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;
long long int gmatrix[100009][64];
long long int basis[100009];
void rref(long long int pos, long long int index) {
  for (long long int i = 0; i < pos; i++) {
    if (gmatrix[index][pos] & ((long long int)1 << i))
      gmatrix[index][pos] ^= gmatrix[index][i];
  }
  for (long long int i = 62; i > pos; i--) {
    if (gmatrix[index][i] & ((long long int)1 << pos))
      gmatrix[index][i] ^= gmatrix[index][pos];
  }
}
void add(long long int x, long long int index) {
  basis[index] = basis[index - 1];
  for (long long int i = 62; i >= 0; i--) {
    gmatrix[index][i] = gmatrix[index - 1][i];
  }
  for (long long int i = 62; i >= 0; i--) {
    if (x & ((long long int)1 << i)) {
      if (gmatrix[index][i])
        x ^= gmatrix[index][i];
      else {
        gmatrix[index][i] = x;
        basis[index]++;
        return;
      }
    }
  }
}
bool check(long long int x, long long int index) {
  for (long long int i = 62; i >= 0; i--) {
    if (x & ((long long int)1 << i)) {
      if (gmatrix[index][i])
        x ^= gmatrix[index][i];
      else
        return 0;
    }
  }
  return 1;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long int n, q;
  cin >> n >> q;
  long long int ans[q];
  long long int x, y;
  long long int p[n + 1];
  p[0] = 1;
  for (long long int i = 1; i <= n; i++) {
    cin >> x;
    add(x, i);
    p[i] = (p[i - 1] * 2) % 1000000007;
  }
  for (long long int i = 0; i < q; i++) {
    cin >> y >> x;
    if (check(x, y))
      cout << p[y - basis[y]] << '\n';
    else
      cout << 0 << '\n';
  }
}
