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 MAX = 1e5 + 9;
const long long int mod = 1e9 + 7;
bool vis[(1 << 20)] = {0};
int main() {
  int i, j, k, n, a[MAX], q;
  cin >> n >> q;
  vector<pair<int, int> > v[MAX];
  for (i = 0; i < n; i++) {
    cin >> a[i];
  }
  int l, x;
  for (i = 0; i < q; i++) {
    cin >> l >> x;
    v[l - 1].push_back(make_pair(x, i));
  }
  long long int ans = 1, res[MAX] = {0};
  vector<int> s;
  vis[0] = 1;
  s.push_back(0);
  for (i = 0; i < n; i++) {
    if (vis[a[i]]) {
      ans = (ans * 2) % mod;
    } else {
      int tmp = s.size();
      for (int j = 0; j < tmp; j++) {
        s.push_back(s[j] ^ a[i]);
        vis[s.back()] = 1;
      }
    }
    for (int j = 0; j < v[i].size(); j++) {
      res[v[i][j].second] = ans * vis[v[i][j].first];
    }
  }
  for (i = 0; i < q; i++) cout << res[i] << "\n";
}
