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 int INF = 1 << 30;
const double eps = 1e-6;
const int mod = 1000000007;
struct Linear_Basis {
  static const int N = 20;
  long long d[N + 5];
  vector<long long> v;
  bool zero;
  void init() {
    zero = 0;
    memset(d, 0, sizeof d);
    v.clear();
  }
  void insert(long long x) {
    for (int i = N; i >= 0; i--) {
      if (((x >> i) & 1) == 0) continue;
      if (!d[i]) {
        d[i] = x;
        break;
      }
      x ^= d[i];
    }
  }
  void build() {
    for (int i = N; i >= 0; i--)
      for (int j = i - 1; j >= 0; j--)
        if (d[i] & (1ll << j)) d[i] ^= d[j];
  }
  bool que_exit(long long x) {
    for (int i = 62; i >= 0 && x; i--)
      if (x & (1ll << i)) x ^= d[i];
    return x == 0;
  }
  int que_base() {
    long long res = 0;
    for (int i = 0; i <= N; i++)
      if (d[i]) res++;
    return res;
  }
} lb;
int n, q;
int a[maxn];
vector<pair<int, int> > v[maxn];
int ans[maxn];
int main() {
  scanf("%d%d", &n, &q);
  for (int i = 0; i < n; i++) scanf("%d", a + i);
  for (int i = 0; i < q; i++) {
    int l, x;
    scanf("%d%d", &l, &x);
    v[l - 1].push_back(make_pair(x, i));
  }
  lb.init();
  int res = 1;
  for (int i = 0; i < n; i++) {
    if (lb.que_exit(a[i]))
      res = res * 2 % mod;
    else
      lb.insert(a[i]);
    for (int j = 0; j < v[i].size(); j++)
      if (lb.que_exit(v[i][j].first)) ans[v[i][j].second] = res;
  }
  for (int i = 0; i < q; i++) printf("%d\n", ans[i]);
  return 0;
}
