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 d = 20;
const int N = 100005;
int sz, basis[d], n, a[N], q;
long long int modularExponentiation(long long int x, long long int n) {
  int result = 1;
  while (n > 0) {
    if (n % 2 == 1) result = (result * x) % 1000000007;
    x = (x * x) % 1000000007;
    n = n / 2;
  }
  return result;
}
void insertVector(int mask) {
  for (int i = 0; i < d; i++) {
    if ((mask & 1 << i) == 0) continue;
    if (!basis[i]) {
      basis[i] = mask;
      ++sz;
      return;
    }
    mask ^= basis[i];
  }
}
bool insertVector1(int mask) {
  for (int i = 0; i < d; i++) {
    if ((mask & 1 << i) == 0) continue;
    if (!basis[i]) {
      return 0;
    }
    mask ^= basis[i];
  }
  return 1;
}
void solve() {
  cin >> n >> q;
  for (long long int i = 0; i < n; i++) cin >> a[i];
  pair<long long int, pair<long long int, long long int> > queries[q];
  for (long long int i = 0; i < q; i++) {
    cin >> queries[i].first >> queries[i].second.first;
    queries[i].first--;
    queries[i].second.second = i;
  }
  sort(queries, queries + q);
  long long int j = 0;
  long long int ans[q];
  for (long long int i = 0; i < n; i++) {
    insertVector(a[i]);
    while (j < q && queries[j].first <= i) {
      bool chk = insertVector1(queries[j].second.first);
      long long int temp = 1;
      if (chk == 0) {
        temp = 0;
      } else {
        long long int ex = (i + 1) - sz;
        temp = modularExponentiation(2, ex);
      }
      ans[queries[j].second.second] = temp;
      j++;
    }
  }
  for (long long int i = 0; i < q; i++) cout << ans[i] << "\n";
}
int main() {
  ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0);
  srand(time(NULL));
  ;
  long long int t = 1;
  while (t--) {
    solve();
  }
}
