#line 1 "c.cpp" #include #include #define rep(i,n) for (int i = 0; i < int(n); ++i) #define repp(i,n,m) for (int i = m; i < int(n); ++i) #define repb(i,n) for (int i = int(n)-1; i >= 0; --i) #define all(v) v.begin(),v.end() using namespace std; using namespace atcoder; using ll = long long; using ld = long double; using P = pair; using PL = pair; using pdd = pair; using pil = pair; using pli = pair; using ppi = pair; using pip = pair; const int INF = 1001001007; const long long mod1 = 1000000007LL; const long long mod2 = 998244353LL; const ll inf = 2e18; const ld pi = 3.14159265358979323; const ld eps = 1e-7; templatevoid o(T a); templateistream &operator>>(istream &is,vector &v){for(auto &e:v)is>>e;return is;} templateistream &operator>>(istream &is,vector> &v){for(auto &e:v)is>>e;return is;} templatebool range(T a,T b,T x){return (a<=x&&xbool rrange(T a,T b,T c,T d,T x,T y){return (range(a,c,x)&&range(b,d,y));} templatevoid rev(vector &v){reverse(v.begin(),v.end());} void revs(string &s) {reverse(s.begin(),s.end());} templatevoid sor(vector &v, int f=0){sort(v.begin(),v.end());if(f!=0) rev(v);} templatebool chmin(T &a,const T &b){if(a>b){a=b;return true;}return false;} templatebool chmax(T &a,const T &b){if(avoid uniq(vector &v){sor(v);v.erase(unique(v.begin(),v.end()),v.end());} templateT cel(T a,T b){return (a+b-1)/b;} templatevoid print(pair a); templatevoid print(vector v); templatevoid print(vector> v); void print(){ putchar(' '); } void print(bool a){ printf("%d", a); } void print(int a){ printf("%d", a); } void print(long a){ printf("%ld", a); } void print(long long a){ printf("%lld", a); } void print(char a){ printf("%c", a); } void print(char a[]){ printf("%s", a); } void print(const char a[]){ printf("%s", a); } void print(long double a){ printf("%.15Lf", a); } void print(const string& a){ for(auto&& i : a) print(i); } template void print(const T& a){ cout << a; } int out(){ putchar('\n'); return 0; } template int out(const T& t){ print(t); putchar('\n'); return 0; } template int out(const Head& head, const Tail&... tail){ print(head); putchar(' '); out(tail...); return 0; } void o(){cout<<"!?"<void o(T a){cout<void print(pair a){print(a.first);print(),print(a.second);} templatevoid print(vector v){for(auto ite=v.begin();ite!=v.end();){print(*ite);if(++ite!=v.end())print();}} templatevoid print(vector> v){for(auto ite=v.begin();ite!=v.end();){print(*ite);if(++ite!=v.end())out();}} void yes(){out("Yes");} void no (){out("No");} void yn (bool t){if(t)yes();else no();} templatevoid dame(bool t, T s){if(!t){out(s);exit(0);}} vector dx = {0,1,0,-1,1,1,-1,-1}; vector dy = {1,0,-1,0,1,-1,-1,1}; const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"; const string alp = "abcdefghijklmnopqrstuvwxyz"; const string NUM = "0123456789"; ll gcd(ll a,ll b){return b?gcd(b,a%b):a;} ll lcm(ll a,ll b){return a/gcd(a,b)*b;} ll mpow(ll x,ll n,ll m){if(n==0)return 1LL;x%=m;ll a=mpow(x,n/2,m);a=a*a%m;return (n&1)?a*x%m:a;} using mint = modint998244353; void out(vector a){vector b(a.size()); rep(i,a.size()) b[i] = a[i].val(); out(b);} void out(vector> a){for (auto v : a) out(v);} #line 2 "binom.hpp" #line 4 "binom.hpp" template struct MINT{ MINT(int lim = -1){init(lim);} static T factrial(int x){init(x); return kaijo[x];} static T inv_fact(int x){init(x); return kainv[x];} static T ncr(int n, int r){ if (n < r || r < 0) return T(0); init(n); return kaijo[n] * kainv[r] * kainv[n-r]; } static T npr(int n, int r){ if (n < r || r < 0) return T(0); init(n); return kaijo[n] * kainv[n-r]; } static T inv(long long n){ n %= T::mod(); assert(n != 0); if (n < invs.size()) return invs[n]; return T(n).inv(); } private: static vector invs, kaijo, kainv; static void init(int lim){ if (lim <= -1) lim = 300000; if (kaijo.size() > lim) return ; int siz = kaijo.size(); invs.resize(lim+1), kaijo.resize(lim+1), kainv.resize(lim+1); for (int i = siz; i <= lim; i++) invs[i] = -invs[T::mod()%i] * T(T::mod()/i); for (int i = siz; i <= lim; i++) kaijo[i] = kaijo[i-1] * T(i); for (int i = siz; i <= lim; i++) kainv[i] = kainv[i-1] * invs[i]; } }; template std::vectorMINT::kaijo = vector(2,T(1)); template std::vectorMINT::kainv = vector(2,T(1)); template std::vectorMINT::invs = vector(2,T(1)); #line 77 "c.cpp" void solve(){ MINT m; ll n, k, x; cin >> n >> k >> x; mint ans = 0; repp(i,n+1,1){ if (i < k){ ll a = i-1; ll s = (n-a) * (n-a-1) / 2 - x + 1 + a; mint pl = mint(s) * m.ncr(n-1,a); //out(pl.val()); pl -= mint(n-x) * m.ncr(n-2,a-1); //out(pl.val()); ans += pl * m.factrial(a) * m.factrial(n-i-1) * m.factrial(n-i); } else if (i > k){ ll a = i-1; ans += m.npr(n-1,a-1) * mint((n-a)*(n-a-1)/2) * m.factrial(n-i) * m.factrial(n-i); } else { ans += mint(x-1) * m.npr(n-2,k-1) * m.factrial(n-i) * m.factrial(n-i); //out(ans.val()); //out((mint(x-1) * m.factrial(n-i) * m.factrial(n-i)).val()); } //out(ans.val()); } out(ans.val()); } int main(){ int t = 1; //cin >> t; while(t--) solve(); }