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 long long MOD = 1e9 + 7;
struct base {
  long long b[30], size;
  void ins(long long num) {
    for (long long i = 23; i >= 0; i--) {
      if (num & (1 << i)) {
        if (b[i] == 0) {
          b[i] = num;
          this->size++;
          break;
        } else {
          num ^= b[i];
        }
      }
    }
  }
  void maintain() {
    for (int i = 0; i <= 23; i++) {
      for (int j = i + 1; j <= 23; j++) {
        if (b[j] & (1 << i)) {
          b[j] ^= b[i];
        }
      }
    }
  }
  long long test(long long num) {
    for (int i = 23; i >= 0; i--) {
      if (num & (1 << i)) num ^= b[i];
    }
    return num;
  }
};
void copy_base(base a, base &b) {
  memcpy(b.b, a.b, sizeof a.b);
  b.size = a.size;
}
base data[100005];
int n, q;
int ksm(long long x, int y) {
  long long ret = 1;
  while (y) {
    if (y & 1) ret = (ret * x) % MOD;
    x = (x * x) % MOD;
    y >>= 1;
  }
  return ret;
}
int main() {
  scanf("%d%d", &n, &q);
  for (int i = 1; i <= n; i++) {
    int tmp;
    scanf("%d", &tmp);
    copy_base(data[i - 1], data[i]);
    data[i].ins(tmp);
    data[i].maintain();
  }
  for (int i = 1; i <= q; i++) {
    int a, b;
    scanf("%d%d", &a, &b);
    if (b == -1) {
      if (a > data[a].size) {
        printf("%d\n", ksm(2, a - data[a].size));
      } else {
        puts("0");
      }
    } else {
      int value = data[a].test(b);
      if (value == 0) {
        printf("%d\n", ksm(2, a - data[a].size));
      } else {
        puts("0");
      }
    }
  }
  return 0;
}
