#pragma GCC optimize ("O3") #pragma GCC target ("avx") #include using namespace std; using ll = long long int; #define all(v) (v).begin(),(v).end() #define repeat(cnt,l) for(typename remove_const::type>::type cnt={};(cnt)<(l);++(cnt)) #define rrepeat(cnt,l) for(auto cnt=(l)-1;0<=(cnt);--(cnt)) #define iterate(cnt,b,e) for(auto cnt=(b);(cnt)!=(e);++(cnt)) #define diterate(cnt,b,e) for(auto cnt=(b);(cnt)!=(e);--(cnt)) const long long MD = 998244353; const long double PI = 3.1415926535897932384626433832795L; template inline ostream& operator <<(ostream &o, const pair p) { o << '(' << p.first << ':' << p.second << ')'; return o; } template inline T& chmax(T& to, const T& val) { return to = max(to, val); } template inline T& chmin(T& to, const T& val) { return to = min(to, val); } void bye(string s, int code = 0) { cout << s << endl; exit(code); } mt19937_64 randdev(8901016); template::value>::type* = nullptr> inline T rand(T l, T h, Random& rand = randdev) { return uniform_int_distribution(l, h)(rand); } template::value>::type* = nullptr> inline T rand(T l, T h, Random& rand = randdev) { return uniform_real_distribution(l, h)(rand); }template static ostream& operator<<(ostream& o, const std::vector& v) { o << "[ "; for(const auto& e : v) o< struct MyRangeFormat{ I b,e; MyRangeFormat(I _b, I _e):b(_b),e(_e){} }; template static ostream& operator<<(ostream& o, const MyRangeFormat& f) { o << "[ "; iterate(i,f.b,f.e) o<<*i<<' '; return o << ']'; } template struct MyMatrixFormat{ const I& p; long long n, m; MyMatrixFormat(const I& _p, long long _n, long long _m):p(_p),n(_n),m(_m){} }; template static ostream& operator<<(ostream& o, const MyMatrixFormat& f) { o<<'\n'; repeat(i,(f.n)) { repeat(j,f.m) o<(m,m+w)) #define FMTR(b,e) (MyRangeFormat(b,e)) #define FMTV(v) FMTR(v.begin(),v.end()) #define FMTM(m,h,w) (MyMatrixFormat(m,h,w)) #if defined(_WIN32) || defined(_WIN64) #define getc_x _getc_nolock #define putc_x _putc_nolock #elif defined(__GNUC__) #define getc_x getc_unlocked #define putc_x putc_unlocked #else #define getc_x getc #define putc_x putc #endif class MaiScanner { FILE* fp_; constexpr bool isvisiblechar(char c) noexcept { return (0x21<=(c)&&(c)<=0x7E); } public: inline MaiScanner(FILE* fp):fp_(fp){} template void input_integer(T& var) noexcept { var = 0; T sign = 1; int cc = getc_x(fp_); for (; cc < '0' || '9' < cc; cc = getc_x(fp_)) if (cc == '-') sign = -1; for (; '0' <= cc && cc <= '9'; cc = getc_x(fp_)) var = (var << 3) + (var << 1) + cc - '0'; var = var * sign; } inline int c() noexcept { return getc_x(fp_); } template::value, nullptr_t>::type = nullptr> inline MaiScanner& operator>>(T& var) noexcept { input_integer(var); return *this; } inline MaiScanner& operator>>(string& var) { int cc = getc_x(fp_); for (; !isvisiblechar(cc); cc = getc_x(fp_)); for (; isvisiblechar(cc); cc = getc_x(fp_)) var.push_back(cc); return *this; } template inline void in(IT begin, IT end) { for (auto it = begin; it != end; ++it) *this >> *it; } }; class MaiPrinter { FILE* fp_; public: inline MaiPrinter(FILE* fp):fp_(fp){} template void output_integer(T var) noexcept { if (var == 0) { putc_x('0', fp_); return; } if (var < 0) putc_x('-', fp_), var = -var; char stack[32]; int stack_p = 0; while (var) stack[stack_p++] = '0' + (var % 10), var /= 10; while (stack_p) putc_x(stack[--stack_p], fp_); } inline MaiPrinter& operator<<(char c) noexcept { putc_x(c, fp_); return *this; } template::value, nullptr_t>::type = nullptr> inline MaiPrinter& operator<<(T var) noexcept { output_integer(var); return *this; } inline MaiPrinter& operator<<(char* str_p) noexcept { while (*str_p) putc_x(*(str_p++), fp_); return *this; } inline MaiPrinter& operator<<(const string& str) { const char* p = str.c_str(); const char* l = p + str.size(); while (p < l) putc_x(*p++, fp_); return *this; } template void join(IT begin, IT end, char sep = ' ') { for (bool b = 0; begin != end; ++begin, b = 1) b ? *this << sep << *begin : *this << *begin; } }; MaiScanner scanner(stdin); MaiPrinter printer(stdout); bool kado(int x, int y, int z) { return (x!=z)&&((xz)||(x>y&&y> N >> K; repeat(i, K) { repeat(j, K) { dp1[0][i][j] = i != j; } } repeat(i, K) { repeat(j, K) { dp2[0][i][j] = i != j ? i + j : 0; } } repeat(j, K) { repeat(k, K) { repeat(i, K) { if (kado(i,j,k)) { cjk[j][k] += 1; } } } } repeat(c, N-2) { int p1 = c&1; int p2 = !p1; fill(dp1[p2][0], dp1[p2][K], 0); fill(dp2[p2][0], dp2[p2][K], 0); repeat(j, K) { ll t1kj = 0, t2kj = 0; for (int i = 0; i < j; ++i) { // if (i == k) continue; t1kj += dp1[p1][i][j]; t2kj += dp2[p1][i][j]; } t1kj %= MD; t2kj %= MD; ll t1jk = 0, t2jk = 0; for (int i = j+1; i < K; ++i) { // if (i == k) continue; t1jk += dp1[p1][i][j]; t2jk += dp2[p1][i][j]; } t1jk %= MD; t2jk %= MD; repeat(k, K) { if (j > k) { ll t1 = (t1kj - dp1[p1][k][j] + MD)%MD; // reduce i == k ll t2 = (t2kj - dp2[p1][k][j] + MD)%MD; // reduce i == k dp1[p2][j][k] += t1; dp1[p2][j][k] %= MD; dp2[p2][j][k] += (ll(t2) + ll(t1)*k)%MD; dp2[p2][j][k] %= MD; // for (int i = 0; i < j; ++i) { // if (i == k) continue; // dp1[p2][j][k] += dp1[p1][i][j]; // dp1[p2][j][k] %= MD; // dp2[p2][j][k] += (ll(dp2[p1][i][j]) + ll(dp1[p1][i][j])*k)%MD; // dp2[p2][j][k] %= MD; // } } else if (j < k) { ll t1 = (t1jk - dp1[p1][k][j] + MD)%MD; // reduce i == k ll t2 = (t2jk - dp2[p1][k][j] + MD)%MD; // reduce i == k dp1[p2][j][k] += t1; dp1[p2][j][k] %= MD; dp2[p2][j][k] += (ll(t2) + ll(t1)*k)%MD; dp2[p2][j][k] %= MD; // for (int i = j+1; i < K; ++i) { // if (i == k) continue; // dp1[p2][j][k] += dp1[p1][i][j]; // dp1[p2][j][k] %= MD; // dp2[p2][j][k] += (ll(dp2[p1][i][j]) + ll(dp1[p1][i][j])*k)%MD; // dp2[p2][j][k] %= MD; // } } } } } const int p = N&1; ll total1 = 0, total2 = 0; repeat(i, K) { repeat(j, K) { total1 += dp1[p][i][j]; } } repeat(i, K) { repeat(j, K) { total2 += dp2[p][i][j]; } } cout << (total1%MD) << ' ' << (total2%MD) << endl; return 0; }