
                                    return -1;
                    }
                    return buf[curChar++];
            }

            public int nextInt() {
                    int c = snext();
                    while (isSpaceChar(c)) {
                            c = snext();
                    }
                    int sgn = 1;
                    if (c == '-') {
                            sgn = -1;
                            c = snext();
                    }
                    int res = 0;
                    do {
                            if (c < '0' || c > '9')
                                    throw new InputMismatchException();
                            res *= 10;
                            res += c - '0';
                            c = snext();
                    } while (!isSpaceChar(c));
                    return res * sgn;
            }

            public long nextLong() {
                    int c = snext();
                    while (isSpaceChar(c)) {
                            c = snext();
                    }
                    int sgn = 1;
                    if (c == '-') {
                            sgn = -1;
                            c = snext();
                    }
                    long res = 0;
                    do {
                            if (c < '0' || c > '9')
                                    throw new InputMismatchException();
                            res *= 10;
                            res += c - '0';
                            c = snext();
                    } while (!isSpaceChar(c));
                    return res * sgn;
            }

            public int[] nextIntArray(int n) {
                    int a[] = new int[n];
                    for (int i = 0; i < n; i++) {
                            a[i] = nextInt();
                    }
                    return a;
            }

            public long[] nextLongArray(int n) {
                    long a[] = new long[n];
                    for (int i = 0; i < n; i++) {
                            a[i] = nextInt();
                    }
                    return a;
            }

            public String readString() {
                    int c = snext();
                    while (isSpaceChar(c)) {
                            c = snext();
                    }
                    StringBuilder res = new StringBuilder();
                    do {
                            res.appendCodePoint(c);
                            c = snext();
                    } while (!isSpaceChar(c));
                    return res.toString();
            }

            public String nextLine() {
                    int c = snext();
                    while (isSpaceChar(c))
                            c = snext();
                    StringBuilder res = new StringBuilder();
                    do {
                            res.appendCodePoint(c);
                            c = snext();
                    } while (!isEndOfLine(c));
                    return res.toString();
            }

            public boolean isSpaceChar(int c) {
                    if (filter != null)
                            return filter.isSpaceChar(c);
                    return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
            }

            private boolean isEndOfLine(int c) {
                    return c == '\n' || c == '\r' || c == -1;
            }

            public interface SpaceCharFilter {
                    public boolean isSpaceChar(int ch);
            }
    }
}    
