#pragma GCC optimize ("Ofast") #include using namespace std; #define MD (998244353U) template struct cLtraits_identity{ using type = T; } ; template using cLtraits_try_make_signed = typename conditional< is_integral::value, make_signed, cLtraits_identity >::type; template struct cLtraits_common_type{ using tS = typename cLtraits_try_make_signed::type; using tT = typename cLtraits_try_make_signed::type; using type = typename common_type::type; } ; void*wmem; char memarr[96000000]; template inline auto min_L(S a, T b) -> typename cLtraits_common_type::type{ return (typename cLtraits_common_type::type) a <= (typename cLtraits_common_type::type) b ? a : b; } struct Modint{ unsigned val; Modint(){ val=0; } Modint(int a){ val = ord(a); } Modint(unsigned a){ val = ord(a); } Modint(long long a){ val = ord(a); } Modint(unsigned long long a){ val = ord(a); } inline unsigned ord(unsigned a){ return a%MD; } inline unsigned ord(int a){ a %= (int)MD; if(a < 0){ a += MD; } return a; } inline unsigned ord(unsigned long long a){ return a%MD; } inline unsigned ord(long long a){ a %= (int)MD; if(a < 0){ a += MD; } return a; } inline unsigned get(){ return val; } inline Modint &operator++(){ val++; if(val >= MD){ val -= MD; } return *this; } inline Modint &operator--(){ if(val == 0){ val = MD - 1; } else{ --val; } return *this; } inline Modint operator++(int a){ Modint res(*this); val++; if(val >= MD){ val -= MD; } return res; } inline Modint operator--(int a){ Modint res(*this); if(val == 0){ val = MD - 1; } else{ --val; } return res; } inline Modint &operator+=(Modint a){ val += a.val; if(val >= MD){ val -= MD; } return *this; } inline Modint &operator-=(Modint a){ if(val < a.val){ val = val + MD - a.val; } else{ val -= a.val; } return *this; } inline Modint &operator*=(Modint a){ val = ((unsigned long long)val*a.val)%MD; return *this; } inline Modint &operator/=(Modint a){ return *this *= a.inverse(); } inline Modint operator+(Modint a){ return Modint(*this)+=a; } inline Modint operator-(Modint a){ return Modint(*this)-=a; } inline Modint operator*(Modint a){ return Modint(*this)*=a; } inline Modint operator/(Modint a){ return Modint(*this)/=a; } inline Modint operator+(int a){ return Modint(*this)+=Modint(a); } inline Modint operator-(int a){ return Modint(*this)-=Modint(a); } inline Modint operator*(int a){ return Modint(*this)*=Modint(a); } inline Modint operator/(int a){ return Modint(*this)/=Modint(a); } inline Modint operator+(long long a){ return Modint(*this)+=Modint(a); } inline Modint operator-(long long a){ return Modint(*this)-=Modint(a); } inline Modint operator*(long long a){ return Modint(*this)*=Modint(a); } inline Modint operator/(long long a){ return Modint(*this)/=Modint(a); } inline Modint operator-(void){ Modint res; if(val){ res.val=MD-val; } else{ res.val=0; } return res; } inline operator bool(void){ return val!=0; } inline operator int(void){ return get(); } inline operator long long(void){ return get(); } inline Modint inverse(){ int a = val; int b = MD; int u = 1; int v = 0; int t; Modint res; while(b){ t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } if(u < 0){ u += MD; } res.val = u; return res; } inline Modint pw(unsigned long long b){ Modint a(*this); Modint res; res.val = 1; while(b){ if(b&1){ res *= a; } b >>= 1; a *= a; } return res; } inline bool operator==(int a){ return ord(a)==val; } inline bool operator!=(int a){ return ord(a)!=val; } } ; inline Modint operator+(int a, Modint b){ return Modint(a)+=b; } inline Modint operator-(int a, Modint b){ return Modint(a)-=b; } inline Modint operator*(int a, Modint b){ return Modint(a)*=b; } inline Modint operator/(int a, Modint b){ return Modint(a)/=b; } inline Modint operator+(long long a, Modint b){ return Modint(a)+=b; } inline Modint operator-(long long a, Modint b){ return Modint(a)-=b; } inline Modint operator*(long long a, Modint b){ return Modint(a)*=b; } inline Modint operator/(long long a, Modint b){ return Modint(a)/=b; } inline int my_getchar_unlocked(){ static char buf[1048576]; static int s = 1048576; static int e = 1048576; if(s == e && e == 1048576){ e = fread_unlocked(buf, 1, 1048576, stdin); s = 0; } if(s == e){ return EOF; } return buf[s++]; } inline void rd(int &x){ int k; int m=0; x=0; for(;;){ k = my_getchar_unlocked(); if(k=='-'){ m=1; break; } if('0'<=k&&k<='9'){ x=k-'0'; break; } } for(;;){ k = my_getchar_unlocked(); if(k<'0'||k>'9'){ break; } x=x*10+k-'0'; } if(m){ x=-x; } } struct MY_WRITER{ char buf[1048576]; int s; int e; MY_WRITER(){ s = 0; e = 1048576; } ~MY_WRITER(){ if(s){ fwrite_unlocked(buf, 1, s, stdout); } } } ; MY_WRITER MY_WRITER_VAR; void my_putchar_unlocked(int a){ if(MY_WRITER_VAR.s == MY_WRITER_VAR.e){ fwrite_unlocked(MY_WRITER_VAR.buf, 1, MY_WRITER_VAR.s, stdout); MY_WRITER_VAR.s = 0; } MY_WRITER_VAR.buf[MY_WRITER_VAR.s++] = a; } inline void wt_L(char a){ my_putchar_unlocked(a); } inline void wt_L(int x){ int s=0; int m=0; char f[10]; if(x<0){ m=1; x=-x; } while(x){ f[s++]=x%10; x/=10; } if(!s){ f[s++]=0; } if(m){ my_putchar_unlocked('-'); } while(s--){ my_putchar_unlocked(f[s]+'0'); } } inline void wt_L(Modint x){ int i; i = (int)x; wt_L(i); } template struct Matrix{ int r; int c; int mem; T*dat; Matrix(){ r=c=mem = 0; } Matrix(const int rr, const int cc){ if(rr == 0 || cc == 0){ r = c = 0; } else{ r = rr; c = cc; } mem = r * c; if(mem > 0){ dat = new T[mem]; } } Matrix(const Matrix &a){ int i; r = a.r; c = a.c; mem = r * c; dat = new T[mem]; for(i=(0);i<(mem);i++){ dat[i] = a.dat[i]; } } ~Matrix(){ if(mem){ delete [] dat; } } void changeSize(const int rr, const int cc){ if(rr==0 || cc==0){ r = c = 0; } else{ r = rr; c = cc; } if(mem < r*c){ if(mem){ delete [] dat; } mem = r*c; dat = new T[mem]; } } Matrix& operator=(const Matrix &a){ int i; int j; r = a.r; c = a.c; j = r * c; changeSize(r,c); for(i=(0);i<(j);i++){ dat[i] = a.dat[i]; } return *this; } Matrix& operator=(const int a){ int i; int j; j = r * c; for(i=(0);i<(j);i++){ dat[i] = 0; } j =min_L(r, c); for(i=(0);i<(j);i++){ dat[i*c+i] = a; } return *this; } Matrix& operator+=(const Matrix &a){ int i; int j; if(r==0 || r!=a.r || c!=a.c){ changeSize(0,0); return *this; } j = r*c; for(i=(0);i<(j);i++){ dat[i] += a.dat[i]; } return *this; } Matrix operator+(const Matrix &a){ return Matrix(*this) += a; } Matrix& operator-=(const Matrix &a){ int i; int j; if(r==0 || r!=a.r || c!=a.c){ changeSize(0,0); return *this; } j = r*c; for(i=(0);i<(j);i++){ dat[i] -= a.dat[i]; } return *this; } Matrix operator-(const Matrix &a){ return Matrix(*this) -= a; } Matrix& operator*=(const Matrix &a){ int i; int j; int k; int x; T*m; if(r==0 || c!=a.r){ changeSize(0,0); return *this; } m = (T*)wmem; x = r * a.c; for(i=(0);i<(x);i++){ m[i] = 0; } for(i=(0);i<(r);i++){ for(k=(0);k<(c);k++){ for(j=(0);j<(a.c);j++){ m[i*a.c+j] += dat[i*c+k] * a.dat[k*a.c+j]; } } } changeSize(r, a.c); for(i=(0);i<(x);i++){ dat[i] = m[i]; } return *this; } Matrix operator*(const Matrix &a){ return Matrix(*this) *= a; } Matrix& operator*=(const int a){ int i; int j; j = r * c; for(i=(0);i<(j);i++){ dat[i] *= a; } return *this; } Matrix& operator*=(const long long a){ int i; int j; j = r * c; for(i=(0);i<(j);i++){ dat[i] *= a; } return *this; } Matrix& operator*=(const double a){ int i; int j; j = r * c; for(i=(0);i<(j);i++){ dat[i] *= a; } return *this; } inline T* operator[](const int a){ return dat+a*c; } } ; template Matrix operator*(const int a, const Matrix &b){ return Matrix(b)*=a; } template Matrix operator*(const Matrix &b, const int a){ return Matrix(b)*=a; } template Matrix operator*(const long long a, const Matrix &b){ return Matrix(b)*=a; } template Matrix operator*(const Matrix &b, const long long a){ return Matrix(b)*=a; } template Matrix operator*(const double a, const Matrix &b){ return Matrix(b)*=a; } template Matrix operator*(const Matrix &b, const double a){ return Matrix(b)*=a; } template inline Matrix pow_L(Matrix a, S b){ int i; int j; Matrix res; res.changeSize(a.r, a.c); res = 1; while(b){ if(b&1){ res *= a; } b >>= 1; a *= a; } return res; } template inline T pow_L(T a, S b){ T res = 1; res = 1; for(;;){ if(b&1){ res *= a; } b >>= 1; if(b==0){ break; } a *= a; } return res; } inline double pow_L(double a, double b){ return pow(a,b); } struct dimcomp3{ int B; int C; dimcomp3(){ } ; dimcomp3(int b, int c){ B = b; C = c; } dimcomp3(int a, int b, int c){ B = b; C = c; } inline void set(int b, int c){ B = b; C = c; } inline void set(int a, int b, int c){ B = b; C = c; } inline int mask(int a, int b, int c){ return (a * B + b) * C + c; } inline int operator()(int a, int b, int c){ return (a * B + b) * C + c; } inline void para(int mask, int &a, int &b, int &c){ a = mask / (B*C); b = mask % (B*C) / C; c = mask % C; } inline void operator()(int mask, int &a, int &b, int &c){ a = mask / (B*C); b = mask % (B*C) / C; c = mask % C; } } ; int isKado(int x,int y,int z){ if(x==y||y==z||z==x){ return 0; } if(x < y && y < z){ return 0; } if(x > y && y > z){ return 0; } return 1; } int main(){ int i; wmem = memarr; int N; rd(N); int K; rd(K); Modint res1 = 0; Modint res2 = 0; Matrix mt(2*(K+1)*(K+1), 2*(K+1)*(K+1)); dimcomp3 dm(2,K+1,K+1); for(i=(0);i<(K+1);i++){ int j; for(j=(0);j<(K+1);j++){ int k; for(k=(0);k<(K);k++){ if(j==k){ continue; } if(i!=K && j!=K && !isKado(i,j,k)){ continue; } mt[dm(0,i,j)][dm(0,j,k)]++; mt[dm(1,i,j)][dm(1,j,k)]++; mt[dm(0,i,j)][dm(1,j,k)]+=k; } } } (mt = pow_L(mt,N)); for(i=(0);i<(K+1);i++){ int j; for(j=(0);j<(K+1);j++){ res1 += mt[dm(0,K,K)][dm(0,i,j)]; } } for(i=(0);i<(K+1);i++){ int j; for(j=(0);j<(K+1);j++){ res2 += mt[dm(0,K,K)][dm(1,i,j)]; } } wt_L(res1); wt_L(' '); wt_L(res2); wt_L('\n'); return 0; } // cLay version 20210508-1 [beta] // --- original code --- // #define MD 998244353 // // int isKado(int x,int y,int z){ // if(x==y||y==z||z==x) return 0; // if(x < y < z) return 0; // if(x > y > z) return 0; // return 1; // } // // { // int @N, @K; // Modint res1 = 0, res2 = 0; // Matrix mt(2*(K+1)*(K+1), 2*(K+1)*(K+1)); // dimcomp3 dm(2,K+1,K+1); // // rep(i,K+1) rep(j,K+1) rep(k,K){ // if(j==k) continue; // if(i!=K && j!=K && !isKado(i,j,k)) continue; // mt[dm(0,i,j)][dm(0,j,k)]++; // mt[dm(1,i,j)][dm(1,j,k)]++; // mt[dm(0,i,j)][dm(1,j,k)]+=k; // } // mt **= N; // rep(i,K+1) rep(j,K+1) res1 += mt[dm(0,K,K)][dm(0,i,j)]; // rep(i,K+1) rep(j,K+1) res2 += mt[dm(0,K,K)][dm(1,i,j)]; // wt(res1,res2); // }