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>
#pragma GCC target("avx2")
#pragma GCC optimization("O3")
#pragma GCC optimization("unroll-loops")
using namespace std;
template <class T1, class T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
  os << "{" << p.first << "," << p.second << "}";
  return os;
}
const int N = 3e5 + 5;
const int oo = 1e9 + 7;
const int LOGN = 30;
long long bigmod(long long a, long long p, long long m) {
  long long res = 1;
  long long x = a;
  while (p) {
    if (p & 1) {
      res = (res * x) % m;
    }
    x = (x * x) % m;
    p = p >> 1;
  }
  return res;
}
int basis[N][LOGN];
void insert_vec(int t, int x) {
  for (int i = LOGN - 1; i >= 0; i--) basis[t][i] = basis[t - 1][i];
  for (int i = LOGN - 1; i >= 0; i--) {
    if ((x >> i) & 1) {
      if (!basis[t][i]) {
        basis[t][i] = x;
        return;
      } else {
        x ^= basis[t][i];
      }
    }
  }
}
int ans(int t, int x) {
  int tot = t;
  for (int i = LOGN - 1; i >= 0; i--) {
    if (basis[t][i]) {
      tot--;
      if ((x >> i) & 1) x ^= basis[t][i];
    } else {
      if ((x >> i) & 1) return 0;
    }
  }
  return bigmod(2, tot, oo);
}
int32_t main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int n, q;
  cin >> n >> q;
  for (int i = 1; i <= n; i++) {
    int x;
    cin >> x;
    insert_vec(i, x);
  }
  while (q--) {
    int l, x;
    cin >> l >> x;
    cout << ans(l, x) << "\n";
  }
}
