Problem: A running competition is going to be held soon. The stadium where the competition will be held can be represented by several segments on the coordinate plane:

  * two horizontal segments: one connecting the points (0, 0) and (x, 0), the other connecting the points (0, y) and (x, y); 
  * n + 1 vertical segments, numbered from 0 to n. The i-th segment connects the points (a_i, 0) and (a_i, y); 0 = a_0 < a_1 < a_2 < ... < a_{n - 1} < a_n = x. 



For example, here is a picture of the stadium with x = 10, y = 5, n = 3 and a = [0, 3, 5, 10]:

<image>

A lap is a route that goes along the segments, starts and finishes at the same point, and never intersects itself (the only two points of a lap that coincide are its starting point and ending point). The length of a lap is a total distance travelled around it. For example, the red route in the picture representing the stadium is a lap of length 24.

The competition will be held in q stages. The i-th stage has length l_i, and the organizers want to choose a lap for each stage such that the length of the lap is a divisor of l_i. The organizers don't want to choose short laps for the stages, so for each stage, they want to find the maximum possible length of a suitable lap.

Help the organizers to calculate the maximum possible lengths of the laps for the stages! In other words, for every l_i, find the maximum possible integer L such that l_i mod L = 0, and there exists a lap of length exactly L.

If it is impossible to choose such a lap then print -1.

Input

The first line contains three integers n, x and y (1 ≤ n, x, y ≤ 2 ⋅ 10^5, n ≤ x).

The second line contains n + 1 integers a_0, a_1, ..., a_n (0 = a_0 < a_1 < a_2 < ... < a_{n - 1} < a_n = x).

The third line contains one integer q (1 ≤ q ≤ 2 ⋅ 10^5) — the number of stages.

The fourth line contains q even integers l_1, l_2, ..., l_q (4 ≤ l_i ≤ 10^6) — the lengths of the stages. 

Output

Print q numbers. The i-th number should be equal to the maximum possible length of a suitable lap for the i-th stage, or -1 if it is impossible to choose a lap for that stage.

Example

Input


3 10 5
0 3 5 10
6
24 30 14 16 18 10


Output


24 30 14 16 -1 -1 

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int mod = 998244353;
int mul(int x, int y) { return (long long)x * y % mod; }
int add(int x, int y) {
  x += y;
  return x >= mod ? x - mod : x;
}
int sub(int x, int y) {
  x -= y;
  return x < 0 ? x + mod : x;
}
int powmod(int x, int k) {
  int ans = 1;
  for (; k; k >>= 1, x = mul(x, x))
    if (k & 1) ans = mul(ans, x);
  return ans;
}
int mul_inv(int x) { return powmod(x, mod - 2); }
void fft(int a[], int n, bool inv) {
  for (int i = 1, j = 0; i < n; i++) {
    int k = n;
    do j ^= k >>= 1;
    while (~j & k);
    if (j > i) swap(a[i], a[j]);
  }
  for (int j = 2; j <= n; j <<= 1) {
    int ang = powmod(3, (mod - 1) / j);
    if (inv) ang = mul_inv(ang);
    for (int i = 0; i < n / j; i++) {
      int cur = 1;
      for (int k = i * j; k < i * j + j / 2; k++) {
        int tmp = mul(cur, a[k + j / 2]);
        a[k + j / 2] = sub(a[k], tmp);
        a[k] = add(a[k], tmp);
        cur = mul(cur, ang);
      }
    }
  }
  int m = mul_inv(n);
  if (inv)
    for (int i = 0; i < n; i++) a[i] = mul(a[i], m);
}
const int N = 1 << 19;
int a[N], b[N], c[N];
int can[N << 2];
int main() {
  int n, x, y;
  scanf("%i %i %i", &n, &x, &y);
  for (int i = 1; i <= n + 1; i++) {
    int tmp;
    scanf("%i", &tmp);
    a[tmp] = 1;
    b[x - tmp] = 1;
  }
  fft(a, N, 0);
  fft(b, N, 0);
  for (int i = 0; i < N; i++) a[i] = mul(a[i], b[i]);
  fft(a, N, 1);
  for (int i = x + 1; i < N; i++) c[i - x] = a[i] > 0;
  for (int i = 1; i < N; i++)
    if (c[i]) {
      int len = i * 2 + y * 2;
      can[len] = 1;
    }
  int q;
  scanf("%i", &q);
  while (q--) {
    int o, ans = -1;
    scanf("%i", &o);
    for (int i = 1; i * i <= o; i++)
      if (o % i == 0) {
        if (can[i]) ans = max(ans, i);
        if (can[o / i]) ans = max(ans, o / i);
      }
    printf("%i ", ans);
  }
  return 0;
}