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;
int n, q;
const int mod = 1e9 + 7;
int a[100001];
bool vis[1 << 20];
vector<int> s{0};
int ans[100001];
vector<pair<int, int> > que[100001];
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cin >> n >> q;
  for (int i = 0; i < n; i++) cin >> a[i];
  for (int i = 0; i < q; i++) {
    int l, x;
    cin >> l >> x;
    que[l].push_back({i, x});
  }
  int ret = 1;
  vis[0] = true;
  for (int i = 0; i < n; i++) {
    int t = a[i];
    if (!vis[t]) {
      vis[t] = true;
      int sz = s.size();
      for (int j = 0; j < sz; j++) {
        vis[s[j] ^ t] = true;
        s.push_back(s[j] ^ t);
      }
    } else
      ret *= 2;
    ret %= mod;
    for (auto e : que[i + 1]) ans[e.first] = vis[e.second] * ret;
  }
  for (int i = 0; i < q; i++) cout << ans[i] << '\n';
  return 0;
}
