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 N = 1e5 + 10, LOG_A = 21;
long long int basis[LOG_A];
long long int sz = 0;
void insertVector(long long int mask) {
  for (long long int i = 0; i < LOG_A; i++) {
    if ((mask & 1LL << i) == 0) continue;
    if (!basis[i]) {
      basis[i] = mask;
      sz++;
      return;
    }
    mask ^= basis[i];
  }
}
bool check(long long int mask) {
  for (long long int i = 0; i < LOG_A; i++) {
    if ((mask & (1LL << i)) == 0) continue;
    if (basis[i] == 0) {
      return false;
    }
    mask = mask ^ basis[i];
  }
  return true;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int n, q;
  cin >> n >> q;
  int arr[n + 4];
  for (int i = 1; i <= n; i++) {
    cin >> arr[i];
  }
  vector<pair<int, int>> v[n + 3];
  for (int i = 1; i <= q; i++) {
    int k, x;
    cin >> k >> x;
    v[k].push_back({x, i});
  }
  int pow2[N];
  pow2[0] = 1;
  for (int i = 1; i < N; i++) pow2[i] = (pow2[i - 1] * 2) % 1000000007;
  int ans_mp[q + 3];
  for (int i = 1; i <= n; i++) {
    insertVector(arr[i]);
    for (auto j : v[i]) {
      if (check(j.first))
        ans_mp[j.second] = pow2[i - sz];
      else
        ans_mp[j.second] = 0;
    }
  }
  for (int i = 1; i <= q; i++) cout << ans_mp[i] << '\n';
}
