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>
const int N = 1e5 + 1, INF = 1e9 + 7;
struct TQuery {
  int l, x, idx;
};
int a[N], ans[N];
TQuery b[N];
inline bool operator<(TQuery lhs, TQuery rhs) { return lhs.l < rhs.l; }
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) scanf("%d%d", &b[i].l, &b[i].x);
  for (int i = 1; i <= q; ++i) b[i].idx = i;
  std::sort(b + 1, b + q + 1);
  std::set<int> s;
  s.insert(0);
  int res = 1, pos = 1;
  for (int i = 1; i <= n; ++i) {
    if (s.find(a[i]) != s.end())
      res = res * 2 % INF;
    else
      for (auto x : s) s.insert(x ^ a[i]);
    while (pos <= q && b[pos].l == i) {
      if (s.find(b[pos].x) != s.end()) ans[b[pos].idx] = res;
      ++pos;
    }
  }
  for (int i = 1; i <= q; ++i) printf("%d\n", ans[i]);
  return 0;
}
