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>
const int N = 100005, bit = 22, mod = 1e9 + 7;
int n, m, siz, a[N], base[bit], ans[N];
struct Query {
  int l, x, id;
  inline bool operator<(const Query &rhs) const { return l < rhs.l; }
} q[N];
inline void insert(int x) {
  for (int i = bit - 1; ~i; --i) {
    if ((x >> i) & 1) {
      if (base[i])
        x ^= base[i];
      else {
        base[i] = x;
        ++siz;
        break;
      }
    }
  }
}
inline bool check(int x) {
  for (int i = bit - 1; ~i; --i) {
    if ((x >> i) & 1) {
      if (base[i])
        x ^= base[i];
      else
        return false;
    }
  }
  return true;
}
inline long long qpow(long long x, int exp) {
  long long res = 1;
  while (exp) {
    if (exp & 1) res = res * x % mod;
    x = x * x % mod;
    exp >>= 1;
  }
  return res;
}
int main() {
  scanf("%d%d", &n, &m);
  for (int i = 1; i <= n; ++i) {
    scanf("%d", &a[i]);
  }
  for (int i = 1; i <= m; ++i) {
    scanf("%d%d", &q[i].l, &q[i].x);
    q[i].id = i;
  }
  std::sort(q + 1, q + m + 1);
  for (int i = 1, cnt = 0; i <= m; ++i) {
    while (cnt < q[i].l) insert(a[++cnt]);
    if (check(q[i].x)) ans[q[i].id] = qpow(2, cnt - siz);
  }
  for (int i = 1; i <= m; ++i) printf("%d\n", ans[i]);
  return 0;
}
