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 = 1e18 + 5LL;
const long long mod = 1e9 + 7LL;
void solve();
void ITO();
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  ITO();
  long long t = 1;
  while (t--) solve();
  return 0;
}
const long long N = (1e7 + 1);
long long modular_exp(long long a, long long n) {
  if (n == 0) return 1;
  long long res = 1;
  while (n > 0) {
    if (n % 2 != 0) res *= a;
    a = (a * a) % mod;
    n = n / 2;
    res = res % mod;
  }
  res = (res % mod);
  return res;
}
void solve() {
  long long n, q;
  cin >> n >> q;
  string s;
  cin >> s;
  long long pre[n];
  for (long long i = 0; i < n; i++) {
    pre[i] = s[i] - '0';
    if (i > 0) pre[i] += pre[i - 1];
  }
  while (q--) {
    long long l, r;
    cin >> l >> r;
    l--, r--;
    long long o = pre[r] - (l - 1 >= 0 ? pre[l - 1] : 0);
    long long z = (r - l + 1) - o;
    long long res = modular_exp(2, (r - l + 1)) - 1;
    res -= (modular_exp(2, z) - 1);
    res += mod;
    res %= mod;
    cout << res << "\n";
  }
  cout << "\n";
  return;
}
void ITO() {}