#include "inv.h"
#include<bits/stdc++.h>
#define For(i,a,b) for(int i=(a);i<=(b);++i)
#define Rep(i,a,b) for(int i=(a);i>=(b);--i)
#define ll long long
#define ull unsigned long long
using namespace std;

#define getchar()(p1==p2&&(p2=(p1=buf)+fread(buf,1,1<<21,stdin),p1==p2)?EOF:*p1++)
char buf[1<<21],*p1=buf,*p2=buf;
inline int read()
{
	char c=getchar();int x=0;bool f=0;
	for(;!isdigit(c);c=getchar())f^=!(c^45);
	for(;isdigit(c);c=getchar())x=(x<<1)+(x<<3)+(c^48);
	if(f)x=-x;return x;
}

#define mod 998244353
struct modint{
	int x;
	modint(int o=0){x=o;}
	modint &operator = (int o){return x=o,*this;}
	modint &operator +=(modint o){return x=x+o.x>=mod?x+o.x-mod:x+o.x,*this;}
	modint &operator -=(modint o){return x=x-o.x<0?x-o.x+mod:x-o.x,*this;}
	modint &operator *=(modint o){return x=1ll*x*o.x%mod,*this;}
	modint &operator ^=(int b){
		modint a=*this,c=1;
		for(;b;b>>=1,a*=a)if(b&1)c*=a;
		return x=c.x,*this;
	}
	modint &operator /=(modint o){return *this *=o^=mod-2;}
	friend modint operator +(modint a,modint b){return a+=b;}
	friend modint operator -(modint a,modint b){return a-=b;}
	friend modint operator *(modint a,modint b){return a*=b;}
	friend modint operator /(modint a,modint b){return a/=b;}
	friend modint operator ^(modint a,int b){return a^=b;}
	friend bool operator ==(modint a,int b){return a.x==b;}
	friend bool operator !=(modint a,int b){return a.x!=b;}
	bool operator ! () {return !x;}
	modint operator - () {return x?mod-x:0;}
	bool operator <(const modint&b)const{return x<b.x;}
};
inline modint qpow(modint x,int y){return x^y;}

vector<modint> fac,ifac,iv;
inline void initC(int n)
{
	if(iv.empty())fac=ifac=iv=vector<modint>(2,1);
	int m=iv.size(); ++n;
	if(m>=n)return;
	iv.resize(n),fac.resize(n),ifac.resize(n);
	For(i,m,n-1){
		iv[i]=iv[mod%i]*(mod-mod/i);
		fac[i]=fac[i-1]*i,ifac[i]=ifac[i-1]*iv[i];
	}
}
inline modint C(int n,int m){
	if(m<0||n<m)return 0;
	return initC(n),fac[n]*ifac[m]*ifac[n-m];
}
inline modint sign(int n){return (n&1)?(mod-1):(1);}

#define fi first
#define se second
#define pb push_back
#define mkp make_pair
typedef pair<int,int>pii;
typedef vector<int>vi; 

#define maxn 300005
#define inf 0x3f3f3f3f

struct DIV {
	ull x;
	inline void init(int v) { x = -1ull / v + 1; }
};
inline ull operator / (const ull & x, const DIV & y) {
	return (__uint128_t) x * y.x >> 64;
}

namespace Inv{

int n=1000,m=1000000,sum[1000005],frac[1000005];
int f[maxn],len,V;
DIV ivn,ivmod; 
void init(){
	V=5*m,initC(V);
	ivn.init(n),ivmod.init(mod);
	For(q,1,n-1)
		For(p,0,q){
			int i=p*m/q;
			if(!sum[i])sum[i]=1,frac[i]=p*n+q;
		}
	For(i,1,m)sum[i]+=sum[i-1];
	For(i,0,m)if(frac[i])f[len++]=frac[i];
}
modint inv(modint X){
	int a=X.x,j=sum[(1ull*a*m)/ivmod],p,q;
	if(j<len){
		p=f[j]/ivn,q=f[j]-p*n;
		ll t=1ll*a*q-1ll*p*mod;
		if(abs(t)<=V)return (t>0?iv[t]:-iv[-t])*q;
	}
	--j;
	if(j>=0){
		p=f[j]/ivn,q=f[j]-p*n;
		ll t=1ll*a*q-1ll*p*mod;
		if(abs(t)<=V)return (t>0?iv[t]:-iv[-t])*q;
	}
	return -1;
}

}

void init(int p){
	Inv::init(); 
}
int inv(int x){
	int res=(Inv::inv(x)).x;
	return res;
}