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 = (int)1e9 + 7;
const int INF = (int)1e9 + 9;
const int MX = (int)1e5 + 5;
struct XorBasis {
  int loga = 20;
  vector<int> basis;
  int sz;
  XorBasis() {
    basis.resize(loga, 0);
    sz = 0;
  }
  void insertVector(int mask) {
    for (int i = 0; i < loga; i++) {
      if ((mask & 1 << i) == 0) continue;
      if (!basis[i]) {
        basis[i] = mask;
        sz++;
        break;
      }
      mask ^= basis[i];
    }
  }
  bool isXorPos(int mask) {
    for (int i = 0; i < loga; i++) {
      if ((mask & 1 << i) == 0) continue;
      if (!basis[i]) return false;
      mask ^= basis[i];
    }
    return true;
  }
};
int n;
int inp[MX];
int q;
pair<int, int> q_data[MX];
vector<int> q_at[MX];
int ans[MX];
int powers[MX];
void aux() {
  powers[0] = 1;
  for (int i = 1; i < MX; i++) powers[i] = (powers[i - 1] * 2LL) % MOD;
}
int main() {
  aux();
  cin >> n >> q;
  for (int i = 1; i <= n; i++) {
    cin >> inp[i];
  }
  int l, x;
  for (int i = 1; i <= q; i++) {
    cin >> l >> x;
    q_data[i] = {l, x};
    q_at[l].push_back(i);
  }
  XorBasis xb;
  for (int i = 1; i <= n; i++) {
    xb.insertVector(inp[i]);
    for (auto j : q_at[i]) {
      int l = q_data[j].first;
      int x = q_data[j].second;
      if (xb.isXorPos(x)) {
        int nonBasisVec = l - xb.sz;
        ans[j] = powers[nonBasisVec];
      }
    }
  }
  for (int i = 1; i <= q; i++) {
    cout << ans[i] << endl;
  }
  return 0;
}
