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 = 1e9 + 7;
struct xxj {
  int a[30], sz, n;
  void it(int x) {
    for (int i = 25; i >= 0; i--)
      if ((x >> i) & 1) {
        if (!a[i]) {
          a[i] = x;
          sz++;
          return;
        }
        x ^= a[i];
        if (!x) return;
      }
  }
  bool in(int x) {
    for (int i = 25; i >= 0; i--)
      if ((x >> i) & 1) {
        if (!a[i]) return 0;
        x ^= a[i];
      }
    return 1;
  }
} lb[100010];
long long qp(int x) {
  long long bs = 2ll, ret = 1ll;
  while (x) {
    if (x & 1) ret = ret * bs % mod;
    bs = bs * bs % mod, x >>= 1;
  }
  return ret;
}
int main() {
  int n, q;
  scanf("%d%d", &n, &q);
  for (int i = 1, s; i <= n; i++) {
    lb[i] = lb[i - 1], lb[i].n = lb[i - 1].n + 1;
    scanf("%d", &s);
    lb[i].it(s);
  }
  while (q--) {
    int x, y;
    scanf("%d%d", &x, &y);
    if (lb[x].in(y))
      printf("%lld\n", qp(x - lb[x].sz));
    else
      puts("0");
  }
}
