#pragma GCC target("avx2") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using namespace atcoder; using mint = modint998244353; #define rep(i,n) for (int i=0;i using vec = vector; template using vvec = vec>; template using vvvec = vec>; using ll = long long; using pii = pair; using pll = pair; template bool chmin(T &a, T b){ if (a>b){ a = b; return true; } return false; } template bool chmax(T &a, T b){ if (a T sum(vec x){ T res=0; for (auto e:x){ res += e; } return res; } template void printv(vec x){ for (auto e:x){ cout< ostream& operator<<(ostream& os, const vec& A){ os << "{"; rep(i,A.size()){ os << A[i]; if (i!=A.size()-1){ os << ", "; } } os << "}" ; return os; } template ostream& operator<<(ostream& os, const deque& A){ os << "deque{["; rep(i,A.size()){ os << A[i]; if (i!=A.size()-1){ os << ", "; } } os << "]}" ; return os; } template ostream& operator<<(ostream& os, const pair& A){ os << "("; os << A.first ; os << ", "; os << A.second; os << ")"; return os; } pair omega_prod(pair X,pair Y){ auto [a,b] = X; auto [c,d] = Y; return {(a*d+b*c-a*c),b*d-a*c}; }; pair omega_pow(pair X,int N){ pair res = {0,1}; while (N){ if ((N&1)){ res = omega_prod(res,X); } X = omega_prod(X,X); N >>= 1; } return res; } ostream& operator<<(ostream& os, const mint a){ os << a.val(); return os; } int main() { ios::sync_with_stdio(false); cin.tie(nullptr); int N,M; cin>>N>>M; vec>> dp(2*M+1,vec>(2*M+1,{0,0})); pair zero = {0,0}; dp[M][M] = {0,1}; mint i3 = mint(3).inv(); for (int _=0;_>> ndp(2*M+1,vec>(2*M+1,{0,0})); for (int i=0;i<=2*M;i++){ for (int j=0;j<=2*M;j++){ if (dp[i][j] == zero) continue; auto e = dp[i][j]; ndp[i][j+1].first += e.first * i3; ndp[i][j+1].second += e.second * i3; e = omega_prod(e,{1,0}); ndp[i-1][j-1].first += e.first * i3; ndp[i-1][j-1].second += e.second * i3; e = omega_prod(e,{1,0}); ndp[i+1][j].first += e.first * i3; ndp[i+1][j].second += e.second * i3; } } swap(dp,ndp); } mint res = 0; for (int i=0;i<=2*M;i++){ for (int j=0;j<=2*M;j++){ auto e = omega_pow({i-M,j-M},N); auto f = omega_prod(dp[i][j],e); res += f.second; } } cout << res.val() << endl; }