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.io.*;
import java.lang.reflect.Array;
import java.util.*;

/**
 * Created by noureldin on 2/20/17.
 */

public class main {

    private static int mod = 1000*1000*1000 + 7,MAX = 200*1000 + 10;
    private static int [] F = new int[MAX];
    private static int [] r = new int[MAX];

    private static int mul(int x,int y){
        return (int)((x*1L*y)%mod);
    }
    private static int add(int x,int y){
        x += y;
        if(x >= mod) x -= mod;
        return x;
    }

    private static int C(int n,int k){
        if (n < k) return 0;
        return mul(mul(F[n],r[k]),r[n - k]);
    }
    private static int pow_mod(int x,int p){
        if(p == 0) return 1;
        int y = 1;
        for(;p > 1;p >>= 1){
            if(p%2 == 1) y = mul(x,y);
            x = mul(x,x);
        }
        return mul(x,y);
    }
    private static void init(){
        F[0] = r[0] = 1;
        for (int i = 0;i < MAX - 1;i++){
            F[i + 1] = mul(F[i],i + 1);
            r[i + 1] = pow_mod(F[i + 1],mod - 2);
        }
    }

    public static void main(String[] args) throws Exception{
        IO io = new IO(null,null);
        init();
        char [] I = io.getNext().toCharArray();
        int open = 0;
        for (char c : I) open += (c == '(') ? 1 : 0;
        int ans = 0,cnt = 0;
        for (int i = 0;i < I.length;i++){
            if (I[i] == ')') continue;
            cnt ++;
            int m = I.length - open - i - 1 + cnt;
//            System.out.println(cnt + " " + m + " " + C(m + cnt - 2,m - 1));
            ans = add(ans,C(m + cnt - 1,cnt ));
        }
        io.println(ans);
        io.close();
    }
}

class event implements Comparable<event>{
    int t,type;
    public event(int t,int type){
        this.t = t;
        this.type = type;
    }
    @Override
    public int compareTo(event o){
        if (this.t != o.t) return this.t - o.t;
        return this.type - o.type;
    }
}


class IO{
    private BufferedReader br;
    private StringTokenizer st;
    private PrintWriter writer;
    private String inputFile,outputFile;

    public String getNext() throws FileNotFoundException, IOException{
        while(st == null || !st.hasMoreTokens()) st = new StringTokenizer(br.readLine());
        return st.nextToken();
    }

    public String getNextLine() throws FileNotFoundException, IOException{
        return br.readLine();
    }

    public int getNextInt() throws FileNotFoundException, IOException{
        return Integer.parseInt(getNext());
    }
    public long getNextLong() throws FileNotFoundException, IOException{
        return Long.parseLong(getNext());
    }

    public void print(double x,int num_digits) throws  IOException{
        writer.printf("%." + num_digits + "f" ,x);
    }
    public void println(double x,int num_digits) throws  IOException{
        writer.printf("%." + num_digits + "f\n" ,x);
    }
    public void print(Object o) throws  IOException{
        writer.print(o.toString());
    }

    public void println(Object o) throws  IOException{
        writer.println(o.toString());
    }
    public IO(String x,String y) throws FileNotFoundException, IOException{
        inputFile = x;
        outputFile = y;
        if(x != null) br = new BufferedReader(new FileReader(inputFile));
        else br = new BufferedReader(new InputStreamReader(System.in));
        if(y != null) writer = new PrintWriter(new BufferedWriter(new FileWriter(outputFile)));
        else writer = new PrintWriter(new OutputStreamWriter(System.out));
    }

    protected void close() throws IOException{
        br.close();
        writer.close();
    }
}

