Problem: JATC loves Banh-mi (a Vietnamese food). His affection for Banh-mi is so much that he always has it for breakfast. This morning, as usual, he buys a Banh-mi and decides to enjoy it in a special way.

First, he splits the Banh-mi into n parts, places them on a row and numbers them from 1 through n. For each part i, he defines the deliciousness of the part as x_i ∈ \{0, 1\}. JATC's going to eat those parts one by one. At each step, he chooses arbitrary remaining part and eats it. Suppose that part is the i-th part then his enjoyment of the Banh-mi will increase by x_i and the deliciousness of all the remaining parts will also increase by x_i. The initial enjoyment of JATC is equal to 0.

For example, suppose the deliciousness of 3 parts are [0, 1, 0]. If JATC eats the second part then his enjoyment will become 1 and the deliciousness of remaining parts will become [1, \\_, 1]. Next, if he eats the first part then his enjoyment will become 2 and the remaining parts will become [\\_, \\_, 2]. After eating the last part, JATC's enjoyment will become 4.

However, JATC doesn't want to eat all the parts but to save some for later. He gives you q queries, each of them consisting of two integers l_i and r_i. For each query, you have to let him know what is the maximum enjoyment he can get if he eats all the parts with indices in the range [l_i, r_i] in some order.

All the queries are independent of each other. Since the answer to the query could be very large, print it modulo 10^9+7.

Input

The first line contains two integers n and q (1 ≤ n, q ≤ 100 000).

The second line contains a string of n characters, each character is either '0' or '1'. The i-th character defines the deliciousness of the i-th part.

Each of the following q lines contains two integers l_i and r_i (1 ≤ l_i ≤ r_i ≤ n) — the segment of the corresponding query.

Output

Print q lines, where i-th of them contains a single integer — the answer to the i-th query modulo 10^9 + 7.

Examples

Input

4 2
1011
1 4
3 4


Output

14
3


Input

3 2
111
1 2
3 3


Output

3
1

Note

In the first example: 

  * For query 1: One of the best ways for JATC to eats those parts is in this order: 1, 4, 3, 2. 
  * For query 2: Both 3, 4 and 4, 3 ordering give the same answer. 



In the second example, any order of eating parts leads to the same answer.

Solution (in JAVA):

Solution:
import java.util.Arrays;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.TreeSet;

public class PROG4{

    private static InputReader sc;
    private static PrintWriter pw;
    private static TreeSet<Integer> primeSet;

    private static long gcd(long a, long b){ return (b == 0)?a:gcd(b, a%b); }

    private static long lcm(long a, long b){ return (a/gcd(a, b))*b; }

    private static void genPrime(int lim){
        boolean isPrime[] = new boolean[lim+1];
        Arrays.fill(isPrime, true);

        for(int i=2; i<=lim; i++){
            if(isPrime[i]){
                primeSet.add(i);
                for(long j=(long)i*i; j<=lim; j+=i)
                    isPrime[(int)j] = false;
            }
        }
    }

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

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

        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++];
        }

        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;
        }

        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;
        }

        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();
        }

        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();
        }

        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 {
            boolean isSpaceChar(int ch);
        }
    }

    public static void main(String args[]) {
        sc = new InputReader(System.in);
        pw = new PrintWriter(System.out);
        primeSet = new TreeSet<>();

        solve();

        pw.flush();
        pw.close();
    }

    private static long count[][], mod;

    private static long count0(int node){
        if(node < 0) return 0;
        return count[0][node];
    }

    private static long count1(int node){
        if(node < 0) return 0;
        return count[1][node];
    }

    private static long ans(long count0, long count1){
        return ( exp(count0)%mod * ((exp(count1)%mod) -1 + mod)%mod)%mod;
    }

    private static long exp(long count){
        long ans = 1;

        if(count == 0)
            return ans;

        long p = exp(count/2);
        ans = (p%mod * p%mod)%mod;

        if(count % 2 != 0)
            ans = (ans%mod * 2)%mod;

        return ans;
    }

    private static void solve(){
        int n = sc.nextInt(), q = sc.nextInt();
        count = new long[2][n];
        mod = 1000000007;

        String s = sc.readString();
        for(int i=0; i<n; i++) {
            if(i>0){
                count[0][i] = count[0][i-1];
                count[1][i] = count[1][i-1];
            }

            count[s.charAt(i) - '0'][i]++;
        }/*
        for(int i=0; i<n; i++)
            pw.println(count[0][i]+" "+count[1][i]);*/

        while(q-->0){
            int l = sc.nextInt()-1, r = sc.nextInt()-1;
            pw.println(ans(count0(r)-count0(l-1), count1(r)-count1(l-1)));
        }
    }
}