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;
void toSolve() {
  int N = 200000;
  int n, q;
  int a, b;
  cin >> n >> q;
  int arr[n + 4];
  int finalans[q + 2];
  for (int i = 0; i < n; i++) cin >> arr[i + 1];
  vector<vector<pair<int, int>>> queries(N);
  for (int i = 0; i < q; i++) {
    cin >> a >> b;
    queries[a].push_back({b, i});
  }
  set<int> s;
  s.insert(0);
  long long ans = 1;
  for (int i = 1; i <= n; i++) {
    if (s.find(arr[i]) != s.end()) {
      ans = (ans * 2) % 1000000007;
    } else {
      vector<int> v;
      for (auto x : s) {
        v.push_back(x ^ arr[i]);
      }
      for (auto k : v) {
        s.insert(k);
      }
    }
    for (auto it : queries[i]) {
      if (s.find(it.first) != s.end()) {
        finalans[it.second] = ans;
      } else {
        finalans[it.second] = 0;
      }
    }
  }
  for (int i = 0; i < q; i++) cout << finalans[i] << '\n';
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  toSolve();
  return 0;
}
