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;
long long mod = 0;
vector<long long> fact;
long long gcd(long long a, long long b, long long& x, long long& y) {
  if (a == 0) {
    x = 0;
    y = 1;
    return b;
  }
  long long x1, y1;
  long long d = gcd(b % a, a, x1, y1);
  x = y1 - (b / a) * x1;
  y = x1;
  return d;
}
long long reverse_value(long long a) {
  long long x, y;
  long long g = gcd(a, mod, x, y);
  if (g != 1)
    return 0;
  else {
    x = (x % mod + mod) % mod;
    return x;
  }
}
long long C(long long n, long long k) {
  long long V1 = reverse_value(fact[k]);
  long long V2 = reverse_value(fact[n - k]);
  return fact[n] * V1 * V2 % mod;
}
int32_t main() {
  long long n, m, a, q;
  cin >> n >> m >> a >> q;
  vector<long long> pows(1e6 + 1, 1);
  for (long long i = 1; i <= 1e6; ++i) {
    pows[i] = pows[i - 1] * a % q;
    if (pows[i] == 1 && mod == 0) {
      mod = i;
    }
  }
  fact.resize(1e6 + 124, 1);
  for (long long i = 1; i < 1e6 + 124; ++i) {
    fact[i] = (fact[i - 1] * i) % mod;
  }
  vector<long long> ans(1, 0);
  long long C_n = m;
  long long C_k = 0;
  for (long long i = 0; i < n; ++i) {
    if (C_k <= C_n) {
      ans.push_back((ans[ans.size() - 1] + C(C_n, C_k)) % mod);
    } else {
      ans.push_back(ans[ans.size() - 1]);
    }
    C_k += 1;
  }
  reverse(ans.begin(), ans.end());
  for (long long i = 0; i < n; ++i) {
    cout << pows[ans[i]] << " ";
  }
}
