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 = 100000 + 77, Mod = 1000000007;
int n, q, a[N], A[N], Qle[N], Qx[N], now = 1;
vector<int> Q[N], V;
inline void Add(int t) {
  for (int& x : V) t = min(t, x ^ t);
  if (t == 0) {
    now = (now << 1) % Mod;
    return;
  }
  for (int& x : V) x = min(x, x ^ t);
  V.push_back(t);
}
inline bool Get(int t) {
  for (int& x : V) t = min(t, t ^ x);
  return (t < 1);
}
int main() {
  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", Qle + i, Qx + i), Q[Qle[i]].push_back(i);
  for (int i = 1; i <= n; ++i) {
    Add(a[i]);
    for (int id : Q[i]) A[id] = Get(Qx[id]) * now;
  }
  for (int i = 1; i <= q; ++i) printf("%d\n", A[i]);
  return 0;
}
