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>
std::vector<int> V, Q[1 << 17];
int n, m, a[1 << 17], b[1 << 17], c[1 << 17], A = 1, x;
int C(int x) {
  for (auto o : V) x = std::min(x, x ^ o);
  return x;
}
int main() {
  scanf("%d%d", &n, &m);
  for (int i = 1; i <= n; ++i) scanf("%d", &a[i]);
  for (int i = 1; i <= m; ++i) scanf("%d%d", &x, &b[i]), Q[x].push_back(i);
  for (int i = 1; i <= n; ++i) {
    C(a[i]) ? V.push_back(C(a[i])), 0 : (A *= 2) %= 1000000007;
    for (auto o : Q[i]) c[o] = C(b[o]) ? 0 : A;
  }
  for (int i = 1; i <= m; ++i) printf("%d\n", c[i]);
}
