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;
int power(int x, int p) {
  if (p == 0) return 1;
  if (p % 2) return (x * 1LL * power(x, p - 1)) % MOD;
  int y = power(x, p / 2) % MOD;
  return (y * 1LL * y) % MOD;
}
const int LOG_A = 20;
const int N = 1e5;
int basis[N][LOG_A];
int sz[N];
int totsz;
void insertVector(int mask, int j) {
  for (int i = 0; i < (LOG_A); i++)
    if (j) basis[j][i] = basis[j - 1][i];
  for (int i = 0; i < (LOG_A); i++) {
    if ((mask & 1 << i) == 0) continue;
    if (!basis[j][i]) {
      basis[j][i] = mask;
      totsz++;
      return;
    }
    mask ^= basis[j][i];
  }
}
bool is_representable_using_basis(int mask, int j) {
  for (int i = 0; i < (LOG_A); i++) {
    if ((mask & 1 << i) == 0) continue;
    if (!basis[j][i]) {
      return false;
    }
    mask ^= basis[j][i];
  }
  return true;
}
void solve() {
  int n, q;
  cin >> n >> q;
  int arr[n];
  for (int i = 0; i < (n); i++) cin >> arr[i];
  for (int i = 0; i < (n); i++) {
    insertVector(arr[i], i);
    sz[i] = totsz;
  }
  while (q--) {
    int l, x;
    cin >> l >> x;
    if (is_representable_using_basis(x, l - 1)) {
      cout << power(2, l - sz[l - 1]) << endl;
    } else {
      cout << "0" << endl;
    }
  }
}
signed main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int t;
  t = 1;
  while (t--) solve();
}
