#include<bits/stdc++.h>
#define L(i, j, k) for(int i = (j); i <= (k); ++i)
#define R(i, j, k) for(int i = (j); i >= (k); --i)
#define ll long long 
#define vi vector < int > 
#define sz(a) ((int) (a).size())
#define ll long long 
#define ull unsigned long long
#define me(a, x) memset(a, x, sizeof(a)) 
using namespace std;
const int N = 1 << 19, mod = 164511353;
int qpow(int x, int y = mod - 2) {
	int res = 1;
	for(; y; x = (ll) x * x % mod, y >>= 1) if(y & 1) res = (ll) res * x % mod;
	return res;
}
int fac[N], ifac[N], inv[N];
void init(int x) {
	fac[0] = ifac[0] = inv[1] = 1;
	L(i, 2, x) inv[i] = (ll) (mod - mod / i) * inv[mod % i] % mod;
	L(i, 1, x) fac[i] = (ll) fac[i - 1] * i % mod, ifac[i] = (ll) ifac[i - 1] * inv[i] % mod;
} 
int C(int x, int y) {
	return x < y || y < 0 ? 0 : (ll) fac[x] * ifac[y] % mod * ifac[x - y] % mod;
}
inline int sgn(int x) {
	return (x & 1) ? mod - 1 : 1;
}

const int r = 41;
int n, k, m, type;
int prm[N], mt[N], rmt[N], cnt[N], top;
int sum[N];
int fen[N];
int val[N];

template < int N > struct deq {
	int L, R;
	int dp[N][41];
	int stk[N], top;
	deq() {
		L = 0, R = -1;
		me(dp[0], 0), dp[0][1] = 1;
	}
	void undo() {
		--top;
	}
	
	int ndp[41];
	void pb(int x) {
		stk[++top] = x;
		memcpy(dp[top], dp[top - 1], sizeof(dp[top]));
		L(i, 1, ::top) {
			int A = mod - qpow(prm[i], x + mod - 1);
			int m1 = mt[i] % 41, m2 = rmt[i] % 41;
			me(ndp, 0);
			L(j, 0, 40) {
				(ndp[m1 * j % 41] += (ll)A * dp[top][j] % mod) %= mod;
				(ndp[m2 * j % 41] += dp[top][j]) %= mod;
			} 
			swap(ndp, dp[top]);
		}
	}
	void move(int l, int r) {
		if(L > R) L = l, R = l - 1;
		// assert(L <= l && R <= r) 
		R(i, r, R + 1) pb(i);
		R = r;
		int tmp = 0;
		vi Z;
		int cnt = 0;
		while(tmp != l - L) Z.emplace_back(stk[top]), tmp += stk[top] < l, undo(), ++cnt;
		while(top && cnt--) Z.emplace_back(stk[top]), undo();
		sort(Z.begin(), Z.end());
		R(i, sz(Z) - 1, 0) if(Z[i] >= l) pb(Z[i]);
		L = l;
	}
} ;
deq < N > T;

int main() {
	ios :: sync_with_stdio(false); 
	cin.tie(0); cout.tie(0);
	init(N - 10);
	cin >> n >> k >> m;
	cin >> type;
	if(type == 1) {
	
	L(i, 2, k) if(k % i == 0) {
		int c = 0;
		while(k % i == 0) k /= i, ++c;
		++top, prm[top] = i, cnt[top] = c, mt[top] = rmt[top] = 1;
		L(j, 1, c) mt[top] *= i;
		L(j, 1, c - 1) rmt[top] *= i;
	} 
	
	L(c, 0, m) {
	T.move(c - n + 1, c);
	int MUL = 1;
	L(i, 1, top) 
		MUL = (ll) MUL * qpow(qpow(rmt[i], c), n) % mod * 
			qpow(prm[i], (ll)n * (n - 1) / 2 % (mod - 1)) % mod * sgn(n) % mod;
	L(x, 0, 40) {
		int pr = (ll)T.dp[T.top][x] * qpow(2, x) % mod;
		(sum[c] += pr) %= mod;
	}
	sum[c] = (ll) sum[c] * MUL % mod;
	}
	
	vi mul(m + 1);
	mul[0] = 1;
	L(i, 0, m) {
		if(i) {
			R(j, i - 1, 0) {
				(mul[j + 1] += mul[j]) %= mod;
				mul[j] = (ll) mul[j] * (mod - (i - 1)) % mod;
			}
		}
		L(j, 0, i) {
			(fen[i] += (ll) mul[j] * sum[j] % mod) %= mod;
		}
	}
	
	L(i, 0, m) 
		fen[i] = (ll)fen[i] * qpow(qpow(2), i) % mod * ifac[i] % mod; 
	L(i, 0, m) {
		L(j, 0, i) {
			(val[j] += (ll)fen[i] * sgn(i - j) % mod * C(i, j) % mod) %= mod;
		}
	}
	
	int ANS = 0;
	L(i, 0, m) {
		(ANS += (ll)val[i] * qpow(i, m) % mod) %= mod;
	}
	cout << ANS << '\n';
	
	}
	return 0;
}