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 + 5;
const int mod = 1e9 + 7;
int n, q, x, y;
int a[MAX];
int s[MAX];
bool m[1 << 22];
vector<int> v;
vector<pair<int, int> > g[MAX];
int main() {
  scanf("%d%d", &n, &q);
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
  }
  for (int i = 1; i <= q; i++) {
    scanf("%d%d", &x, &y);
    g[x].push_back({y, i});
  }
  v.push_back(0);
  m[0] = true;
  int ans = 1;
  for (int i = 1; i <= n; i++) {
    if (m[a[i]]) {
      ans = (ans * 2) % mod;
    } else {
      vector<int> v1;
      for (int u : v) {
        v1.push_back(u ^ a[i]);
        m[u ^ a[i]] = true;
      }
      for (int u : v1) v.push_back(u);
    }
    for (auto u : g[i]) {
      if (m[u.first]) s[u.second] = ans;
    }
  }
  for (int i = 1; i <= q; i++) printf("%d\n", s[i]);
  return 0;
}
