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;
struct Query {
  int prefixe, nombre;
  int id;
  bool operator<(const Query& autre) const { return prefixe < autre.prefixe; }
};
const int MAXP = 20;
const int MAXN = 100 * 1000 + 10;
const int MOD = 1000 * 1000 * 1000 + 7;
bool prise[MAXP];
int puissance[MAXN];
int iConcerne[MAXP];
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  puissance[0] = 1;
  for (int i = 1; i < MAXN; i++) {
    puissance[i] = (puissance[i - 1] * 2) % MOD;
  }
  int nbNombres, nbQuestions;
  cin >> nbNombres >> nbQuestions;
  int nombres[nbNombres];
  for (int i = 0; i < nbNombres; i++) {
    cin >> nombres[i];
  }
  Query questions[nbQuestions];
  int solution[nbQuestions];
  for (int i = 0; i < nbQuestions; i++) {
    cin >> questions[i].prefixe >> questions[i].nombre;
    questions[i].prefixe--;
    questions[i].id = i;
  }
  sort(questions, questions + nbQuestions);
  int inQuestion = 0;
  int nbPris = 0;
  for (int iN = 0; iN < nbNombres; iN++) {
    for (int i = 0; i < nbPris; i++) {
      if (nombres[iN] & (1 << iConcerne[i])) nombres[iN] ^= nombres[i];
    }
    for (int i = 0; i < MAXP; i++) {
      if (!prise[i] && (nombres[iN] & (1 << i))) {
        swap(nombres[iN], nombres[nbPris]);
        iConcerne[nbPris] = i;
        nbPris++;
        prise[i] = true;
        break;
      }
    }
    while (inQuestion < nbQuestions && questions[inQuestion].prefixe == iN) {
      for (int i = 0; i < nbPris; i++) {
        if (questions[inQuestion].nombre & (1 << iConcerne[i]))
          questions[inQuestion].nombre ^= nombres[i];
      }
      if (questions[inQuestion].nombre == 0) {
        solution[questions[inQuestion].id] = puissance[iN + 1 - nbPris];
      } else {
        solution[questions[inQuestion].id] = 0;
      }
      inQuestion++;
    }
  }
  for (int i = 0; i < nbQuestions; i++) {
    cout << solution[i] << endl;
  }
}
