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 N = 100005;
const int mod = 1e9 + 7;
const int logA = 20;
int n, q;
int a[N];
pair<int, int> question[N];
int ans[N];
vector<pair<int, int> > query;
int basis[N], sz;
long long power(long long x, long long n) {
  long long ans = 1;
  for (int i = 0; i < logA; ++i) {
    if (((n >> i) & 1)) ans = ans * x % mod;
    x = (x * x) % mod;
  }
  return ans;
}
void insertVector(int mask) {
  for (int i = 0; i < logA; ++i) {
    if (!((mask >> i) & 1)) continue;
    if (!basis[i]) {
      basis[i] = mask;
      sz++;
      return;
    }
    mask ^= basis[i];
  }
}
long long checkVector(int l, int mask) {
  for (int i = 0; i < logA; ++i) {
    if (!((mask >> i) & 1)) continue;
    if (!basis[i]) return 0;
    mask ^= basis[i];
  }
  return power(2, l - sz);
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cin >> n >> q;
  for (int i = 1; i <= n; ++i) {
    cin >> a[i];
    query.push_back({i, -1});
  }
  for (int i = 0; i < q; ++i) {
    int l, x;
    cin >> l >> x;
    question[i] = {l, x};
    query.push_back({l, i});
  }
  sort(query.begin(), query.end());
  for (int i = 0; i < query.size(); ++i) {
    int pos = query[i].first, id = query[i].second;
    if (id == -1)
      insertVector(a[pos]);
    else {
      ans[id] = checkVector(pos, question[id].second);
    }
  }
  for (int i = 0; i < q; ++i) cout << ans[i] << '\n';
}
