Ehab has an array a of n integers. He likes the [bitwise-xor operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) and he likes to bother Mahmoud so he came up with a problem. He gave Mahmoud q queries. In each of them, he gave Mahmoud 2 integers l and x, and asked him to find the number of subsequences of the first l elements of the array such that their bitwise-xor sum is x. Can you help Mahmoud answer the queries?

A subsequence can contain elements that are not neighboring.

Input

The first line contains integers n and q (1 ≤ n, q ≤ 105), the number of elements in the array and the number of queries.

The next line contains n integers a1, a2, ..., an (0 ≤ ai < 220), the elements of the array.

The next q lines, each contains integers l and x (1 ≤ l ≤ n, 0 ≤ x < 220), representing the queries.

Output

For each query, output its answer modulo 109 + 7 in a newline.

Examples

Input

5 5
0 1 2 3 4
4 3
2 0
3 7
5 7
5 8


Output

4
2
0
4
0


Input

3 2
1 1 1
3 1
2 0


Output

4
2

Note

The bitwise-xor sum of the empty set is 0 and the bitwise-xor sum of a set containing one element is that element itself.
#include <bits/stdc++.h>
using namespace std;
const int N = 1e5 + 5, mod = 1e9 + 7;
int n, m, p[N];
vector<int> q[N];
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  p[0] = 1;
  for (int i = 1; i < N; i++) {
    p[i] = (p[i - 1] * 2) % mod;
  }
  cin >> n >> m;
  for (int i = 1; i <= n; i++) {
    int x;
    cin >> x;
    q[i] = q[i - 1];
    for (auto it : q[i]) {
      x = min(x, x ^ it);
    }
    if (!x) {
      continue;
    }
    for (auto &it : q[i]) {
      it = min(it, it ^ x);
    }
    q[i].push_back(x);
    sort(q[i].begin(), q[i].end());
  }
  while (m--) {
    int l, x;
    cin >> l >> x;
    for (auto it : q[l]) {
      x = min(x, x ^ it);
    }
    if (x) {
      cout << "0\n";
    } else {
      cout << p[l - q[l].size()] << "\n";
    }
  }
}
