// >>> TEMPLATES #include using namespace std; using ll = long long; using ld = long double; using i32 = int32_t; using i64 = int64_t; using u32 = uint32_t; using u64 = uint64_t; #define int ll #define rep(i, n) for (int i = 0; i < (int)(n); i++) #define rep1(i, n) for (int i = 1; i <= (int)(n); i++) #define repR(i, n) for (int i = (int)(n)-1; i >= 0; i--) #define rep1R(i, n) for (int i = (int)(n); i >= 1; i--) #define loop(i, a, B) for (int i = a; i B; i++) #define loopR(i, a, B) for (int i = a; i B; i--) #define all(x) begin(x), end(x) #define allR(x) rbegin(x), rend(x) #define rng(x, l, r) begin(x) + (l), begin(x) + (r) #define pb push_back #define eb emplace_back #define fst first #define snd second template constexpr auto mp(A &&a, B &&b) { return make_pair(forward(a), forward(b)); } template constexpr auto mt(T&&... x) { return make_tuple(forward(x)...); } template auto constexpr inf_ = numeric_limits::max()/2-1; auto constexpr INF32 = inf_; auto constexpr INF64 = inf_; auto constexpr INF = inf_; #ifdef LOCAL #include "debug.hpp" #else #define dump(...) (void)(0) #define say(x) (void)(0) #define debug if (0) #endif template struct pque : priority_queue, Comp> { vector &data() { return this->c; } void clear() { this->c.clear(); } }; template using pque_max = pque>; template using pque_min = pque>; template ::value, int> = 0> ostream& operator<<(ostream& os, T const& a) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; } template ::value, int> = 0> ostream& operator<<(ostream& os, const T (&a)[N]) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; } template ())), class = typename enable_if::value>::type> istream& operator>>(istream& is, T &a) { for (auto& x : a) is >> x; return is; } template ostream& operator<<(ostream& os, pair const& p) { return os << p.first << " " << p.second; } template istream& operator>>(istream& is, pair& p) { return is >> p.first >> p.second; } struct IOSetup { IOSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } iosetup; template struct FixPoint : private F { constexpr FixPoint(F&& f) : F(forward(f)) {} template constexpr auto operator()(T&&... x) const { return F::operator()(*this, forward(x)...); } }; struct MakeFixPoint { template constexpr auto operator|(F&& f) const { return FixPoint(forward(f)); } }; #define MFP MakeFixPoint()| #define def(name, ...) auto name = MFP [&](auto &&name, __VA_ARGS__) template struct vec_impl { using type = vector::type>; template static type make_v(size_t n, U&&... x) { return type(n, vec_impl::make_v(forward(x)...)); } }; template struct vec_impl { using type = T; static type make_v(T const& x = {}) { return x; } }; template using vec = typename vec_impl::type; template auto make_v(Args&&... args) { return vec_impl::make_v(forward(args)...); } template void quit(T const& x) { cout << x << endl; exit(0); } template constexpr bool chmin(T& x, U const& y) { if (x > y) { x = y; return true; } return false; } template constexpr bool chmax(T& x, U const& y) { if (x < y) { x = y; return true; } return false; } template constexpr auto sumof(It b, It e) { return accumulate(b, e, typename iterator_traits::value_type{}); } template int sz(T const& x) { return x.size(); } template int lbd(C const& v, T const& x) { return lower_bound(begin(v), end(v), x)-begin(v); } template int ubd(C const& v, T const& x) { return upper_bound(begin(v), end(v), x)-begin(v); } constexpr int64_t mod(int64_t x, int64_t m) { assert(m > 0); return (x %= m) < 0 ? x+m : x; } constexpr int64_t div_floor(int64_t x, int64_t y) { assert(y != 0); return x/y - ((x^y) < 0 and x%y); } constexpr int64_t div_ceil(int64_t x, int64_t y) { assert(y != 0); return x/y + ((x^y) > 0 and x%y); } constexpr int dx[] = { 1, 0, -1, 0, 1, -1, -1, 1 }; constexpr int dy[] = { 0, 1, 0, -1, 1, 1, -1, -1 }; constexpr int popcnt(ll x) { return __builtin_popcountll(x); } mt19937_64 seed_{random_device{}()}; template Int rand(Int a, Int b) { return uniform_int_distribution(a, b)(seed_); } i64 irand(i64 a, i64 b) { return rand(a, b); } // [a, b] u64 urand(u64 a, u64 b) { return rand(a, b); } // template void shuffle(It l, It r) { shuffle(l, r, seed_); } template vector &operator--(vector &v) { for (T &x : v) --x; return v; } template vector &operator++(vector &v) { for (T &x : v) ++x; return v; } // <<< // >>> modint template class modint { static_assert(md < (1u<<31), ""); using M = modint; using i64 = int64_t; uint32_t x; public: static constexpr uint32_t mod = md; constexpr modint(i64 x = 0) : x((x%=md) < 0 ? x+md : x) { } constexpr i64 val() const { return x; } constexpr explicit operator i64() const { return x; } constexpr bool operator==(M r) const { return x == r.x; } constexpr bool operator!=(M r) const { return x != r.x; } constexpr M operator+() const { return *this; } constexpr M operator-() const { return M()-*this; } constexpr M& operator+=(M r) { x += r.x; x = (x < md ? x : x-md); return *this; } constexpr M& operator-=(M r) { x += md-r.x; x = (x < md ? x : x-md); return *this; } constexpr M& operator*=(M r) { x = (uint64_t(x)*r.x)%md; return *this; } constexpr M& operator/=(M r) { return *this *= r.inv(); } constexpr M operator+(M r) const { return M(*this) += r; } constexpr M operator-(M r) const { return M(*this) -= r; } constexpr M operator*(M r) const { return M(*this) *= r; } constexpr M operator/(M r) const { return M(*this) /= r; } friend constexpr M operator+(i64 x, M y) { return M(x)+y; } friend constexpr M operator-(i64 x, M y) { return M(x)-y; } friend constexpr M operator*(i64 x, M y) { return M(x)*y; } friend constexpr M operator/(i64 x, M y) { return M(x)/y; } constexpr M inv() const { assert(x > 0); return pow(md-2); } constexpr M pow(i64 n) const { assert(not (x == 0 and n == 0)); if (n < 0) return inv().pow(-n); M v = *this, r = 1; for (; n > 0; n >>= 1, v *= v) if (n&1) r *= v; return r; } #ifdef LOCAL friend string to_s(M r) { return to_s(r.val(), mod); } #endif friend ostream& operator<<(ostream& os, M r) { return os << r.val(); } friend istream& operator>>(istream& is, M &r) { i64 x; is >> x; r = x; return is; } }; // <<< constexpr int64_t MOD = 998244353; //constexpr int64_t MOD = 1e9+7; using mint = modint; mint sign(int n) { return n & 1 ? -1 : +1; } // >>> mod table template struct ModTable { vector fact, finv; void calc(int n) { int old = fact.size(); if (n < old) return; n += 1000; fact.resize(n+1); finv.resize(n+1); if (old == 0) { fact[0] = fact[1] = finv[0] = finv[1] = 1; old = 2; } for (auto i = old; i <= n; i++) fact[i] = fact[i-1] * i; finv[n] = mint(1) / fact[n]; for (auto i = n-1; i >= old; i--) finv[i] = finv[i+1] * (i+1); } }; ModTable mod_tab; mint fact(int n) { assert(0 <= n); return mod_tab.calc(n), mod_tab.fact[n]; } mint finv(int n) { assert(0 <= n); return mod_tab.calc(n), mod_tab.finv[n]; } mint comb(int n, int k) { if (n < 0 || k < 0 || n < k) return 0; mod_tab.calc(n); return mod_tab.fact[n] * mod_tab.finv[k] * mod_tab.finv[n-k]; } mint perm(int n, int k) { assert(k >= 0); assert(n >= k); mod_tab.calc(n); return mod_tab.fact[n] * mod_tab.finv[n-k]; } // <<< // >>> matrix (vector) template decltype(T::one()) semi_ring_one(signed) { return T::one(); } template constexpr T semi_ring_one(long) { return 1; } template struct Matrix { int n, m; vector a; Matrix() {} Matrix(int n, int m) : n(n), m(m), a(n*m) { assert(n > 0 && m > 0); } Matrix(initializer_list> init) { n = init.size(); assert(n > 0); m = init.begin()->size(); assert(m > 0); a.resize(n*m); int i = 0; for (auto const& ls : init) { assert((int)ls.size() == m); for (auto const& x : ls) { a[i++] = x; } } } auto operator[](int i) const { assert(0 <= i); assert(i < n); return a.begin() + i*m; } auto operator[](int i) { assert(0 <= i); assert(i < n); return a.begin() + i*m; } bool operator==(Matrix const& x) const { if (n != x.n || m != x.m) return false; rep (i, n) rep (j, m) if ((*this)[i][j] != x[i][j]) return false; return true; } bool operator!=(Matrix const& x) const { return !(*this == x); } Matrix operator+() const { return *this; } Matrix operator+(Matrix const& x) const { return Matrix(*this) += x; } Matrix& operator+=(Matrix const& x) { assert(n == x.n && m == x.m); rep (i, n) rep (j, m) (*this)[i][j] += x[i][j]; return *this; } Matrix operator*(Matrix const& x) const { assert(m == x.n); Matrix ret(n, x.m); rep (i, n) rep (j, m) { auto A = ret[i]; auto B = (*this)[i][j]; auto C = x[j]; rep (k, x.m) A[k] += B * C[k]; } return ret; } Matrix& operator*=(Matrix const& x) { auto res = (*this)*x; swap(a, res.a); return *this; } Matrix operator*(T const& c) const { return Matrix(*this) *= c; } Matrix& operator*=(T const& c) { rep (i, n) rep (j, m) (*this)[i][j] *= c; return *this; } friend Matrix operator*(T const& c, Matrix const& x) { Matrix ret = x; rep (i, x.n) rep (j, x.m) ret[i][j] = c*x[i][j]; return ret; } static Matrix identity(int n) { Matrix ret(n, n); rep (i, n) ret[i][i] = semi_ring_one(0); return ret; } Matrix pow(ll k) const { assert(n == m); assert(k >= 0); Matrix v = *this, r = Matrix::identity(n); for ( ; k > 0; k >>= 1, v *= v) if (k & 1) r *= v; return r; } #if 1 Matrix operator-() const { Matrix x = *this; rep (i, n) rep (j, m) x[i][j] = -x[i][j]; return x; } Matrix& operator-=(Matrix const& x) { assert(n == x.n && m == x.m); rep (i, n) rep (j, m) (*this)[i][j] -= x[i][j]; return *this; } Matrix operator-(Matrix const& x) const { return Matrix(*this) -= x; } Matrix& operator/=(T const& c) { rep (i, n) rep (j, m) (*this)[i][j] /= c; return *this; } Matrix operator/(T const& c) const { return Matrix(*this) /= c; } #endif friend istream& operator>>(istream& is, Matrix& x) { rep (i, x.n) rep (j, x.m) is >> x[i][j]; return is; } #ifdef LOCAL friend string to_s(Matrix const& x) { string ret; rep (i, x.n) { ret += "\n("; rep (j, x.m) ret += " " + to_s(x[i][j]); ret += " )"; } return ret += "\n"; } #endif }; // <<< int32_t main() { int n, k; cin >> n >> k; int N = 2*k*k; auto id = [&](int t, int i, int j) { return i*k*2 + j*2 + t; }; Matrix A(N, N); rep (x, k) rep (y, k) rep (z, k) { if (x == y or y == z or z == x) continue; if (not (x < y and y > z) and not (x > y and y < z)) continue; A[id(0, x, y)][id(0, y, z)] += 1; A[id(1, x, y)][id(1, y, z)] += 1; A[id(1, x, y)][id(0, y, z)] += z; } A = A.pow(n-2); mint cnt = 0; mint sum = 0; rep (x, k) rep (y, k) rep (z, k) rep (w, k) { if (x == y) continue; cnt += A[id(0, z, w)][id(0, x, y)] * 1 + A[id(0, z, w)][id(1, x, y)] * (x + y); sum += A[id(1, z, w)][id(0, x, y)] * 1 + A[id(1, z, w)][id(1, x, y)] * (x + y); } cout << cnt << " " << sum << '\n'; }