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 + 5;
const int MOD = 1e9 + 7;
vector<pair<int, int> > adj[N];
int A[N];
int res[N];
bitset<1 << 20> bs;
vector<int> S;
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  int n, q;
  cin >> n >> q;
  for (int i = 1; i <= n; i++) {
    cin >> A[i];
  }
  for (int i = 1; i <= q; i++) {
    int l, x;
    cin >> l >> x;
    adj[l].emplace_back(x, i);
  }
  bs[0] = 1;
  S.push_back(0);
  int ans = 1;
  for (int i = 1; i <= n; i++) {
    if (bs[A[i]]) {
      ans += ans;
      if (ans >= MOD) ans -= MOD;
    } else {
      int sz = S.size();
      for (int j = 0; j < sz; j++) {
        int ele = S[j] ^ A[i];
        bs[ele] = 1;
        S.push_back(ele);
      }
    }
    for (auto it : adj[i]) {
      if (bs[it.first]) res[it.second] = ans;
    }
  }
  for (int i = 1; i <= q; i++) {
    cout << res[i] << "\n";
  }
  return 0;
}
