#include using namespace std; using Int = long long; template inline void chmin(T1 &a,T2 b){if(a>b) a=b;} template inline void chmax(T1 &a,T2 b){if(a struct Mint{ T v; Mint():v(0){} Mint(signed v):v(v){} Mint(long long t){v=t%MOD;if(v<0) v+=MOD;} Mint pow(long long k){ Mint res(1),tmp(v); while(k){ if(k&1) res*=tmp; tmp*=tmp; k>>=1; } return res; } Mint inv(){return pow(MOD-2);} Mint& operator+=(Mint a){v+=a.v;if(v>=MOD)v-=MOD;return *this;} Mint& operator-=(Mint a){v+=MOD-a.v;if(v>=MOD)v-=MOD;return *this;} Mint& operator*=(Mint a){v=1LL*v*a.v%MOD;return *this;} Mint& operator/=(Mint a){return (*this)*=a.inv();} Mint operator+(Mint a) const{return Mint(v)+=a;}; Mint operator-(Mint a) const{return Mint(v)-=a;}; Mint operator*(Mint a) const{return Mint(v)*=a;}; Mint operator/(Mint a) const{return Mint(v)/=a;}; Mint operator-(){return v?MOD-v:v;} bool operator==(const Mint a)const{return v==a.v;} bool operator!=(const Mint a)const{return v!=a.v;} bool operator <(const Mint a)const{return v dp; dp.reserve(sq); Mint res(1); for(int r=0;r0) return idx; } res*=p; } return T(-1); } static vector fact,finv,invs; static void init(int n){ if(n+1<=(signed)fact.size()) return; fact.assign(n+1,1); finv.assign(n+1,1); invs.assign(n+1,1); for(int i=1;i<=n;i++) fact[i]=fact[i-1]*Mint(i); finv[n]=Mint(1)/fact[n]; for(int i=n;i>=1;i--) finv[i-1]=finv[i]*Mint(i); for(int i=1;i<=n;i++) invs[i]=finv[i]*fact[i-1]; } static Mint comb(long long n,int k){ Mint res(1); for(int i=0;i > D(int n,int m){ vector > dp(n+1,vector(m+1,0)); dp[0][0]=Mint(1); for(int i=0;i<=n;i++){ for(int j=1;j<=m;j++){ if(i-j>=0) dp[i][j]=dp[i][j-1]+dp[i-j][j]; else dp[i][j]=dp[i][j-1]; } } return dp; } static Mint B(int n,int k){ Mint res; for(int j=1;j<=k;j++) res+=S(n,j); return res; } static Mint montmort(int n){ Mint res; init(n); for(int k=2;k<=n;k++){ if(k&1) res-=finv[k]; else res+=finv[k]; } return res*=fact[n]; } static Mint LagrangePolynomial(vector &y,Mint t){ int n=y.size()-1; if(t.v<=n) return y[t.v]; init(n+1); Mint num(1); for(int i=0;i<=n;i++) num*=t-Mint(i); Mint res; for(int i=0;i<=n;i++){ Mint tmp=y[i]*num/(t-Mint(i))*finv[i]*finv[n-i]; if((n-i)&1) res-=tmp; else res+=tmp; } return res; } }; template vector > Mint::fact = vector >(); template vector > Mint::finv = vector >(); template vector > Mint::invs = vector >(); template struct Matrix{ typedef vector arr; typedef vector mat; mat dat; Matrix(size_t r,size_t c):dat(r,arr(c,K())){} Matrix(mat dat):dat(dat){} size_t size() const{return dat.size();}; bool empty() const{return size()==0;}; arr& operator[](size_t k){return dat[k];}; const arr& operator[](size_t k) const {return dat[k];}; static Matrix cross(const Matrix &A,const Matrix &B){ Matrix res(A.size(),B[0].size()); for(int i=0;i<(int)A.size();i++) for(int j=0;j<(int)B[0].size();j++) for(int k=0;k<(int)B.size();k++) res[i][j]+=A[i][k]*B[k][j]; return res; } static Matrix identity(size_t n){ Matrix res(n,n); for(int i=0;i<(int)n;i++) res[i][i]=K(1); return res; } Matrix pow(long long n) const{ Matrix a(dat),res=identity(size()); while(n){ if(n&1) res=cross(res,a); a=cross(a,a); n>>=1; } return res; } template using ET = enable_if::value>; template using EF = enable_if::value>; template::type* = nullptr> static bool is_zero(T x){return abs(x)<1e-8;} template::type* = nullptr> static bool is_zero(T x){return x==T(0);} static Matrix gauss_jordan(const Matrix &A,const Matrix &B){ int n=A.size(),l=B[0].size(); Matrix C(n,n+l); for(int i=0;i; using MM = Matrix; Int b,c,d; cin>>b>>c>>d; MM A(2,2); A[0][0]=M(c);A[0][1]=M(b); A[1][0]=M(0);A[1][1]=M(1); MM B(2,1); B[0][0]=M(0); B[1][0]=M(1); cout<<((MM::cross(A.pow(d),B))[0][0]*M(c)).v<