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 + 87, M = 1e9 + 7, C = 1 << 20;
int a[N], ans[N];
vector<pair<int, int> > qq[N];
bool b[C];
vector<int> v;
int main() {
  ios::sync_with_stdio(0);
  int n, q;
  cin >> n >> q;
  for (int i = 1; i <= n; ++i) cin >> a[i];
  for (int i = 0; i < q; ++i) {
    int l, x;
    cin >> l >> x;
    qq[l].emplace_back(i, x);
  }
  int w = 1;
  b[0] = true;
  v = {0};
  for (int i = 1; i <= n; ++i) {
    if (b[a[i]]) {
      w = w * 2 % M;
    } else {
      int m = v.size();
      for (int j = 0; j < m; ++j) {
        v.push_back(v[j] ^ a[i]);
        b[v.back()] = true;
      }
    }
    for (const auto& p : qq[i]) ans[p.first] = b[p.second] * w;
  }
  for (int i = 0; i < q; ++i) cout << ans[i] << '\n';
}
