#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

using Int = long long;

template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
#define COLOR(s) ("\x1b[" s "m")

////////////////////////////////////////////////////////////////////////////////
template <unsigned M_> struct ModInt {
  static constexpr unsigned M = M_;
  unsigned x;
  constexpr ModInt() : x(0U) {}
  constexpr ModInt(unsigned x_) : x(x_ % M) {}
  constexpr ModInt(unsigned long long x_) : x(x_ % M) {}
  constexpr ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
  constexpr ModInt(long long x_) : x(((x_ %= static_cast<long long>(M)) < 0) ? (x_ + static_cast<long long>(M)) : x_) {}
  ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; }
  ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; }
  ModInt &operator*=(const ModInt &a) { x = (static_cast<unsigned long long>(x) * a.x) % M; return *this; }
  ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); }
  ModInt pow(long long e) const {
    if (e < 0) return inv().pow(-e);
    ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b;
  }
  ModInt inv() const {
    unsigned a = M, b = x; int y = 0, z = 1;
    for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast<int>(q) * z; y = z; z = w; }
    assert(a == 1U); return ModInt(y);
  }
  ModInt operator+() const { return *this; }
  ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; }
  ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); }
  ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); }
  ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); }
  ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); }
  template <class T> friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); }
  template <class T> friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); }
  template <class T> friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); }
  template <class T> friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); }
  explicit operator bool() const { return x; }
  bool operator==(const ModInt &a) const { return (x == a.x); }
  bool operator!=(const ModInt &a) const { return (x != a.x); }
  friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; }
};
////////////////////////////////////////////////////////////////////////////////

constexpr unsigned MO = 164511353;
using Mint = ModInt<MO>;

constexpr int A = 41;
static_assert(((1LL << A) - 1) % MO == 0);

/*
  F[n](x) := \sum[<T> = R^n] x^|T|
  F[0](x) = 1 + x
  
  pi: R^n = R^(n-1) * R -> R^(n-1)
  <T> = R^n ==> <pi(T)> = R^(n-1)
  F[n](x) = \sum[d|K] \mu(d) #{T | <\pi(T)> = R^(n-1) && T \cap \pi^-1(0) \subseteq d R}
          = \sum[d|K] \mu(d) d^(n-1) F[n-1]((x+1)^(K/d)-1)
  
  G[n](y) := F[n](y-1)
  G[0](y) = y
  G[n](y) = \sum[d|K] \mu(d) G[n-1](y^(K/d))
  
  K = \prod[i] P[i]^E[i]
  G[n](y) =: \sum[f] H[n][f] y^(P^f)
  H[0](z) = 1
  H[n](z) = (\prod[i] (z[i]^E[i] - P[i]^(n-1) z[i]^(E[i]-1))) H[n-1](z)
  
  ans = (x (d/dx))^M F[N](x) |[x=1]
      = \sum[k] S(M,k) x^k (d/dx)^k F[N](x) |[x=1]
      = \sum[k] S(M,k) (d/dy)^k G[N](y) |[y=2]
      = \sum[k] S(M,k) (d/dy)^k \sum[f] H[n][f] y^(P^f) |[y=2]
      = \sum[k] S(M,k) \sum[f] H[n][f] (P^f)^(fall k) 2^(P^f-k)
      = \sum[k] S(M,k) \sum[f] H[n][f] \sum[l] s(k,l) (P^f)^l 2^(P^f-k)
      = \sum[l] (\sum[k] S(M,k) s(k,l) 2^-k) \sum[f] H[n][f] (P^f)^l 2^(P^f)
  
  z^f |-> (P^f)^l  (z <- P^l z)
  z^f |-> 2^(P^f) == 2^(P^f mod A)
  
  \prod[0<=n<N] (p^(le) z^e - p^n p^(l(e-1)) z^(e-1))
  = (-1)^N p^(binom(N,2) Nl(e-1)) \prod[0<=n<N] (1 - p^(l-n) z)
*/

// \prod (1 - c z)  mod (z^A - z)
namespace que {
int lens[2];
Mint css[2][101'010];
Mint dss[2][101'010][A];
void init() {
  for (int i = 0; i < 2; ++i) {
    lens[i] = 0;
    fill(dss[i][0], dss[i][0] + A, 0);
    dss[i][0][0] = 1;
  }
}
void push(int i, Mint c) {
  css[i][++lens[i]] = c;
  Mint *crt = dss[i][lens[i] - 1];
  Mint *nxt = dss[i][lens[i]];
  for (int f = 0; f < A; ++f) nxt[f] = crt[f];
  for (int f = 0; f < A - 1; ++f) nxt[f + 1] -= crt[f] * c;
  nxt[1] -= crt[A - 1] * c;
}
void push(Mint c) {
  push(1, c);
}
void pop() {
  if (!lens[0]) {
    for (int j = lens[1]; j > 0; --j) push(0, css[1][j]);
    lens[1] = 0;
  }
  assert(lens[0]);
  --lens[0];
}
Mint prod[2 * A - 1];
void get() {
  fill(prod, prod + (2 * A - 1), 0);
  for (int f0 = 0; f0 < A; ++f0) for (int f1 = 0; f1 < A; ++f1) {
    prod[f0 + f1] += dss[0][lens[0]][f0] * dss[1][lens[1]][f1];
  }
  for (int f = 1; f < A; ++f) {
    prod[f] += prod[A - 1 + f];
  }
}
}  // que

int N, K, M;
int T;

Mint s[1010][1010];
Mint S[1010][1010];

int I;
vector<int> P, E;

Mint hss[1010][A];

int main() {
  for (; ~scanf("%d%d%d", &N, &K, &M); ) {
    scanf("%d", &T);
    assert(T == 1);
    
    for (int m = 0; m <= M; ++m) {
      s[m][0] = 0;
      s[m][m] = 1;
      for (int k = 1; k < m; ++k) {
        s[m][k] = s[m - 1][k - 1] - (m - 1) * s[m - 1][k];
      }
    }
    for (int m = 0; m <= M; ++m) {
      S[m][0] = 0;
      S[m][m] = 1;
      for (int k = 1; k < m; ++k) {
        S[m][k] = S[m - 1][k - 1] + k * S[m - 1][k];
      }
    }
    
    P.clear();
    E.clear();
    {
      int k = K;
      for (int p = 2; p * p <= k; ++p) if (k % p == 0) {
        int e = 0;
        do {
          ++e;
          k /= p;
        } while (k % p == 0);
        P.push_back(p);
        E.push_back(e);
      }
      if (k > 1) {
        P.push_back(k);
        E.push_back(1);
      }
    }
    I = P.size();
cerr<<"N = "<<N<<", K = "<<K<<", M = "<<M<<", I = "<<I<<", P = "<<P<<", E = "<<E<<endl;
    
    memset(hss, 0, sizeof(hss));
    for (int l = 0; l <= M; ++l) {
      hss[l][0] = 1;
    }
    for (int i = 0; i < I; ++i) {
      que::init();
      Mint pl = Mint(P[i]).pow(-N);
      for (int n = N; --n >= 1; ) {
        pl *= P[i];
        que::push(pl);
      }
      for (int l = 0; l <= M; ++l) {
        // (l-N, l]
        pl *= P[i];
        que::push(pl);
        que::get();
        {
          const Mint coef = ((N&1)?-1:+1) * Mint(P[i]).pow(1LL*N*(N-1)/2 + 1LL*N*l*(E[i]-1));
          Mint tmp[A] = {};
          int pf = 1;
          for (int f = 0; f < A; ++f) {
            const Mint t = coef * que::prod[f];
            for (int a = 0; a < A; ++a) {
              tmp[(a + pf) % A] += hss[l][a] * t;
            }
            (pf *= P[i]) %= A;
          }
          copy(tmp, tmp + A, hss[l]);
        }
        que::pop();
      }
    }
    
    Mint ans = 0;
    for (int l = 0; l <= M; ++l) {
      // (\sum[k] S(M,k) s(k,l) 2^-k)
      Mint coef = 0;
      {
        Mint two = Mint(2).pow(-M);
        for (int k = M; k >= l; --k) {
          coef += S[M][k] * s[k][l] * two;
          two *= 2;
        }
      }
      Mint sum = 0;
      for (int a = 0; a < A; ++a) {
        sum += hss[l][a] * Mint(1LL << a);
      }
      ans += coef * sum;
    }
    printf("%u\n", ans.x);
  }
  return 0;
}