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.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Comparator;
import java.util.HashMap;
import java.util.InputMismatchException;

public class Q3 {
    public static int mod = (int) 1e9 + 7;

    public static long[] pow = new long[100003];

    public static void main(String[] args) {
        InputReader s = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);
        int t = 1;
//        t = s.nextInt();
        pow[0] = 1;
        for (int i = 1; i < 100003; i++) {
            pow[i] = pow[i - 1] * 2;
            if (pow[i] >= mod) {
                pow[i] -= mod;
            }
        }
        nexttest:
        while (t-- > 0) {
            int n = s.nextInt();
            int m = s.nextInt();

            char[] xx = s.nextLine().toCharArray();

            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                if (xx[i] == '1') {
                    a[i] = 1;
                }
            }
            Query[] q = new Query[m];
            for (int i = 0; i < m; i++) {
                q[i] = new Query(s.nextInt() - 1, s.nextInt() - 1);
            }

            long[] res = processQueries(a, q);

            printArray(res, out);

        }

        out.close();
    }

    public static class Query {
        int index;
        int a;
        int b;

        public Query(int a, int b) {
            this.a = a;
            this.b = b;
        }
    }

    static int count = 0;
    static long invmod = pow(2, mod - 2, mod);

    static long add(int[] a, int i, long cur) {
        count++;
        if (a[i] == 1) {
            return (cur + pow[count - 1]) >= mod ? cur + pow[count - 1] - mod : cur + pow[count - 1];
        }
        return (cur * 2) >= mod ? cur * 2 - mod : cur * 2;
    }

    static long remove(int[] a, int i, long cur) {
        count--;
        if (a[i] == 1) {
            return (cur - pow[count])  < 0 ? (cur - pow[count] + mod) : (cur - pow[count]);
        }
        return cur * invmod % mod;
    }

    public static long[] processQueries(int[] a, Query[] queries) {
        for (int i = 0; i < queries.length; i++) {
            queries[i].index = i;
        }
        int sqrtn = (int) Math.sqrt(a.length);
        Arrays.sort(queries, Comparator.comparingInt((Query q) -> q.a / sqrtn).thenComparingInt(q -> q.b));
        long[] res = new long[queries.length];
        int L = 0;
        int R = 0;
        long cur = a[0];
        count = 1;

        for (Query query : queries) {
            while (L > query.a) {
                cur = add(a, --L, cur);
//                System.out.println(2 +" " + cur);
            }
            while (R < query.b) {
                cur = add(a, ++R, cur);
//                System.out.println(3 + " " + cur);
            }
            while (L < query.a) {
                cur = remove(a, L++, cur);
//                System.out.println(1 + " " + cur);
            }
            while (R > query.b) {
                cur = remove(a, R--, cur);
//                System.out.println(4 + " " + cur);
            }
            res[query.index] = cur;
        }
        return res;
    }


    public static void printArray(long[] a, PrintWriter out) {
        for (int i = 0; i < a.length; i++) {
            out.println(a[i]);
        }
    }

    public static int pow(long x, long n, int mod) {
        long res = 1;
        for (long p = x; n > 0; n >>= 1, p = (p * p) % mod) {
            if ((n & 1) != 0) {
                res = (res * p % mod);
            }
        }
        return (int) res;
    }

    static long gcd(long n1, long n2) {
        long r;
        while (n2 != 0) {
            r = n1 % n2;
            n1 = n2;
            n2 = r;
        }
        return n1;
    }


    static class InputReader {

        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;
        private InputReader.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 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);
        }
    }
}