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.Scanner;

public class Main {
    static long mod = 1000000007;
    static long getPow(long n, long mod){
        if(n == 0) return 1 % mod;
        if(n == 1) return 2 % mod;

        long res = getPow(n / 2, mod);
        if(n % 2 == 0) return  (res * res) % mod;
        else return (res * res * 2) % mod;
    }
    public static void main(String[] arg) {
        Scanner scanner = new Scanner(System.in);

        int n = scanner.nextInt();
        int m = scanner.nextInt();

        String str = scanner.next();

        int[] array = new int[n + 1];
        for(int i = 0; i < n; i++) array[i + 1] = array[i] +  (str.charAt(i) == '0'? 0: 1);

        StringBuilder res = new StringBuilder();
        for(int i = 0; i < m; i++){
            int l = scanner.nextInt();
            int r = scanner.nextInt();

            int oneCount = array[r] - array[l - 1];
            int zeroCount = r - l + 1 - oneCount;

            long subRes1 = getPow(oneCount, mod) - 1;
            long subRes0 = (subRes1 * (getPow(zeroCount, mod) - 1)) % mod;
            res.append((subRes1 + subRes0) % mod + "\n");
        }

        System.out.println(res.toString());
    }
}