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 MAX_ENTIERS = (100 * 1000 + 1);
const int MAX_BITS = 20;
const int MOD = (1000 * 1000 * 1000 + 7);
int Vecteurs[MAX_ENTIERS];
int Atteint[MAX_BITS];
int Sol[MAX_ENTIERS];
pair<int, int> Requetes[MAX_ENTIERS];
int nbEntiers, nbRequetes;
void Init() {
  for (int i = 0; i < MAX_BITS; i++) {
    Atteint[i] = -1;
  }
  return;
}
void Read() {
  scanf("%d%d", &nbEntiers, &nbRequetes);
  for (int i = 0; i < nbEntiers; i++) {
    scanf("%d", &Vecteurs[i]);
  }
  for (int i = 0; i < nbRequetes; i++) {
    scanf("%d%d", &Requetes[i].first, &Requetes[i].second);
  }
  return;
}
void Soustrait(int a, int b) {
  for (int i = 0; i < MAX_BITS; i++) {
    Vecteurs[b] ^= (1 << i) & Vecteurs[a];
  }
  return;
}
void SubAll(int a, int bit) {
  for (int i = a + 1; i < MAX_ENTIERS; i++) {
    if (i != a && (Vecteurs[i] & (1 << bit)) > 0) {
      Soustrait(a, i);
    }
  }
  return;
}
void Treat(int act) {
  for (int i = 0; i < MAX_BITS; i++) {
    if ((Vecteurs[act] & (1 << i)) > 0) {
      if (Atteint[i] >= 0) {
        Soustrait(Atteint[i], act);
      } else {
        Atteint[i] = act;
        SubAll(act, i);
        return;
      }
    }
  }
  return;
}
void FillSol() {
  int nb = 1;
  for (int i = 0; i < MAX_ENTIERS; i++) {
    Sol[i] = nb;
    if (Vecteurs[i] == 0) {
      nb = (2 * nb) % MOD;
    }
  }
  return;
}
int Count(int target, int borne) {
  for (int i = 0; i < MAX_BITS; i++) {
    if ((target & (1 << i)) > 0) {
      if (Atteint[i] < 0 || Atteint[i] >= borne) {
        return 0;
      } else {
        target ^= Vecteurs[Atteint[i]];
      }
    }
  }
  if (target != 0) {
    return 0;
  }
  return Sol[borne];
}
void Solve() {
  for (int i = 0; i < MAX_ENTIERS; i++) {
    Treat(i);
  }
  FillSol();
  for (int i = 0; i < nbRequetes; i++) {
    printf("%d\n", Count(Requetes[i].second, Requetes[i].first));
  }
  return;
}
void Print() {
  printf("\n");
  for (int i = 0; i < 10; i++) {
    printf("%d\n", Sol[i]);
  }
  return;
}
int main() {
  Init();
  Read();
  Solve();
  return 0;
}
