Consider an array A with N elements, all being the same integer a.

Define the product transformation as a simultaneous update Ai = Ai·Ai + 1, that is multiplying each element to the element right to it for <image>, with the last number AN remaining the same. For example, if we start with an array A with a = 2 and N = 4, then after one product transformation A = [4, 4, 4, 2], and after two product transformations A = [16, 16, 8, 2].

Your simple task is to calculate the array A after M product transformations. Since the numbers can get quite big you should output them modulo Q.

Input

The first and only line of input contains four integers N, M, a, Q (7 ≤ Q ≤ 109 + 123, 2 ≤ a ≤ 106 + 123, <image>, <image> is prime), where <image> is the multiplicative order of the integer a modulo Q, see notes for definition.

Output

You should output the array A from left to right.

Example

Input

2 2 2 7


Output

1 2 

Note

The multiplicative order of a number a modulo Q <image>, is the smallest natural number x such that ax mod Q = 1. For example, <image>.
#include <bits/stdc++.h>
using namespace std;
const int maxn = 1e6 + 150;
int n, m, a;
long long q;
long long cm[maxn];
long long partial[maxn];
int mod;
long long powmod(long long a, long long b, long long m) {
  long long tempo;
  if (b == 0) {
    tempo = 1;
  } else if (b == 1)
    tempo = a;
  else {
    long long temp = powmod(a, b / 2, m);
    if (b % 2 == 0) {
      tempo = (temp * temp) % m;
    } else {
      tempo = ((temp * temp) % m) * (a % m);
    }
  }
  return (tempo + m) % m;
}
long long inv(long long x) { return powmod(x, mod - 2, mod); }
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> m >> a >> q;
  mod = 1;
  long long mm = (a + q) % q;
  while (mm != 1) {
    mm *= a;
    mm = (mm + q) % q;
    mod++;
  }
  cm[0] = 1;
  for (int i = 1; i <= n && i <= m; i++) {
    cm[i] = ((cm[i - 1] * (m - (i - 1)) % mod) * inv(i)) % mod;
  }
  partial_sum(cm, cm + maxn, partial);
  for (int i = 0; i < n; i++) {
    printf("%d ", static_cast<int>(powmod(a, partial[n - 1 - i], q)));
  }
  puts("");
}
