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 mod = 1e9 + 7;
int a[100005], ans[100005];
vector<pair<int, int> > Q[100005];
bool vis[2000000];
vector<int> dp;
int main() {
  int n, q;
  scanf("%d%d", &n, &q);
  for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
  for (int i = 1; i <= q; i++) {
    int l, x;
    scanf("%d%d", &l, &x);
    Q[l].push_back(pair<int, int>(x, i));
  }
  int res = 1;
  vis[0] = 1;
  dp.push_back(0);
  for (int i = 1; i <= n; i++) {
    if (vis[a[i]])
      res = (res * 2) % mod;
    else {
      for (int j = dp.size() - 1; j >= 0; j--) {
        int x = dp[j];
        dp.push_back(x ^ a[i]);
        vis[x ^ a[i]] = 1;
      }
    }
    for (int j = 0; j < Q[i].size(); j++) {
      int x = Q[i][j].first;
      int idx = Q[i][j].second;
      ans[idx] = res * vis[x];
    }
  }
  for (int i = 1; i <= q; i++) printf("%d\n", ans[i]);
}
