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 inf = (1 << 30);
inline long long in() {
  char ch = getchar();
  long long f = 1, tmp = 0;
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    tmp = (tmp << 1) + (tmp << 3) + (ch - '0');
    ch = getchar();
  }
  return tmp * f;
}
const int mod = 1e9 + 7;
const int N = 100010;
int n, m;
long long a[N], mi[N];
struct LB {
  long long a[61], cnt;
  bool ins(long long x) {
    for (int i = 60; i >= 0; i--)
      if (x & (1ll << i)) {
        if (!a[i]) {
          a[i] = x;
          cnt++;
          break;
        }
        x ^= a[i];
      }
    return x > 0;
  }
} Xor[100];
long long query(const LB &c, long long x, int p) {
  for (int i = 60; i >= 0; i--)
    if (x & (1ll << i)) {
      if (!c.a[i]) return 0;
      x ^= c.a[i];
    }
  if (x > 0) return 0;
  return mi[p - c.cnt];
}
int tot, bel[N];
int main() {
  n = in();
  m = in();
  mi[0] = 1;
  for (int i = 1; i < N; i++) mi[i] = mi[i - 1] * 2 % mod;
  for (int i = 1; i <= n; i++) {
    long long x = in();
    LB cur = Xor[tot];
    if (cur.ins(x)) Xor[++tot] = cur;
    bel[i] = tot;
  }
  for (int i = 1; i <= m; i++) {
    long long l = in(), x = in();
    printf("%I64d\n", query(Xor[bel[l]], x, l));
  }
  return 0;
}
