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:
# -*- coding:utf-8 -*-

"""

created by shuangquan.huang at 11/19/18

"""

N, M = map(int, input().split())
A = [int(x) for x in input()]

memo = [-1] * (N+1)


def pow(n):
    if n == 0:
        return 1

    if n < 30:
        return 1 << n

    if memo[n] >= 0:
        return memo[n]

    half = pow(n // 2)

    ans = half * half
    if n % 2 != 0:
        ans *= 2
    ans %= MOD
    memo[n] = ans

    return ans


MOD = 10 ** 9 + 7

left = [0] * (N + 1)
for i in range(1, N + 1):
    left[i] = left[i - 1] + A[i - 1]

ans = []
for qi in range(M):
    l, r = map(int, input().split())
    ones = left[r] - left[l - 1]
    zeros = r - l + 1 - ones
    x = pow(ones) - 1
    y = x * (pow(zeros)- 1)
    ans.append((x + y) % MOD)

print('\n'.join(map(str, ans)))