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 int64_t M1 = 998244353;
const int64_t M2 = 1000000007;
mt19937 rng((uint64_t)chrono::steady_clock::now().time_since_epoch().count());
void solve() {
  int64_t n, q;
  cin >> n >> q;
  vector<int64_t> a(n);
  for (int64_t &i : a) cin >> i;
  vector<pair<int64_t, int64_t>> qry[n];
  vector<int64_t> ans(q);
  for (int64_t i = 0; i < q; i++) {
    int64_t l, x;
    cin >> l >> x;
    qry[l - 1].push_back({x, i});
  }
  vector<int64_t> values({0});
  vector<int64_t> mark(2e6, 0);
  mark[0] = 1;
  int64_t x = 1;
  for (int64_t i = 0; i < n; i++) {
    if (mark[a[i]]) {
      x = (x + x) % M2;
    } else {
      int64_t sz = values.size();
      for (int64_t j = 0; j < sz; j++) {
        values.push_back(values[j] ^ a[i]);
        mark[values.back()] = 1;
      }
    }
    for (auto [xi, ind] : qry[i]) ans[ind] = x * mark[xi];
  }
  for (int64_t i = 0; i < q; i++) cout << ans[i] << "\n";
}
int32_t main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  solve();
}
