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 MOD = 1e9 + 7;
long long power(long long b, long long p) {
  return p ? ((p & 1 ? b : 1) * power((b * b) % MOD, p >> 1)) % MOD : 1LL;
}
const int d = 20;
vector<vector<long long> > basis;
vector<long long> sz;
void init(int n) {
  basis.resize(n, vector<long long>(d));
  sz.resize(n);
}
bool poss(int l, int x) {
  for (int i = 0; i < d; i++) {
    if (!(x & (1 << i))) continue;
    if (!basis[l][i]) {
      return false;
    }
    x ^= basis[l][i];
  }
  return true;
}
void insertVector(int mask, vector<long long>& basis, int& sz) {
  for (int i = 0; i < d; i++) {
    if (!(mask & (1 << i))) continue;
    if (!basis[i]) {
      basis[i] = mask;
      ++(sz);
      break;
    }
    mask ^= basis[i];
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  ;
  int n, q;
  cin >> n >> q;
  vector<long long> a(n);
  for (auto& i : a) cin >> i;
  vector<pair<long long, long long> > query(q);
  for (int i = 0; i < q; i++) {
    cin >> query[i].first >> query[i].second;
    --query[i].first;
  }
  init(n);
  for (int i = 0; i < n; i++) {
    int size = 0;
    if (i > 0) {
      for (int j = 0; j < d; j++) basis[i] = basis[i - 1];
      size = sz[i - 1];
    }
    insertVector(a[i], basis[i], size);
    sz[i] = size;
  }
  for (auto i : sz) cerr << i << " ";
  cerr << '\n';
  for (int i = 0; i < q; i++) {
    int ans = 0;
    if (poss(query[i].first, query[i].second)) {
      ans = power(2, query[i].first + 1 - sz[query[i].first]);
    }
    cout << ans << '\n';
  }
  return 0;
}
