#include <bits/stdc++.h>

using namespace std;
typedef long long ll;
typedef __int128 i128;

const int N = 1e6 + 5, mod = 998244353;
ll p;
mt19937_64 rng(1293128);
map<ll, int> mp;
set<ll> qwq;
int qpow(int x, int y)
{
	int ans = 1;
	while(y)
	{
		if(y & 1)
			ans = (ll)ans * x % mod;
		x = (ll)x * x % mod;
		y >>= 1;
	}
	return ans;
}
ll qpow_p(ll x, ll y)
{
	ll ans = 1;
	while(y)
	{
		if(y & 1)
			ans = (i128)ans * x % p;
		x = (i128)x * x % p;
		y >>= 1;
	}
	return ans;
}
void mul_f(vector<ll> &A, vector<ll> B)
{
	int i, j, n, m;
	if(A.empty() || B.empty())
	{
		A.clear();
		return ;
	}
	n = (int)A.size() - 1;
	m = (int)B.size() - 1;
	A.resize(n + m + 1);
	for(i = n + 1; i <= n + m; i++)
		A[i] = 0;
	for(i = n; i >= 0; i--)
	{
		for(j = 1; j <= m; j++)
			A[i + j] = (A[i + j] + (i128)A[i] * B[j]) % p;
		A[i] = (i128)A[i] * B[0] % p;
	}
}
void mod_f(vector<ll> &A, vector<ll> B)
{
	int i, j, n, m;
	ll q;
	while(!B.empty() && !B.back())
		B.pop_back();
	n = (int)A.size() - 1;
	m = (int)B.size() - 1;
	if(n < m)
		return ;
	q = qpow_p(B.back(), p - 2);
	for(auto &o: B)
		o = (i128)o * q % p;
	for(i = n; i >= m; i--)
	{
		q = p - A[i];
		for(j = 1; j <= m; j++)
			A[i - j] = (A[i - j] + (i128)q * B[m - j]) % p;
		A[i] = 0;
	}
	while(!A.empty() && !A.back())
		A.pop_back();
}
vector<ll> qpow_f(vector<ll> A, vector<ll> B, ll y)
{
	vector<ll> ans = {1};
	while(y)
	{
		if(y & 1)
		{
			mul_f(ans, A);
			mod_f(ans, B);
		}
		mul_f(A, A);
		mod_f(A, B);
		y >>= 1;
	}
	return ans;
}
vector<ll> gcd_f(vector<ll> A, vector<ll> B)
{
	ll q;
	while(!A.empty() && !A.back())
		A.pop_back();
	while(!B.empty() && !B.back())
		B.pop_back();
	while(!A.empty())
	{
		B.swap(A);
		if(A.empty())
			break;
		mod_f(A, B);
	}
	q = qpow_p(B.back(), p - 2);
	for(auto &o: B)
		o = (i128)o * q % p;
	return B;
}
vector<ll> facto(vector<ll> A) // A.back() = 1
{
	vector<ll> ans, B, C;
	int i, j, n, m;
	if(A.size() == 1)
		return {};
	if(A.size() == 2)
		return {(p - A[0]) % p};
	do
	{
		B.resize(A.size() - 1);
		for(auto &o: B)
			o = rng() % p;
		B = qpow_f(B, A, (p - 1) / 2);
		while(B.empty())
			B.emplace_back(0);
		B[0] = (B[0] + p - 1) % p;
		B = gcd_f(A, B);
	}
	while(B.size() == 1 || B.size() == A.size());
	n = (int)A.size() - 1;
	m = (int)B.size() - 1;
	C.resize(n - m + 1);
	for(i = n - m; i >= 0; i--)
	{
		C[i] = A[i + m];
		for(j = 0; j < m; j++)
			A[i + j] = (A[i + j] + (i128)(p - C[i]) * B[j]) % p;
		A[i + m] = 0;
	}
	ans = facto(B);
	C = facto(C);
	for(auto o: C)
		ans.emplace_back(o);
	return ans;
}
vector<ll> fact(vector<ll> A)
{
	while(!A.empty() && !A.back())
		A.pop_back();
	if(A.size() <= 1)
		return {};
	vector<ll> B = {0, 1};
	B = qpow_f(B, A, p);
	while(B.size() < 2)
		B.emplace_back(0);
	B[1] = (B[1] + p - 1) % p;
	return facto(gcd_f(A, B));
}
bool ntp[N];
ll prime[N];
int cnt;
ll res[N], val[N], awa[N];
void sieve(int n)
{
	int i, j;
	for(i = 2; i <= n; i++)
	{
		if(!ntp[i])
			prime[++cnt] = i;
		for(j = 1; j <= cnt && i * prime[j] <= n; j++)
		{
			ntp[i * prime[j]] = 1;
			if(!(i % prime[j]))
				break;
		}
	}
}

int main()
{
	// freopen("sqr.in", "r", stdin);
	// freopen("sqr.out", "w", stdout);
	int n, a, b, c, i, j, S, ans = 1;
	ll x, k;
	vector<ll> tmp;
	scanf("%d%d%d%d", &a, &b, &c, &n);
	x = (ll)a * n * n + (ll)b * n + c;
	S = n;
	while((ll)(S + 1) * (S + 1) * (S + 1) <= x)
		S++;
	while((ll)(S + 1) * (S + 1) <= 2ll * n * a + b)
		S++;
	sieve(S);
	for(i = 0; i <= 2 * n; i++)
		awa[i] = (ll)a * i + b;
	for(i = 0; i <= n; i++)
		val[i] = res[i] = (ll)a * i * i + (ll)b * i + c;
	for(i = 1; i <= cnt; i++)
	{
		p = prime[i];
		if(!(a % p))
		{
			if(b % p)
				continue;
			for(j = 1; j <= 2 * n; j++)
				while(!(awa[j] % p))
					awa[j] /= p;
			continue;
		}
		j = (ll)qpow_p(a % p, p - 2) * (p - b % p) % p;
		for(k = (j ? j : p); k <= 2 * n; k += p)
			while(!(awa[k] % p))
				awa[k] /= p;
	}
	for(i = 1; i <= 2 * n; i++)
		if(awa[i] > 1)
			qwq.insert(awa[i]);
	for(auto o: qwq)
		prime[++cnt] = o;
	// printf("EE%d\n", cnt);
	for(i = 1; i <= cnt; i++)
	{
		p = prime[i];
		// if(i > 24300)
		// 	printf("!!%d %lld\n", i, p);
		if(p > 10)
		{
			tmp = fact({c % p, b % p, a % p});
			for(auto o: tmp)
				for(k = (o ? o : p); k <= n; k += p)
					while(!(res[k] % p))
					{
						res[k] /= p;
						mp[p]++;
					}
		}
		else
			for(j = 0; j < p; j++)
				if(!(val[j] % p))
					for(k = (j ? j : p); k <= n; k += p)
						while(!(res[k] % p))
						{
							res[k] /= p;
							mp[p]++;
						}
	}
	for(i = 1; i <= n; i++)
		if(res[i] > 1)
		{
			S = sqrt(res[i]);
			while((ll)(S + 1) * (S + 1) <= res[i])
				S++;
			while((ll)S * S > res[i])
				S--;
			if((ll)S * S == res[i])
				mp[S] += 2;
			else
				mp[res[i]]++;
		}
	for(auto o: mp)
		ans = (ll)ans * qpow(o.first % mod, o.second / 2) % mod;
	ans = (ll)ans * ans % mod;
	printf("%d\n", ans);
	return 0;
}