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 long long int maxC = (1 << 21) + 5, maxN = 1e5 + 22625, MOD = 1e9 + 7;
struct Que {
  long long int l, x, ind;
  Que() {}
  Que(long long int L, long long int X, long long int I) : l(L), x(X), ind(I) {}
};
long long int reachable[maxC], arr[maxN], n, q, ans[maxN], l, x, basisCnt = 1;
Que ques[maxN];
inline void add(long long int x) {
  if (!reachable[x]) {
    basisCnt++;
    for (long long int i = 0; i < maxC; i++) {
      if (reachable[i] && ((i ^ x) < maxC)) reachable[i ^ x] = true;
    }
  }
}
long long int modexp(long long int b, long long int e) {
  if (!b) return 0;
  if (!e) return 1;
  long long int res = modexp(b, e / 2);
  res = res * res % MOD;
  if (e % 2) res = res * b % MOD;
  return res;
}
signed main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  ;
  cin >> n >> q;
  for (long long int i = 0; i < n; i++) cin >> arr[i];
  for (long long int i = 0; i < q; i++) {
    cin >> ques[i].l >> ques[i].x;
    ques[i].l--;
    ques[i].ind = i;
  }
  sort(ques, ques + q, [](const Que a, const Que b) { return a.l < b.l; });
  fill(reachable, reachable + maxC, false);
  reachable[0] = true;
  long long int ci = 0;
  Que cq;
  for (long long int i = 0; i < q; i++) {
    cq = ques[i];
    while (cq.l >= ci) {
      add(arr[ci++]);
    }
    if (!reachable[cq.x])
      ans[cq.ind] = 0;
    else
      ans[cq.ind] = modexp(2, 2 + cq.l - basisCnt);
  }
  for (long long int i = 0; i < q; i++) cout << ans[i] << '\n';
}
