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;
using llint = long long;
const int N = 1e6 + 200;
int phi;
int n, m, a, q;
llint fac[N];
llint inv[N];
llint cm[N];
llint dd[N];
llint mul(llint a, llint b, llint m) {
  a %= m, b %= m;
  a = a * b % m;
  if (a < 0) a += m;
  return a;
}
llint mypw(llint a, llint b, llint phi) {
  llint ret = 1;
  while (b) {
    if (b & 1) ret = ret * a % phi;
    a = a * a % phi;
    b >>= 1;
  }
  return ret;
}
void init() {
  fac[0] = 1;
  for (int i = 1; i < N; ++i) {
    fac[i] = fac[i - 1] * i % phi;
  }
  for (int i = 0; i < N; ++i) {
    inv[i] = mypw(fac[i], phi - 2, phi);
  }
}
llint C(int a, int b) {
  if (a < 0 || b < 0 || a < b) return 0;
  return fac[a] * inv[b] % phi * inv[a - b] % phi;
}
llint add(llint a, llint b, int phi) {
  a = (a + b) % phi;
  if (a < 0) a += phi;
  return a;
}
void run() {
  scanf("%d%d%d%d", &n, &m, &a, &q);
  llint p = 1;
  phi = -1;
  for (int i = 1;; ++i) {
    p = mul(p, a, q);
    if (p == 1) {
      phi = i;
      break;
    }
  }
  init();
  for (int i = 0; i <= m; ++i) {
    cm[i] = C(m, i);
  }
  dd[0] = cm[0];
  for (int i = 1; i <= m; ++i) {
    dd[i] = add(dd[i - 1], cm[i], phi);
  }
  vector<int> coef(n, 0);
  int k = 0;
  for (int i = n - 1; i >= 0; --i) {
    coef[i] = dd[k];
    k++;
    k = min(m, k);
  }
  for (int i = 0; i < n; ++i) {
    printf("%lld%c", mypw(a, coef[i], q), " \n"[i == n - 1]);
  }
}
int main() {
  run();
  return 0;
}
