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 = 1000000007;
vector<pair<int, int>> v[100005];
int n, q, x[100005], ans[100005];
vector<int> s;
bool f[(1 << 20)];
int main() {
  cin >> n >> q;
  for (int i = 1; i <= n; i++) cin >> x[i];
  for (int i = 1; i <= q; i++) {
    int l, x;
    cin >> l >> x;
    v[l].push_back({x, i});
  }
  s.push_back(0);
  f[0] = 1;
  int nr = 1;
  for (int i = 1; i <= n; i++) {
    if (f[x[i]])
      nr = (nr * 2) % mod;
    else {
      int aux = s.size();
      for (int j = 0; j < aux; j++) {
        s.push_back(s[j] ^ x[i]);
        f[s.back()] = 1;
      }
    }
    for (int j = 0; j < v[i].size(); j++)
      ans[v[i][j].second] = nr * f[v[i][j].first];
  }
  for (int i = 1; i <= q; i++) cout << ans[i] << "\n";
}
