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.math.BigInteger;
import java.util.*;
import java.io.*;
import static java.lang.Math.*;


public class Solution {

    static long m = (long)1e9+7;

    static long modPow(int p){
        long res = 1, a = 2;

        while(p!=0){
            if(p%2==1){
                res = res*a;
                p--;
            }
            else if(p%2==0){
                a*=a;
                p/=2;
            }
            res%=m;
            a%=m;
        }

        return res%m;
    }

    public static void main(String[] args) {

        Scanner in = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);

        int n = in.nextInt(), q = in.nextInt(), a[] = new int[n+1];
        char c[] = in.next().toCharArray();
        a[1] = c[0]=='0'?1:0;

        for(int i = 1; i<n; i++){
            if(c[i]=='0') a[i+1]++;
            a[i+1]+=a[i];
        }

        for(; q>0; q--){
            int l = in.nextInt(), r = in.nextInt(), k = r-l+1;
            long ans = (modPow(k)%m - modPow(a[r]-a[l-1])%m)%m;
            while(ans<0) ans+=m;
            out.println(ans);
        }

        out.flush();

    }
}