#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #define int ll #define INT128_MAX (__int128)(((unsigned __int128) 1 << ((sizeof(__int128) * __CHAR_BIT__) - 1)) - 1) #define INT128_MIN (-INT128_MAX - 1) #define pb push_back #define eb emplace_back #define clock chrono::steady_clock::now().time_since_epoch().count() using namespace std; template ostream& operator<<(ostream& os, const pair pr) { return os << pr.first << ' ' << pr.second; } template ostream& operator<<(ostream& os, const array &arr) { for(size_t i = 0; T x : arr) { os << x; if (++i != N) os << ' '; } return os; } template ostream& operator<<(ostream& os, const vector &vec) { for(size_t i = 0; T x : vec) { os << x; if (++i != size(vec)) os << ' '; } return os; } template ostream& operator<<(ostream& os, const set &s) { for(size_t i = 0; T x : s) { os << x; if (++i != size(s)) os << ' '; } return os; } template ostream& operator<<(ostream& os, const map &m) { for(size_t i = 0; pair x : m) { os << x; if (++i != size(m)) os << ' '; } return os; } #ifdef DEBUG #define dbg(...) cerr << '(', _do(#__VA_ARGS__), cerr << ") = ", _do2(__VA_ARGS__) template void _do(T &&x) { cerr << x; } template void _do(T &&x, S&&...y) { cerr << x << ", "; _do(y...); } template void _do2(T &&x) { cerr << x << endl; } template void _do2(T &&x, S&&...y) { cerr << x << ", "; _do2(y...); } #else #define dbg(...) #endif using ll = long long; using ull = unsigned long long; using ldb = long double; using pii = pair; using pll = pair; //#define double ldb template using min_heap = priority_queue, greater>; template using max_heap = priority_queue; template, class OP = plus> void pSum(rng &&v) { if (!v.empty()) for(T p = v[0]; T &x : v | views::drop(1)) x = p = OP()(p, x); } template, class OP> void pSum(rng &&v, OP op) { if (!v.empty()) for(T p = v[0]; T &x : v | views::drop(1)) x = p = op(p, x); } template void Unique(rng &v) { ranges::sort(v); v.resize(unique(v.begin(), v.end()) - v.begin()); } template rng invPerm(rng p) { rng ret = p; for(int i = 0; i < ssize(p); i++) ret[p[i]] = i; return ret; } template rng Permute(rng v, rng2 p) { rng ret = v; for(int i = 0; i < ssize(p); i++) ret[p[i]] = v[i]; return ret; } template vector> readGraph(int n, int m, int base) { vector> g(n); for(int i = 0; i < m; i++) { int u, v; cin >> u >> v; u -= base, v -= base; g[u].emplace_back(v); if constexpr (!directed) g[v].emplace_back(u); } return g; } template void setBit(T &msk, int bit, bool x) { msk = (msk & ~(T(1) << bit)) | (T(x) << bit); } template void flipBit(T &msk, int bit) { msk ^= T(1) << bit; } template bool getBit(T msk, int bit) { return msk >> bit & T(1); } template T floorDiv(T a, T b) { if (b < 0) a *= -1, b *= -1; return a >= 0 ? a / b : (a - b + 1) / b; } template T ceilDiv(T a, T b) { if (b < 0) a *= -1, b *= -1; return a >= 0 ? (a + b - 1) / b : a / b; } template bool chmin(T &a, T b) { return a > b ? a = b, 1 : 0; } template bool chmax(T &a, T b) { return a < b ? a = b, 1 : 0; } //reference: https://github.com/NyaanNyaan/library/blob/master/modint/montgomery-modint.hpp#L10 //note: mod should be an odd prime less than 2^30. template struct MontgomeryModInt { using mint = MontgomeryModInt; using i32 = int32_t; using u32 = uint32_t; using u64 = uint64_t; static constexpr u32 get_r() { u32 res = 1, base = mod; for(i32 i = 0; i < 31; i++) res *= base, base *= base; return -res; } static constexpr u32 get_mod() { return mod; } static constexpr u32 n2 = -u64(mod) % mod; //2^64 % mod static constexpr u32 r = get_r(); //-P^{-1} % 2^32 u32 a; static u32 reduce(const u64 &b) { return (b + u64(u32(b) * r) * mod) >> 32; } static u32 transform(const u64 &b) { return reduce(u64(b) * n2); } MontgomeryModInt() : a(0) {} MontgomeryModInt(const int64_t &b) : a(transform(b % mod + mod)) {} mint pow(u64 k) const { mint res(1), base(*this); while(k) { if (k & 1) res *= base; base *= base, k >>= 1; } return res; } mint inverse() const { return (*this).pow(mod - 2); } u32 get() const { u32 res = reduce(a); return res >= mod ? res - mod : res; } mint& operator+=(const mint &b) { if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod; return *this; } mint& operator-=(const mint &b) { if (i32(a -= b.a) < 0) a += 2 * mod; return *this; } mint& operator*=(const mint &b) { a = reduce(u64(a) * b.a); return *this; } mint& operator/=(const mint &b) { a = reduce(u64(a) * b.inverse().a); return *this; } mint operator-() { return mint() - mint(*this); } bool operator==(mint b) const { return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a); } bool operator!=(mint b) const { return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a); } friend mint operator+(mint c, mint d) { return c += d; } friend mint operator-(mint c, mint d) { return c -= d; } friend mint operator*(mint c, mint d) { return c *= d; } friend mint operator/(mint c, mint d) { return c /= d; } friend ostream& operator<<(ostream& os, const mint& b) { return os << b.get(); } friend istream& operator>>(istream& is, mint& b) { int64_t val; is >> val; b = mint(val); return is; } }; using mint = MontgomeryModInt<998244353>; //#include template struct binomial { vector _fac, _facInv; binomial(int size) : _fac(size), _facInv(size) { _fac[0] = 1; for(int i = 1; i < size; i++) _fac[i] = _fac[i - 1] * i; if (size > 0) _facInv.back() = 1 / _fac.back(); for(int i = size - 2; i >= 0; i--) _facInv[i] = _facInv[i + 1] * (i + 1); } Mint fac(int i) { return i < 0 ? 0 : _fac[i]; } Mint faci(int i) { return i < 0 ? 0 : _facInv[i]; } Mint inv(int i) { return _facInv[i] * _fac[i - 1]; } Mint binom(int n, int r) { return r < 0 or n < r ? 0 : fac(n) * faci(r) * faci(n - r); } Mint catalan(int i) { return binom(2 * i, i) - binom(2 * i, i + 1); } Mint excatalan(int n, int m, int k) { //(+1) * n, (-1) * m, prefix sum > -k if (k > m) return binom(n + m, m); else if (k > m - n) return binom(n + m, m) - binom(n + m, m - k); else return Mint(0); } }; binomial bn(1 << 15); using val = array; val operator+(val a, val b) { val c; for(int i = 0; i < 3; i++) c[i] = a[i] + b[i]; return c; } val operator*(val a, val b) { val c; for(int i = 0; i < 3; i++) for(int j = 0; j < 3; j++) c[(i + j) % 3] += a[i] * b[j]; return c; } val operator*(val a, mint b) { for(mint &x : a) x *= b; return a; } signed main() { ios::sync_with_stdio(false), cin.tie(NULL); int n, m; cin >> n >> m; val d = {1, 2, 3}; dbg(d * d); val ans; for(int f0 = 0; f0 <= m; f0++) { for(int f1 = 0, f2 = m - f0; f2 >= 0; f1++, f2--) { val a = {f0, f1, f2}, b; b[(2 * f1 + 4 * f2) % 3] = 1; int k = n; while(k) { if (k & 1) b = b * a; a = a * a, k >>= 1; } ans = ans + b * (bn.fac(m) * bn.faci(f0) * bn.faci(f1) * bn.faci(f2)); } } assert(ans[1] == ans[2]); cout << (ans[0] - ans[1]) / mint(3).pow(m) << '\n'; return 0; }