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 LOG_D = 20;
struct State {
  long long int size_basis;
  vector<long long int> basis;
  State() {}
  State(long long int size_basis, vector<long long int> basis)
      : size_basis(size_basis), basis(basis) {}
};
vector<long long int> basis(LOG_D);
long long int sz_basis = 0;
const long long int MOD = 1e9 + 7;
void insert_vector(long long int mask) {
  for (int i = LOG_D - 1; i >= 0; i--) {
    if (!(mask & (1LL << i))) continue;
    if (!basis[i]) {
      basis[i] = mask;
      sz_basis++;
      return;
    }
    mask ^= basis[i];
  }
}
bool is_part(long long int mask, vector<long long int> basis) {
  for (int i = LOG_D - 1; i >= 0; i--) {
    if (!(mask & (1LL << i))) continue;
    if (!basis[i]) return false;
    mask ^= basis[i];
  }
  return true;
}
long long int binPow(long long int a, long long int b) {
  long long int res = 1;
  while (b) {
    if (b & 1) res = res * a % MOD;
    b >>= 1;
    a = a * a % MOD;
  }
  return res;
}
int main() {
  ;
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  long long int n, q;
  cin >> n >> q;
  vector<long long int> nums(n);
  vector<State> states(n);
  for (int i = 0; i < n; i++) {
    long long int x;
    cin >> x;
    insert_vector(x);
    states[i] = State(sz_basis, basis);
  }
  while (q--) {
    long long int l, x;
    cin >> l >> x;
    if (is_part(x, states[l - 1].basis)) {
      cout << binPow(2, l - states[l - 1].size_basis) << '\n';
    } else {
      cout << 0 << '\n';
    }
  }
  return 0;
}
