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 maxn = 100005;
const long long INF = 1000000009;
const long long mod = 1000000007;
struct Linear_Basis {
  int cnt, usedcnt;
  int p[70];
  void init() {
    memset(p, 0, sizeof(p));
    cnt = 0;
    usedcnt = 0;
  }
  bool Insert(int x) {
    for (int i = 30; i >= 0; i--) {
      if ((x >> i) & 1) {
        if (!p[i]) {
          p[i] = x;
          usedcnt++;
          break;
        }
        x ^= p[i];
      }
    }
    if (x > 0) cnt++;
    return x > 0;
  }
  bool check(int x) {
    for (int i = 30; i >= 0; i--) {
      if ((x >> i) & 1) {
        if (p[i]) x ^= p[i];
      }
    }
    return x > 0;
  }
} sol;
struct node {
  int l, x, id;
  bool operator<(const node &hs) const { return l < hs.l; }
};
node Q[maxn];
int a[maxn];
long long p2[maxn], ans[maxn];
int main() {
  p2[0] = 1;
  for (int i = 1; i < maxn; i++) p2[i] = p2[i - 1] * 2ll % mod;
  int n, q;
  scanf("%d%d", &n, &q);
  for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
  for (int i = 1; i <= q; i++) scanf("%d%d", &Q[i].l, &Q[i].x), Q[i].id = i;
  sort(Q + 1, Q + q + 1);
  int now = 1;
  sol.init();
  for (int i = 1; i <= q; i++) {
    while (now <= Q[i].l) sol.Insert(a[now]), now++;
    if (!sol.check(Q[i].x)) ans[Q[i].id] = p2[Q[i].l - sol.usedcnt];
  }
  for (int i = 1; i <= q; i++) printf("%lld\n", ans[i]);
  return 0;
}
