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 MAX = 1e5 + 1;
const int MOD = 1e9 + 7;
int otr[(1 << 20) + 1];
vector<pair<int, int>> x[MAX];
void solve() {
  long long a, b;
  cin >> a >> b;
  vector<int> mass(a);
  vector<int> res(b);
  for (int i = 0; i < a; ++i) {
    cin >> mass[i];
  }
  int l, r;
  for (int i = 0; i < b; ++i) {
    cin >> l >> r;
    x[l - 1].push_back(make_pair(i, r));
  }
  otr[0] = 1;
  vector<int> cSt;
  cSt.push_back(0);
  long long ans = 1;
  for (int i = 0; i < a; ++i) {
    if (otr[mass[i]]) {
      ans = (ans * 2) % MOD;
    } else {
      int size = cSt.size();
      for (int j = 0; j < size; ++j) {
        cSt.push_back(mass[i] ^ cSt[j]);
        otr[cSt.back()] = 1;
      }
    }
    for (auto it = x[i].begin(); it != x[i].end(); ++it) {
      res[it->first] = ans * otr[it->second];
    }
  }
  for (int i = 0; i < b; ++i) {
    cout << res[i] << endl;
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cout.setf(ios::fixed);
  cout.precision(2);
  solve();
  return 0;
}
