#include <bits/stdc++.h>
using namespace std;
vector<pair<int, int> > Q[100005];
vector<int> S;
bool chk[1048577];
int n, q, arr[100005], ans[100005];
int main() {
  int i, j, l, x;
  scanf("%d %d", &n, &q);
  for (i = 1; i <= n; i++) scanf("%d", &arr[i]);
  for (i = 1; i <= q; i++) {
    scanf("%d %d", &l, &x);
    Q[l].push_back(make_pair(x, i));
  }
  chk[0] = true;
  S.push_back(0);
  x = 1;
  for (i = 1; i <= n; i++) {
    if (!chk[arr[i]]) {
      for (j = S.size() - 1; j >= 0; j--) {
        if (!chk[arr[i] ^ S[j]]) {
          S.push_back(arr[i] ^ S[j]);
          chk[arr[i] ^ S[j]] = true;
        }
      }
    } else
      x = (x * 2) % 1000000007;
    for (j = Q[i].size() - 1; j >= 0; j--)
      ans[Q[i][j].second] = chk[Q[i][j].first] * x;
  }
  for (i = 1; i <= q; i++) printf("%d\n", ans[i]);
  return 0;
}

### Prompt

Your task is to create a CPP solution to the following problem:

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.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
vector<pair<int, int> > Q[100005];
vector<int> S;
bool chk[1048577];
int n, q, arr[100005], ans[100005];
int main() {
  int i, j, l, x;
  scanf("%d %d", &n, &q);
  for (i = 1; i <= n; i++) scanf("%d", &arr[i]);
  for (i = 1; i <= q; i++) {
    scanf("%d %d", &l, &x);
    Q[l].push_back(make_pair(x, i));
  }
  chk[0] = true;
  S.push_back(0);
  x = 1;
  for (i = 1; i <= n; i++) {
    if (!chk[arr[i]]) {
      for (j = S.size() - 1; j >= 0; j--) {
        if (!chk[arr[i] ^ S[j]]) {
          S.push_back(arr[i] ^ S[j]);
          chk[arr[i] ^ S[j]] = true;
        }
      }
    } else
      x = (x * 2) % 1000000007;
    for (j = Q[i].size() - 1; j >= 0; j--)
      ans[Q[i][j].second] = chk[Q[i][j].first] * x;
  }
  for (i = 1; i <= q; i++) printf("%d\n", ans[i]);
  return 0;
}

```