#include using namespace std; #define ll long long #define rep(i,n) for(int i=0;i=0;i--) #define rrep2(i,n,k) for(int i=n-1;i>=n-k;i--) #define vll(n,i) vector(n,i) #define v2ll(n,m,i) vector>(n,vll(m,i)) #define v3ll(n,m,k,i) vector>>(n,v2ll(m,k,i)) #define v4ll(n,m,k,l,i) vector>>>(n,v3ll(m,k,l,i)) #define all(v) v.begin(),v.end() #define chmin(k,m) k = min(k,m) #define chmax(k,m) k = max(k,m) #define Pr pair #define Tp tuple #define riano_ std::ios::sync_with_stdio(false);std::cin.tie(nullptr) using Graph = vector>; const ll mod = 998244353; template struct modint{ uint64_t val; constexpr modint(const int64_t val_=0) noexcept:val((val_%int64_t(mod)+int64_t(mod))%int64_t(mod)){} constexpr modint operator-() const noexcept{ return modint(*this)=mod-val; } constexpr modint operator+(const modint rhs) const noexcept{ return modint(*this)+=rhs; } constexpr modint operator-(const modint rhs) const noexcept{ return modint(*this)-=rhs; } constexpr modint operator*(const modint rhs) const noexcept{ return modint(*this)*=rhs; } constexpr modint operator/(const modint rhs) const noexcept{ return modint(*this)/=rhs; } constexpr modint &operator+=(const modint rhs) noexcept{ val+=rhs.val; val-=((val>=mod)?mod:0); return (*this); } constexpr modint &operator-=(const modint rhs) noexcept{ val+=((val>=1; } return (*this)*=now; } modint & operator++(){ val++; if (val == mod) val = 0; return *this; } modint operator++(int){ modint res = *this; ++*this; return res; } constexpr bool operator==(const modint rhs) noexcept{ return val==rhs.val; } constexpr bool operator!=(const modint rhs) noexcept{ return val!=rhs.val; } friend constexpr ostream &operator<<(ostream& os,const modint x) noexcept{ return os<<(x.val); } friend constexpr istream &operator>>(istream& is,modint& x) noexcept{ uint64_t t; is>>t,x=t; return is; } }; typedef modint mint; mint pw(long long a,long long b,long long m = mod){ if(a%m==0) return mint(0); if(b==0) return mint(1); else if(b%2==0){ long long x = pw(a,b/2,m).val; return mint(x*x); } else{ long long x = pw(a,b-1,m).val; return mint(a*x); } } mint modinv(long long a, long long m = mod) { long long b = m, u = 1, v = 0; while (b) { long long t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } u %= m; return mint(u); } #define vm(n,i) vector(n,i) #define v2m(n,m,i) vector>(n,vm(m,i)) #define v3m(n,m,k,i) vector>>(n,v2m(m,k,i)) #define v4m(n,m,k,l,i) vector>>>(n,v3m(m,k,l,i)) //Combination2 //10^6くらいまで vector fact; vector invf; ll comb(ll n,ll k){ if(n<0||k<0||k>n) return 0LL; else{ ll a = fact[n]*invf[k]%mod; a = a*invf[n-k]%mod; return a; } } int main() { riano_; mint ans = 0; ll N,K; cin >> N >> K; //main関数内に以下ペースト //N:max fact.assign(N+1,1LL); invf.assign(N+1,1LL); rep(i,N) fact[i+1] = fact[i]*(i+1)%mod; rep(i,N+1) invf[i] = modinv(fact[i],mod).val; if(K==0){ cout << 1 << endl; return 0; } if(K==1){ if(N%2==0){ cout << 2 << endl; } else{ cout << N-2 << endl; } return 0; } ll M = ((N-K)/2)*2; for(int i=0;i<=M;i+=2){ ans += mint(i+1)*mint(comb(N-2-i,K-2)); } cout << ans << endl; }