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 PYTHON3):

Solution:
for _ in range(1):
    n,q = map(int,input().split())
    s = input()
    # s = s[:-2]
    # s = s[1:]
    s = list(s)
    # print(s)
    zeros = [0]*n
    ones = [0]*n
    if (s[0]=='1'):
        ones[0]=1
    else:
        zeros[0]=1
    for i in range(1,n):
        ones[i]+=ones[i-1]
        zeros[i]+=zeros[i-1]
        if (s[i]=='1'):
            ones[i]+=1
        else:
            zeros[i]+=1
    zeros = [0]+zeros
    ones = [0]+ones
    mod = 1000000007
    a= []
    for i in range(q):
        l,r = map(int,input().split())
        x = ones[r]-ones[l-1]
        y = zeros[r]-zeros[l-1]
        # print(x,y)
        ans = (pow(2,x,mod)-1)%mod
        ans = (ans*pow(2,y,mod))%mod 
        # print(ans)
        a.append(str(ans))
    print('\n'.join(map(str,a)))