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 N = 1e5 + 10, p = 1e9 + 7;
int n, m, a[N], v[30], cnt, ans[N];
vector<pair<int, int> > q[N];
inline void Append(int x) {
  for (int i = 1; i <= cnt; ++i)
    if ((x ^ v[i]) < x) x = x ^ v[i];
  v[++cnt] = x;
}
inline bool Ask(int x) {
  for (int i = 1; i <= cnt; ++i)
    if ((x ^ v[i]) < x) x = x ^ v[i];
  return x == 0;
}
int main() {
  scanf("%d%d", &n, &m);
  for (int i = 1; i <= n; ++i) scanf("%d", a + i);
  for (int i = 1, x, y; i <= m; ++i)
    scanf("%d%d", &x, &y), q[x].push_back(pair<int, int>(y, i));
  for (int i = 1, no = 1; i <= n; ++i) {
    if (Ask(a[i]))
      no = no * 2 % p;
    else
      Append(a[i]);
    for (vector<pair<int, int> >::iterator it = q[i].begin(); it != q[i].end();
         ++it)
      ans[it->second] = Ask(it->first) ? no : 0;
  }
  for (int i = 1; i <= m; ++i) printf("%d\n", ans[i]);
  return 0;
}
