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;
int baseres(const vector<int> &base, int v) {
  for (auto x : base) v = min(v, v ^ x);
  return v;
}
int baseres(const vector<int> &base, int len, int v) {
  for (int i = 0; i < len; ++i) v = min(v, v ^ base[i]);
  return v;
}
vector<int> baseof(const vector<int> &sum) {
  vector<int> b;
  int n = sum.size();
  for (int i = 0; i < n; ++i) {
    int v = baseres(b, sum[i]);
    if (v) {
      if (bool byYourChoice = 1)
        b.push_back(v);
      else
        b.push_back(sum[i]);
    }
  }
  return b;
}
const int INT_BITS = 32;
int maxSubarrayXORMy(vector<int> set) {
  int n = set.size();
  int cur = 0;
  vector<int> b = baseof(set);
  for (int i = INT_BITS - 1; i >= 0; --i) {
    int ncur = cur + (1 << i);
    if (baseres(b, ncur) < (1 << i)) {
      cur = ncur;
    }
  }
  return cur;
}
int maxSubarrayXOR(vector<int> set) {
  int n = set.size();
  int index = 0;
  for (int i = INT_BITS - 1; i >= 0; i--) {
    int maxInd = index;
    int maxEle = INT_MIN;
    for (int j = index; j < n; j++) {
      if ((set[j] & (1 << i)) != 0 && set[j] > maxEle)
        maxEle = set[j], maxInd = j;
    }
    if (maxEle == INT_MIN) continue;
    swap(set[index], set[maxInd]);
    maxInd = index;
    for (int j = 0; j < n; j++) {
      if (j != maxInd && (set[j] & (1 << i)) != 0)
        set[j] = set[j] ^ set[maxInd];
    }
    index++;
  }
  int res = 0;
  for (int i = 0; i < n; i++) res ^= set[i];
  return res;
}
long long mod = 1e9 + 7;
long long mypow(long long a, long long n) {
  long long res = 1;
  long long base = a;
  while (n > 0) {
    if (n % 2) res = res * base % mod;
    base = base * base % mod;
    n = n / 2;
  }
  return res;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(NULL);
  cout.tie(NULL);
  int n, q;
  cin >> n >> q;
  vector<int> a(n);
  for (int &i : a) cin >> i;
  vector<int> b;
  vector<int> len(n);
  for (int i = 0; i < n; ++i) {
    int r = baseres(b, a[i]);
    if (r) b.push_back(r);
    len[i] = b.size();
  }
  while (q--) {
    int l, x;
    cin >> l >> x;
    if (l == 0) {
      if (x == 0)
        cout << 1 << "\n";
      else
        cout << 0 << "\n";
    } else {
      int rlen = len[l - 1];
      if (baseres(b, rlen, x))
        cout << "0\n";
      else
        cout << (mypow(2, l - rlen)) << "\n";
    }
  }
}
