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.util.Arrays;
import java.util.StringTokenizer;

/**
 * Created by gouthamvidyapradhan on 24/06/2020
 */
public class AntonAndSchool {
    private static PrintWriter pw = new PrintWriter(new BufferedOutputStream(System.out, 500000));
    static class MyScanner {
        /**
         * Buffered reader
         */
        private static BufferedReader br = new BufferedReader(
                new InputStreamReader(System.in));

        private static StringTokenizer st;

        /**
         * Read integer
         *
         * @return
         * @throws Exception
         */
        public static int readInt() throws Exception {
            try {
                if (st != null && st.hasMoreTokens()) {
                    return parseInt(st.nextToken());
                }
                String str = br.readLine();
                if(str == null) return -2;
                if (!str.trim().equals("")) {
                    st = new StringTokenizer(str);
                    return parseInt(st.nextToken());
                }
            } catch (IOException e) {
                close();
                return -1;
            }
            return -1;
        }

        /**
         * Read integer
         *
         * @return
         * @throws Exception
         */
        public static long readLong() throws Exception {
            try {
                if (st != null && st.hasMoreTokens()) {
                    return Long.parseLong(st.nextToken());
                }
                String str = br.readLine();
                if (str != null && !str.trim().equals("")) {
                    st = new StringTokenizer(str);
                    return Long.parseLong(st.nextToken());
                }
            } catch (IOException e) {
                close();
                return -1;
            }
            return -1;
        }

        /**
         * Read line
         * @return
         * @throws Exception
         */
        public static String readLine() throws Exception
        {
            return br.readLine();
        }

        /**
         * Parse to integer
         * @param in
         * @return integer value
         */
        public static int parseInt(String in)
        {
            // Check for a sign.
            int num  = 0, sign = -1, i = 0;
            final int len  = in.length( );
            final char ch  = in.charAt( 0 );
            if ( ch == '-' )
                sign = 1;
            else
                num = '0' - ch;

            // Build the number.
            i+=1;
            while ( i < len )
                num = num*10 + '0' - in.charAt( i++ );
            return sign * num;
        }

        /**
         * Close BufferedReader
         *
         * @throws Exception
         */
        public static void close() throws Exception {
            br.close();
        }
    }

    static long[] F;
    static final int MOD = (int)1e9+7;
    public static void main(String[] args) throws Exception{
        String line = MyScanner.readLine();
        F = new long[line.length()];
        int[] left = new int[line.length()];
        int[] right = new int[line.length() + 1];
        left[0] = line.charAt(0) == '(' ? 1 : 0;
        right[line.length() - 1] = line.charAt(line.length() - 1) == ')' ? 1 : 0;
        for(int i = 1; i <  line.length(); i ++){
            if(line.charAt(i) == '('){
                left[i] = left[i - 1] + 1;
            } else left[i] = left[i - 1];
        }
        for(int i = line.length() - 2; i >= 0; i --){
            if(line.charAt(i) == ')'){
                right[i] = right[i + 1] + 1;
            } else right[i] = right[i + 1];
        }
        long ans = 0;
        Arrays.fill(F, -1);
        for(int i = 0; i < line.length(); i ++){
            if(line.charAt(i) == '('){
                if(right[i + 1] > 0){
                    int n = left[i] + right[i + 1] - 1;
                    ans = ((ans + NcR(n, left[i])) % MOD);
                }
            }
        }
        pw.println(ans);
        pw.flush();
        pw.close();
        MyScanner.close();
    }

    private static long NcR(int n, int r){
        if(n - r < 0) return 0;
        return ((fact(n) * ((modInverse((int)fact(r)) * modInverse((int)fact(n - r))) % MOD)) % MOD);
    }
    private static long fact(int n){
      if(n == 0 || n == 1) return 1;
      else if(F[n] != -1) return F[n];
      else {
          F[n] = ((n * (fact(n - 1) % MOD)) % MOD);
          return F[n];
      }
    }

    private static int modMul(int a, int b){
        return (int)(((long) a * b) % MOD);
    }

    private static int modAdd(int a, int b){
        return (int)(((long) a + b) % MOD);
    }

    private static long modInverse(int a){
        ExtendedGcd gcdPair = new ExtendedGcd();;
        gcd(a, MOD, gcdPair);
        return (((gcdPair.x % MOD) + MOD) % MOD);
    }

    static class ExtendedGcd{
        long x, y;
    }

    private static long gcd(long a, long b, ExtendedGcd gcdPair){
        if(b == 0) {
            gcdPair.x = 1;
            gcdPair.y = 0;
            return a;
        }
        ExtendedGcd newGcdPair = new ExtendedGcd();
        long r = gcd(b, a % b, newGcdPair);
        gcdPair.x = newGcdPair.y;
        gcdPair.y = newGcdPair.x - newGcdPair.y * (a/b);
        return r;
    }
}
