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 MOD = 1e9 + 7;
int vis[(1 << 21)], ans[(1 << 21)];
vector<int> v;
void solve() {
  int n, q;
  cin >> n >> q;
  ans[0] = 1;
  vis[0] = 1;
  for (int i = 1; i <= n; i++) {
    int x;
    cin >> x;
    if (vis[x]) {
      ans[i] = (2 * ans[i - 1]) % MOD;
    } else {
      int m = v.size();
      for (int j = 0; j < m; j++) {
        v.push_back(x ^ v[j]);
        vis[x ^ v[j]] = i;
      }
      v.push_back(x);
      vis[x] = i;
      ans[i] = ans[i - 1];
    }
  }
  for (int i = 1; i <= q; i++) {
    int l, x;
    cin >> l >> x;
    if (vis[x] == 0) vis[x] = n + 1;
    if (vis[x] <= l)
      cout << ans[l] << '\n';
    else
      cout << 0 << '\n';
  }
}
int32_t main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int t = 1;
  while (t--) {
    solve();
  }
  return 0;
}
