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;
const long long INF = (long long)0x3f3f3f3f3f3f3f, MAX = 9e18, MIN = -9e18;
const int N = 1e6 + 10, M = 2e6 + 10, mod = 1e9 + 7, inf = 0x3f3f3f3f;
long long a[N], sum[N];
long long q_pow(long long a, long long k) {
  long long s = 1;
  while (k) {
    if (k & 1) s = s * a % mod;
    a = a * a % mod;
    k >>= 1;
  }
  return s;
}
int main() {
  ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  int _;
  _ = 1;
  while (_--) {
    long long n, m, inv2 = q_pow(2, mod - 2);
    string s;
    cin >> n >> m >> s;
    s = " " + s;
    for (int i = 1; (i) <= (n); i++) sum[i] = sum[i - 1] + s[i] - '0';
    while (m--) {
      long long l, r;
      cin >> l >> r;
      long long sum1 = sum[r] - sum[l - 1];
      if (sum1 == 0) {
        cout << 0 << '\n';
        continue;
      }
      long long sum0 = r - l + 1 - sum1;
      long long ans = q_pow(2, sum1) - 1;
      long long now = ans;
      ans = (ans + now * (q_pow(2, sum0) - 1) % mod) % mod;
      cout << ans << '\n';
    }
  }
  return 0;
}