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 const M = 2e6 + 10, mod = 1e9 + 7;
int ans[M], vis[M], a[M];
vector<int> good;
int main() {
  int n, q;
  cin >> n >> q;
  for (int i = 1; i <= n; i++) cin >> a[i];
  good.push_back(0);
  vis[0] = 1;
  ans[0] = 1;
  for (int i = 1; i <= n; i++) {
    if (!vis[a[i]]) {
      int en = (int)good.size();
      for (int j = 0; j < en; j++)
        good.push_back(good[j] xor a[i]), vis[good[j] xor a[i]] = i;
      ans[i] = ans[i - 1];
    } else {
      ans[i] = ans[i - 1] * 2;
      ans[i] %= mod;
    }
  }
  for (int i = 1; i <= q; i++) {
    int l, x;
    cin >> l >> x;
    if (vis[x] && vis[x] <= l) {
      cout << ans[l] << "\n";
    } else
      cout << 0 << "\n";
  }
}
