#ifdef DEBUG #include"stdlibrary.h" #else #pragma GCC target("avx") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #include using namespace std; #endif // #include // #include // #include // using namespace __gnu_pbds; // #include // namespace multiprecisioninteger = boost::multiprecision; // using cint=multiprecisioninteger::cpp_int; using ll=long long; using datas=std::pair; using ddatas=std::pair; using tdata=std::pair; using vec=std::vector; using mat=std::vector; using pvec=std::vector; using pmat=std::vector; // using llset=tree,rb_tree_tag,tree_order_statistics_node_update>; #define For(i,a,b) for(i=a;i<(ll)b;++i) #define bFor(i,b,a) for(i=b,--i;i>=(ll)a;--i) #define rep(i,N) For(i,0,N) #define rep1(i,N) For(i,1,N) #define brep(i,N) bFor(i,N,0) #define brep1(i,N) bFor(i,N,1) #define all(v) std::begin(v),std::end(v) #define allr(v) std::rbegin(v),std::rend(v) #define vsort(v) std::sort(all(v)) #define vrsort(v) std::sort(allr(v)) #define uniq(v) vsort(v),(v).erase(std::unique(all(v)),std::end(v)) #define endl "\n" #define popcount __builtin_popcountll #define print(x) std::cout< std::ostream& operator<<(std::ostream& os,const T& v){return os< std::ostream& operator<<(std::ostream& os,const std::vector& v); template std::ostream& operator<<(std::ostream& os,const std::set& v); template std::ostream& operator<<(std::ostream& os,const std::multiset& v); template std::ostream& operator<<(std::ostream& os,const std::map& v); template std::ostream& operator<<(std::ostream& os,const std::pair& p){return os<<"("< std::ostream& operator<<(std::ostream& os,const std::vector& v){ os<<"{";bool f=false; for(auto& x:v){if(f)os<<",";os< std::ostream& operator<<(std::ostream& os,const std::set& v){ os<<"{";bool f=false; for(auto& x:v){if(f)os<<",";os< std::ostream& operator<<(std::ostream& os,const std::multiset& v){ os<<"{";bool f=false; for(auto& x:v){if(f)os<<",";os< std::ostream& operator<<(std::ostream& os,const std::map& v){ os<<"{";bool f=false; for(auto& x:v){if(f)os<<",";os< inline bool chmax(T& a,const T b){bool x=a inline bool chmin(T& a,const T b){bool x=a>b;if(x)a=b;return x;} #ifdef DEBUG void debugg(){std::cout<void debugg(const T& x,const Args&... args){std::cout<<" "<sync_with_stdio(0); cout<size;--i)modncrlistm[i-1]=modncrlistm[i]*i%mod; } return modncrlistp[n]*modncrlistm[r]%mod*modncrlistm[n-r]%mod; } ll modpow(ll a,ll n,const ll m=mod){ if(n<0)return 0; ll res=1; while(n>0){ if(n&1)res=res*a%m; a=a*a%m; n>>=1; } return res; } constexpr ll gcd(const ll a,const ll b) noexcept{return (!b)?abs(a):(a%b==0)?abs(b):gcd(b,a%b);} constexpr ll lcm(const ll a,const ll b) noexcept{return a/gcd(a,b)*b;} #include using mint=atcoder::modint998244353; void operator>>(istream& is,mint& v){long long x;is>>x;v=x;} ll N,M,K,H,W,A,B,C,D; string s,t; ll ans; struct matrix{ mint v[2][2]={}; matrix operator*(const matrix& r)const{ matrix res; ll i,j,k; rep(i,2)rep(k,2)rep(j,2)res.v[i][j]+=v[i][k]*r.v[k][j]; return res; } vector operator*(const vector& ch)const{ return vector({v[0][0]*ch[0]+v[0][1]*ch[1],v[1][0]*ch[0]+v[1][1]*ch[1]}); } matrix operator^(ll n)const{ matrix res; res.v[0][0]=res.v[1][1]=1; matrix a=*this; while(n){ if(n&1)res=res*a; a=a*a; n>>=1; } return res; } }; int main(){ startupcpp(); // int codeforces;cin>>codeforces;while(codeforces--){ ll i,j=1; cin>>N>>M>>K; K%=M; if(K==0||N==1){ print(0); return 0; } vec v; v.emplace_back(1); while(1){ j=v.back()*K%M; ll d=gcd(j,M); if(v.back()==d)break; v.emplace_back(d); } auto make_mat=[](ll d){ matrix ret; ret.v[0][0]=d-1; if(d==0)ret.v[0][0]=M-1; ret.v[0][1]=d; ret.v[1][0]=M-d; if(d==0)ret.v[1][0]=0; ret.v[1][1]=M-d-1; return ret; }; auto ret=make_mat(v.back())^(N-v.size()); vector init=ret*vector({1,0}); reverse(all(v)); for(auto x:v){ init=make_mat(x)*init; } print(init[0].val()); // } }