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:
/*
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 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */

import java.io.BufferedReader;
import java.io.InputStreamReader;

/**
 *
 * @author arvin
 */
public class Banh_mi_food {
    
    public static void main(String args[]) throws Exception
    {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        String a[]=br.readLine().split(" ");
        int n=Integer.parseInt(a[0]);
        int q=Integer.parseInt(a[1]);
        String s=br.readLine();
        int arr[]=new int[n+1];
        int b[]=new int[n+1];
        int mod=1000000007;
        b[1]=1;
        for(int i=2;i<=n;++i) b[i]=(b[i-1]*2)%mod;
	for(int i=1;i<=n;++i) b[i]=(b[i]+b[i-1])%mod;
        for(int i=1;i<=n;i++)
        {
            arr[i]=arr[i-1];
            if(s.charAt(i-1)=='0')
                    arr[i]++;
        }
        while(q--!=0)
        {
            int count=0;
            String t[]=br.readLine().split(" ");
            int l=Integer.parseInt(t[0]);
            int r=Integer.parseInt(t[1]);
            if(r!=l)
                count=arr[r]-arr[l-1];
            else
                count=arr[r]-arr[r-1];
            int ans=(b[r-l+1]-b[count]);
            System.out.println((long)(((long)ans+mod)%(mod)));
        }
        br.close();
    }
}