//#define _GLIBCXX_DEBUG #include using namespace std; #define endl '\n' #define lfs cout<= (ll)(n); i--) using ll = long long; using ld = long double; const ll MOD1 = 1e9+7; const ll MOD9 = 998244353; const ll INF = 1e18; using P = pair; template using PQ = priority_queue; template using QP = priority_queue,greater>; templatebool chmin(T1 &a,T2 b){if(a>b){a=b;return true;}else return false;} templatebool chmax(T1 &a,T2 b){if(avoid ans(bool x,T1 y,T2 z){if(x)cout<void anss(T1 x,T2 y,T3 z){ans(x!=y,x,z);}; templatevoid debug(const T &v,ll h,ll w,string sv=" "){for(ll i=0;ivoid debug(const T &v,ll n,string sv=" "){if(n!=0)cout<void debug(const vector&v){debug(v,v.size());} templatevoid debug(const vector>&v){for(auto &vv:v)debug(vv,vv.size());} templatevoid debug(stack st){while(!st.empty()){cout<void debug(queue st){while(!st.empty()){cout<void debug(deque st){while(!st.empty()){cout<void debug(PQ st){while(!st.empty()){cout<void debug(QP st){while(!st.empty()){cout<void debug(const set&v){for(auto z:v)cout<void debug(const multiset&v){for(auto z:v)cout<void debug(const array &a){for(auto z:a)cout<void debug(const map&v){for(auto z:v)cout<<"["<vector>vec(ll x, ll y, T w){vector>v(x,vector(y,w));return v;} ll gcd(ll x,ll y){ll r;while(y!=0&&(r=x%y)!=0){x=y;y=r;}return y==0?x:y;} vectordx={1,-1,0,0,1,1,-1,-1};vectordy={0,0,1,-1,1,-1,1,-1}; templatevector make_v(size_t a,T b){return vector(a,b);} templateauto make_v(size_t a,Ts... ts){return vector(a,make_v(ts...));} templateostream &operator<<(ostream &os, const pair&p){return os << p.first << " " << p.second;} templateostream &operator<<(ostream &os, const vector &v){for(auto &z:v)os << z << " ";cout<<"|"; return os;} templatevoid rearrange(vector&ord, vector&v){ auto tmp = v; for(int i=0;ivoid rearrange(vector&ord,Head&& head, Tail&&... tail){ rearrange(ord, head); rearrange(ord, tail...); } template vector ascend(const vector&v){ vectorord(v.size());iota(ord.begin(),ord.end(),0); sort(ord.begin(),ord.end(),[&](int i,int j){return v[i] vector descend(const vector&v){ vectorord(v.size());iota(ord.begin(),ord.end(),0); sort(ord.begin(),ord.end(),[&](int i,int j){return v[i]>v[j];}); return ord; } template vector inv_perm(const vector&ord){ vectorinv(ord.size()); for(int i=0;i0);return n>=0?n/div:(n-div+1)/div;} ll CEIL(ll n,ll div){assert(div>0);return n>=0?(n+div-1)/div:n/div;} ll digitsum(ll n){ll ret=0;while(n){ret+=n%10;n/=10;}return ret;} ll modulo(ll n,ll d){return (n%d+d)%d;}; templateT min(const vector&v){return *min_element(v.begin(),v.end());} templateT max(const vector&v){return *max_element(v.begin(),v.end());} templateT acc(const vector&v){return accumulate(v.begin(),v.end(),T(0));}; templateT reverse(const T &v){return T(v.rbegin(),v.rend());}; //mt19937 mt(chrono::steady_clock::now().time_since_epoch().count()); int popcount(ll x){return __builtin_popcountll(x);}; int poplow(ll x){return __builtin_ctzll(x);}; int pophigh(ll x){return 63 - __builtin_clzll(x);}; templateT poll(queue &q){auto ret=q.front();q.pop();return ret;}; templateT poll(priority_queue &q){auto ret=q.top();q.pop();return ret;}; templateT poll(QP &q){auto ret=q.top();q.pop();return ret;}; templateT poll(stack &s){auto ret=s.top();s.pop();return ret;}; ll MULT(ll x,ll y){if(LLONG_MAX/x<=y)return LLONG_MAX;return x*y;} ll POW2(ll x, ll k){ll ret=1,mul=x;while(k){if(mul==LLONG_MAX)return LLONG_MAX;if(k&1)ret=MULT(ret,mul);mul=MULT(mul,mul);k>>=1;}return ret;} ll POW(ll x, ll k){ll ret=1;for(int i=0;i struct edge { int to; T cost; int id; edge():id(-1){}; edge(int to, T cost = 1, int id = -1):to(to), cost(cost), id(id){} operator int() const { return to; } }; template using Graph = vector>>; template Graphrevgraph(const Graph &g){ Graphret(g.size()); for(int i=0;i Graph readGraph(int n,int m,int indexed=1,bool directed=false,bool weighted=false){ Graph ret(n); for(int es = 0; es < m; es++){ int u,v; T w=1; cin>>u>>v;u-=indexed,v-=indexed; if(weighted)cin>>w; ret[u].emplace_back(v,w,es); if(!directed)ret[v].emplace_back(u,w,es); } return ret; } template Graph readParent(int n,int indexed=1,bool directed=true){ Graphret(n); for(int i=1;i>p; p-=indexed; ret[p].emplace_back(i); if(!directed)ret[i].emplace_back(p); } return ret; } template< int mod > struct ModInt { int x; ModInt() : x(0) {} ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {} ModInt &operator+=(const ModInt &p) { if((x += p.x) >= mod) x -= mod; return *this; } ModInt &operator-=(const ModInt &p) { if((x += mod - p.x) >= mod) x -= mod; return *this; } ModInt &operator*=(const ModInt &p) { x = (int) (1LL * x * p.x % mod); return *this; } ModInt &operator/=(const ModInt &p) { *this *= p.inverse(); return *this; } ModInt operator-() const { return ModInt(-x); } friend ModInt operator+(const ModInt& lhs, const ModInt& rhs) { return ModInt(lhs) += rhs; } friend ModInt operator-(const ModInt& lhs, const ModInt& rhs) { return ModInt(lhs) -= rhs; } friend ModInt operator*(const ModInt& lhs, const ModInt& rhs) { return ModInt(lhs) *= rhs; } friend ModInt operator/(const ModInt& lhs, const ModInt& rhs) { return ModInt(lhs) /= rhs; } bool operator==(const ModInt &p) const { return x == p.x; } bool operator!=(const ModInt &p) const { return x != p.x; } ModInt inverse() const { int a = x, b = mod, u = 1, v = 0, t; while(b > 0) { t = a / b; swap(a -= t * b, b); swap(u -= t * v, v); } return ModInt(u); } ModInt pow(int64_t n) const { ModInt ret(1), mul(x); while(n > 0) { if(n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; } friend istream &operator>>(istream &is, ModInt &a) { int64_t t; is >> t; a = ModInt< mod >(t); return (is); } static int get_mod() { return mod; } }; template< typename T > struct Combination { vector< T > _fact, _rfact, _inv; Combination(ll sz) : _fact(sz + 1), _rfact(sz + 1), _inv(sz + 1) { _fact[0] = _rfact[sz] = _inv[0] = 1; for(ll i = 1; i <= sz; i++) _fact[i] = _fact[i - 1] * i; _rfact[sz] /= _fact[sz]; for(ll i = sz - 1; i >= 0; i--) _rfact[i] = _rfact[i + 1] * (i + 1); for(ll i = 1; i <= sz; i++) _inv[i] = _rfact[i] * _fact[i - 1]; } inline T fact(ll k) const { return _fact[k]; } inline T rfact(ll k) const { return _rfact[k]; } inline T inv(ll k) const { return _inv[k]; } T P(ll n, ll r) const { if(r < 0 || n < r) return 0; return fact(n) * rfact(n - r); } T C(ll p, ll q) const { if(q < 0 || p < q) return 0; return fact(p) * rfact(q) * rfact(p - q); } T RC(ll p, ll q) const { if(q < 0 || p < q) return 0; return rfact(p) * fact(q) * fact(p - q); } T H(ll n, ll r) const { if(n < 0 || r < 0) return (0); return r == 0 ? 1 : C(n + r - 1, r); } //+1がn個、-1がm個で prefix sumが常にk以上 T catalan(ll n,ll m,ll k){ if(n>m-k)return 0; else return C(n+m,m)-C(n+m,n+k-1); } }; using modint = ModInt< MOD9 >;modint pow(ll n, ll x){return modint(n).pow(x);}modint pow(modint n, ll x){return n.pow(x);} //using modint=ld; using Comb=Combination; int main(){ cin.tie(nullptr); ios_base::sync_with_stdio(false); ll res=0,buf=0; bool judge = true; ll n,m,k;cin>>n>>m>>k; auto dp1=vec(m+1,m+1,modint(0)); dp1[0][0]=1; rep(i,0,m){ rep(j,0,m){ dp1[i+1][j+1]+=dp1[i][j]; dp1[i+1][min(m,2*j+2)]-=dp1[i][j]; } rep(j,0,m)dp1[i+1][j+1]+=dp1[i+1][j]; } //debug(dp1); vectorcn(m+1,1); rep(i,0,m){ cn[i+1]=cn[i]*(n-i)/(i+1); } //debug(cn); vectora(m+1); rep(i,1,m+1){ rep(j,0,m+1){ a[i]+=dp1[j][i-1]*cn[j]; } } //debug(a); ll sz=15; auto dp2=vec(sz+1,m+1,modint(0)); dp2[0][1]=1; rep(i,0,sz)rep(j,1,m+1){ rep(o,2,m+1){ if(j*o<=m){ dp2[i+1][j*o]+=dp2[i][j]*a[o]; } } } //debug(dp2); vectorck(m+1,1); rep(i,0,m){ ck[i+1]=ck[i]*(k-i)/(i+1); } modint ret=0; rep(i,0,sz+1)rep(j,1,m+1){ ret+=dp2[i][j]*ck[i]; } cout<