#include<cstdio>
#include<algorithm>
#include<cstring>
#include<cassert>
#include<cmath>
#include<random>
#include<unordered_map>
const int Q=300005;
const int INF=(1<<30);
const int mod=998244353;
typedef long long ll;
#define rg register int
#define cint const register int
//char ibuf[1<<21],*IP1=ibuf,*IP2=ibuf;
//#define gc() (__builtin_expect(IP1==IP2,0)&&(IP2=(IP1=ibuf)+fread(ibuf,1,1<<21,stdin),__builtin_expect(IP1==IP2,0))?EOF:*IP1++)
#define gc getchar
#define pc putchar
inline bool ig(const char c){return c>=48&&c<=57;}
inline void read(rg&oi){char c;rg f=1,res=0;while(c=gc(),(!ig(c))&&c^'-');c^'-'?res=(c^48):f=-1;while(c=gc(),ig(c))res=res*10+(c^48);oi=f*res;}
inline void print(rg oi){char io[23];rg l=0;if(oi<0)pc('-'),oi=~oi+1;do io[++l]=(oi%10+48);while(oi/=10);for(;l;--l)pc(io[l]);}
inline void write(cint oi,const char c){print(oi);pc(c);}char _ST_;
inline int max(cint x,cint y){return x>y?x:y;}
inline int powt(rg x,rg y){rg res=1;for(;y;y>>=1,x=1ll*x*x%mod)(y&1)&&(res=1ll*res*x%mod);return res;}
int A,B,C,n,m;ll f[Q],g[Q],dlt;
std::unordered_map<ll,int>cnt;bool divg;
inline void Fdiv(cint o,cint p){if(o>=1&&o<=n){for(ll&x=f[o];x%p==0;x/=p,++cnt[p]);}}
inline void Gdiv(cint o,cint p){if(o>=1&&o<=m){for(ll&x=g[o];x%p==0;x/=p);}}
struct cpl{int x,y;cpl()=default;cpl(cint X,cint Y):x(X),y(Y){}};
std::random_device sd;std::mt19937 rnd(sd());
inline void upd(cint p){
//	printf("upd:%d\n",p);
	if(p<=1)return;if(p==2||std::__gcd(p,A)!=1){
	for(rg i=1;i<=n;++i)Fdiv(i,p);for(rg i=1;i<=m;++i)Gdiv(i,p);return;}
	const auto inc=[&](cint x,cint y){return x+y<p?x+y:x+y-p;};
	const auto dec=[&](cint x,cint y){return x>=y?x-y:x-y+p;};
	const auto mul=[&](cint x,cint y){return 1ll*x*y%p;};
	const auto Mul=[&](rg&x,cint y){x=1ll*x*y%p;};
	const auto pow=[&](rg x,rg y){rg res=1;for(;y;y>>=1,Mul(x,x))(y&1)&&(Mul(res,x),1);return res;};
	const auto Inv=[&](cint x){return pow(x,p-2);};
	rg w=0;const auto mg=[&](cpl x,cpl y){
	return cpl(inc(mul(x.x,y.x),mul(w,mul(x.y,y.y))),inc(mul(x.x,y.y),mul(x.y,y.x)));};
	std::uniform_int_distribution<int>rng(0,p-1);
	const auto powc=[&](cpl x,rg y){
//	printf("powc:%d %d|%d %d\n",x.x,x.y,y,w);
	cpl res=cpl(1,0);for(;y;y>>=1,x=mg(x,x))(y&1)&&(res=mg(res,x),1);return res;};
	const auto Gsqrt=[&](cint x){
//		write(x,'\n');
		if(pow(x,(p-1)>>1)==p-1)return -1;if(!x)return 0;rg y=rng(rnd);w=dec(mul(y,y),x);
		for(;pow(w,(p-1)>>1)!=p-1;y=rng(rnd),w=dec(mul(y,y),x));
//		printf("wrbwev:%d %d %d %d %d\n",x,y,(1ll*y*y-x+p)%p,w,pow(w,(p-1)>>1));
		return powc(cpl(y,1),(p+1)>>1).x;
	};
	cint iv=Inv(2ll*A%p),nB=dec(0,B%p);
	if(divg){rg x=mul(nB,Inv(A%p));x=x?x:p;for(rg i=0;i<=m;i+=p)Gdiv(i+x,p);}
	cint dt=(dlt%p+p)%p,sqt=Gsqrt(dt);if(!~sqt)return;
//	printf("!&*!($F)#!N$_FJ_)!#K$F!@$FVI!U#B$)FH!_#VC!@#V$)ask:%d %d %d\n",dt,sqt,mul(sqt,sqt));
	rg x0=mul(iv,inc(nB,sqt)),x1=mul(iv,dec(nB,sqt));x0=x0?x0:p;x1=x1?x1:p;
	if(x0^x1){for(rg i=0;i<=n;i+=p)Fdiv(i+x0,p),Fdiv(i+x1,p);}
	else{for(rg i=0;i<=n;i+=p)Fdiv(i+x0,p);}
}
int pr[Q],tot;bool isp[Q];
inline void solve1(){
	dlt=1ll*B*B-4ll*A*C;
	cint N=max(n,max(sqrt(g[m]),pow(f[n],1.0/3)))+15;
	for(rg i=2;i<=N;++i){
		if(!isp[i])pr[++tot]=i;
		for(rg j=1;j<=tot&&pr[j]*i<=N;++j){
			isp[pr[j]*i]=1;if(!(i%pr[j]))break;
		}
	}
	divg=1;for(rg i=1;i<=tot;++i)upd(pr[i]);divg=0;
}
inline void solve2(){
//	puts("_____________");
	std::sort(g+1,g+1+m);m=std::unique(g+1,g+1+m)-g-1;
	for(rg i=1;i<=m;++i)upd(g[i]);
}
inline void solve3(){
	for(rg i=1;i<=n;++i)if(f[i]>1){
	const ll x=sqrtl(f[i]);if(x*x==f[i])cnt[x]+=2;}
}
char _ED_;int main(){
	fprintf(stderr,"memory:%llu MB\n",(&_ST_-&_ED_)>>20);
	read(A);read(B);read(C);read(n);m=n<<1;
	for(rg i=1;i<=n;++i)f[i]=1ll*A*i*i+1ll*B*i+C;
	for(rg i=1;i<=m;++i)g[i]=1ll*A*i+B;
	solve1();//small prime
	solve2();//prime left from g[i]
	solve3();//p^2 left from f[i]
	rg res=1;for(auto x:cnt)/*printf("wefwefb e:%d %d\n",x.first,x.second),*/res=1ll*res*
	powt(x.first,x.second-(x.second&1))%mod;write(res,'\n');
	return 0;
}