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;
const int N = 1e5 + 5;
bitset<N * 22> H;
vector<pair<int, int> > Q[N];
vector<int> v;
int A[N], ans[N], n, q, i, j, u, x, t;
int main() {
  cin >> n >> q;
  for (i = 1; i <= n; i++) scanf("%d", A + i);
  for (i = 1; i <= q; i++) {
    scanf("%d%d", &j, &x);
    Q[j].push_back(make_pair(x, i));
  }
  H[0] = 1;
  v.push_back(0);
  for (t = i = 1; i <= n; i++) {
    x = A[i];
    if (H[x])
      t = t * 2 % mod;
    else {
      u = v.size();
      for (j = 0; j < u; j++) {
        v.push_back(v[j] ^ x);
        H[v[j] ^ x] = 1;
      }
    }
    for (auto z : Q[i]) ans[z.second] = H[z.first] ? t : 0;
  }
  for (i = 1; i <= q; i++) cout << ans[i] << endl;
  return 0;
}
