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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
        public static void main(String[] args) {
                InputStream inputStream = System.in;
                OutputStream outputStream = System.out;
                InputReader in = new InputReader(inputStream);
                PrintWriter out = new PrintWriter(outputStream);
                TaskC solver = new TaskC();
                solver.solve(1, in, out);
                out.close();
        }

        static class TaskC {
                long mod = (long) 1e9 + 7;

                public void solve(int testNumber, InputReader in, PrintWriter out) {
                        int n = in.i();
                        int q = in.i();
                        char[] s = in.s().toCharArray();
                        int[] zero = new int[n + 1];
                        int[] one = new int[n + 1];

                        for (int i = 0; i < s.length; i++) {
                                if (s[i] == '0') {
                                        zero[i + 1] = zero[i] + 1;
                                        one[i + 1] = one[i];
                                } else {
                                        one[i + 1] = one[i] + 1;
                                        zero[i + 1] = zero[i];
                                }
                        }

                        while (q-- > 0) {
                                int l = in.i();
                                int r = in.i();
                                int no_zero = zero[r] - zero[l - 1];
                                int no_one = one[r] - one[l - 1];
                                long ans = IntegerUtil.modPow(2, no_zero, mod);
                                ans = ans % mod * (IntegerUtil.modPow(2, no_one, mod) - 1 + mod) % mod;
                                out.println(ans % mod);
                        }
                }

        }

        static class IntegerUtil {
                public static long modPow(long base, long exp, long mod) {
                        long res = 1L;
                        while (exp > 0) {
                                if (exp % 2 == 1)
                                        res = (res * base) % mod;
                                base = (base * base) % mod;
                                exp >>= 1;
                        }
                        return res;
                }

        }

        static class InputReader {
                InputStream is;
                private byte[] inbuf = new byte[1024];
                public int lenbuf = 0;
                public int ptrbuf = 0;

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

                private int readByte() {
                        if (lenbuf == -1) throw new InputMismatchException();
                        if (ptrbuf >= lenbuf) {
                                ptrbuf = 0;
                                try {
                                        lenbuf = is.read(inbuf);
                                } catch (IOException e) {
                                        throw new InputMismatchException();
                                }
                                if (lenbuf <= 0) return -1;
                        }
                        return inbuf[ptrbuf++];
                }

                private boolean isSpaceChar(int c) {
                        return !(c >= 33 && c <= 126);
                }

                private int skip() {
                        int b;
                        while ((b = readByte()) != -1 && isSpaceChar(b)) ;
                        return b;
                }

                public String s() {
                        int b = skip();
                        StringBuilder sb = new StringBuilder();
                        while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
                                sb.appendCodePoint(b);
                                b = readByte();
                        }
                        return sb.toString();
                }

                public int i() {
                        int num = 0, b;
                        boolean minus = false;
                        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
                        if (b == '-') {
                                minus = true;
                                b = readByte();
                        }

                        while (true) {
                                if (b >= '0' && b <= '9') {
                                        num = num * 10 + (b - '0');
                                } else {
                                        return minus ? -num : num;
                                }
                                b = readByte();
                        }
                }

        }
}