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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  int n, q;
  cin >> n >> q;
  string s;
  cin >> s;
  int ao[n + 3];
  memset(ao, 0, sizeof ao);
  for (int i = 0; i < (int)s.size(); i++) {
    ao[i] += (s[i] == '1');
    if (i) ao[i] += ao[i - 1];
  }
  long long sp[100001], asp[100001];
  sp[0] = 1;
  asp[0] = 1;
  for (int i = 1; i < 100001; i++) sp[i] = sp[i - 1] * 2, sp[i] %= 1000000007;
  for (int i = 1; i < 100001; i++)
    asp[i] = sp[i], asp[i] += asp[i - 1], asp[i] %= 1000000007;
  while (q--) {
    int l, r;
    long long ans = 0;
    cin >> l >> r;
    l--;
    r--;
    int ones = (!l ? ao[r] : ao[r] - ao[l - 1]);
    ans += (ones ? asp[ones - 1] : 0);
    long long fac, z = r - l + 1 - ones, u;
    if (ones) {
      fac = sp[ones - 1];
      fac *= 2;
      fac %= 1000000007;
      fac--;
      u = (z ? asp[z - 1] : 0);
      u %= 1000000007;
      u *= fac;
      u %= 1000000007;
      cout << (ans % 1000000007 + u) % 1000000007 << endl;
    } else
      cout << 0 << endl;
  }
  return 0;
}