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:
										/* Rajkin Hossain */
import java.io.*;
import java.util.*;

public class C {
	
    //static FastInput k = new FastInput("/home/rajkin/Desktop/input.txt");
    static FastInput k = new FastInput(System.in);
    static FastOutput z = new FastOutput();
    static int n, q;
    static char [] y;
    static Pair [] data;
    
    static long mod = (long) 1e9 + 7l;
    
    static long pow(long a, long b){
        if(b == 0) return 1l % mod;
        long x = pow(a, b / 2);
        
        x = (x * x) % mod;
        if(b % 2 == 1) x = (x * a) % mod;
        
        return x;
	}
    
    static void startAlgorithm(){
    	while(q-->0){
    		int left = k.nextInt();
    		int right = k.nextInt();
    		
    		Pair p2 = data[right];
    		Pair p1 = data[left-1];
    		
    		long one = p2.one - p1.one;
    		long zero = p2.zero - p1.zero;
    		
    		long oneSum = 0l, zeroSum = 0l;
    		
    		if(one % 2l == 0){
    			oneSum = pow(4l, one/2) - 1l;
    		}
    		else{
    			oneSum = (1l % mod) + ((2l % mod) * (pow(4l, (one-1)/2) - 1l)) % mod;
    			oneSum %= mod;
    		}
    		
    		if(zero % 2 == 0){
    			zeroSum = pow(4l, zero/2) - 1l;
    		}
    		else{
    			zeroSum = (1l % mod) + ((2l % mod) * (pow(4l, (zero-1)/2) - 1l)) % mod;
    			zeroSum %= mod;
    		}
    		
    		zeroSum = ((oneSum % mod) * (zeroSum % mod)) % mod;
    		
    		long ans = ((oneSum % mod) + (zeroSum % mod)) % mod;
    		
    		z.println(ans);
    	}
    }
	
    public static void main(String[] args) throws Exception {
    	while(k.hasNext()){
        	n = k.nextInt();
        	q = k.nextInt();
        	
        	y = k.next().toCharArray();
        	data = new Pair[n+1];
        	
        	data[0] = new Pair(0,0);
        	
        	for(int i = 1; i<=n; i++){
        		if(y[i-1] == '0'){
        			data[i] = new Pair(data[i-1].zero + 1, data[i-1].one);
        		}
        		else{
        			data[i] = new Pair(data[i-1].zero, data[i-1].one + 1);
        		}
        	}
        	
        	startAlgorithm();
    	}
    	
    	z.flush();
    	System.exit(0);
    }
    
    static class Pair {
    	int zero, one;

		public Pair(int zero, int one) {
			this.zero = zero;
			this.one = one;
		}
    }

    public static class FastInput {
        BufferedReader reader;
        StringTokenizer tokenizer;
 
        public FastInput(InputStream stream){
        	reader = new BufferedReader(new InputStreamReader(stream));
        }
        
	    public FastInput(String path){
	        try {
	        	reader = new BufferedReader(new FileReader(path));
			} catch (FileNotFoundException e) {
				// TODO Auto-generated catch block
				e.printStackTrace();
			}
	        tokenizer = null;
	    }
 
        public String next() {
            return nextToken();
        }
        
        public String nextLine() {
            try {
				return reader.readLine();
			} catch (IOException e) {
				// TODO Auto-generated catch block
				e.printStackTrace();
			}
            
            return null;
        }
 
        public boolean hasNext(){
            try {
                return reader.ready();
            } catch (IOException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
            }
            return false;
        }
 
        public String nextToken() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                String line = null;
                try {
                    line = reader.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
                if (line == null) {
                    return null;
                }
                tokenizer = new StringTokenizer(line);
            }
            return tokenizer.nextToken();
        }
 
        public Integer nextInt() {
            return Integer.parseInt(nextToken());
        }
       
        public Long nextLong() {
            return Long.valueOf(nextToken());
        }
    }
    
    public static class FastOutput extends PrintWriter {
    	public FastOutput() { 
            super(new BufferedOutputStream(System.out)); 
    	}
    }
}