#include #pragma GCC optimize("Ofast") #pragma GCC optimize("unroll-loops") using namespace std; using std::cout; using std::cin; using std::endl; using ll=long long; using ld=long double; const ll ILL=2167167167167167167; const int INF=2100000000; const int mod=998244353; #define rep(i,a,b) for (int i=(int)(a);i<(int)(b);i++) #define all(p) p.begin(),p.end() template using _pq = priority_queue, greater>; template ll LB(vector &v,T a){return lower_bound(v.begin(),v.end(),a)-v.begin();} template ll UB(vector &v,T a){return upper_bound(v.begin(),v.end(),a)-v.begin();} template bool chmin(T &a,const T &b){if(a>b){a=b;return 1;}else return 0;} template bool chmax(T &a,const T &b){if(a void So(vector &v) {sort(v.begin(),v.end());} template void Sore(vector &v) {sort(v.begin(),v.end(),[](T x,T y){return x>y;});} void yneos(bool a){if(a) cout<<"Yes\n"; else cout<<"No\n";} template void vec_out(vector &p,int ty=0){ if(ty==2){cout<<'{';for(int i=0;i<(int)p.size();i++){if(i){cout<<",";}cout<<'"'< T vec_min(vector &a){assert(!a.empty());T ans=a[0];for(auto &x:a) chmin(ans,x);return ans;} template T vec_max(vector &a){assert(!a.empty());T ans=a[0];for(auto &x:a) chmax(ans,x);return ans;} template T vec_sum(vector &a){assert(!a.empty());T ans=a[0]-a[0];for(auto &x:a) ans+=x;return ans;} int pop_count(long long a){int res=0;while(a){res+=(a&1),a>>=1;}return res;} ll jyo(ll x,ll y,ll z){ ll H=y; //ここから ll a=1,b=(x%z+z)%z,c=1; while(H>0){ a*=2; if(H%a!=0){ H-=a/2; c*=b; c%=z; } b*=b; b%=z; } //ここまで return c; } template using square_matrix=std::vector>; template square_matrix mul_matrix(square_matrix l,square_matrix r){ int n=l.size(); assert((int)l[0].size()==n&&(int)r.size()==n&&(int)r[0].size()==n); square_matrix val(n,std::vector(n,add_e())); for(int i=0;i square_matrix pow_matrix(square_matrix l,long long times){ int n=l.size(); square_matrix val(n,std::vector(n,add_e())); for(int i=0;i(val,l); } l=mul_matrix(l,l); times>>=1; } return val; } using mat_F=ll; mat_F add_op(mat_F a,mat_F b){ return (a+b)%mod; } mat_F add_e(){ return 0; } mat_F mul_op(mat_F a,mat_F b){ return (a*b)%mod; } mat_F mul_e(){ return 1; } #define calc mat_F,add_op,add_e,mul_op,mul_e void solve(); // oddloop int main() { ios::sync_with_stdio(false); cin.tie(nullptr); int t=1; //cin>>t; rep(i,0,t) solve(); } void solve(){ ll N,M,K; cin>>N>>M>>K; ll B=1; ll X=1,Y=0; ll rp=min(40ll,N); rep(i,0,rp){ ll n_X=X*(B-1)+Y*B; ll n_Y=(X+Y)*(M-1)-n_X; X=n_X%mod; Y=n_Y%mod; ll n_B=gcd(B*K,M); Y=Y*(M/n_B-1)%mod; Y=Y*(jyo(M/B-1,mod-2,mod))%mod; B=n_B; } if(rp==N){ cout<<(X%mod+mod)%mod<<"\n"; return; } vector> p={ {B-1,M-B}, {B,M-B-1} }; p=pow_matrix(p,N-rp); ll ans=X*p[0][0]+Y*p[1][0]; cout<<(ans%mod+mod)%mod<<"\n"; }