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>
int __nextXZW(int v) {
  int t = v | (v - 1);
  int w = (t + 1) | (((~t & -~t) - 1) >> (__builtin_ctz(v) + 1));
  return w;
}
using namespace std;
const long long MOD = (long long)1e9 + 7;
const long long N = 1e5 + 5, inf = 1e9 + 5000;
long long add(long long x, long long y) {
  x += y;
  if (x >= MOD) return x - MOD;
  return x;
}
long long sub(long long x, long long y) {
  x -= y;
  if (x < 0) return x + MOD;
  return x;
}
long long mult(long long x, long long y) { return (x * y) % MOD; }
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
int basis[N][32];
int basis_sz[N];
void insert_vec(int pref, int x) {
  for (int i = 30; i >= 0; i--) {
    if (!(x & (1 << i))) continue;
    if (!basis[pref][i]) {
      basis[pref][i] = x;
      basis_sz[pref]++;
      return;
    }
    x ^= basis[pref][i];
  }
}
bool can(int pref, int x) {
  for (int i = 30; i >= 0; i--) {
    if (!(x & (1 << i))) continue;
    if (!basis[pref][i]) return false;
    x ^= basis[pref][i];
  }
  return true;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  vector<long long> pows2(N, 1);
  for (int i = 1; i < N; i++) pows2[i] = mult(pows2[i - 1], 2);
  int n, q;
  cin >> n >> q;
  for (long long i = 0; i < n; i++) {
    int x;
    cin >> x;
    insert_vec(i, x);
    for (int j = 0; j <= 30; j++) basis[i + 1][j] = basis[i][j];
    basis_sz[i + 1] = basis_sz[i];
  }
  while (q--) {
    int l, x;
    cin >> l >> x;
    l--;
    if (can(l, x))
      cout << pows2[l + 1 - basis_sz[l]] << '\n';
    else
      cout << 0 << '\n';
  }
  return 0;
}
