#include using namespace std; #define REP(i,n) for(ll i=0;i<(ll)n;i++) #define dump(x) cerr << "Line " << __LINE__ << ": " << #x << " = " << (x) << "\n"; #define spa << " " << #define fi first #define se second #define ALL(a) (a).begin(),(a).end() #define ALLR(a) (a).rbegin(),(a).rend() using ld = long double; using ll = long long; using ull = unsigned long long; using pii = pair; using pll = pair; using pdd = pair; template using V = vector; template using P = pair; template vector make_vec(size_t n, T a) { return vector(n, a); } template auto make_vec(size_t n, Ts... ts) { return vector(n, make_vec(ts...)); } template ostream& operator << (ostream& os, const pair v){os << "(" << v.first << ", " << v.second << ")"; return os;} template ostream& operator<<(ostream &os, const vector &v) { for (auto &e : v) os << e << ' '; return os; } template ostream& operator<<(ostream& os, const vector> &v){ for(auto &e : v){os << e << "\n";} return os;} struct fast_ios { fast_ios(){ cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_; template void UNIQUE(vector &x) {sort(ALL(x));x.erase(unique(ALL(x)), x.end());} template bool chmax(T &a, const T &b) { if (a bool chmin(T &a, const T &b) { if (a>b) { a=b; return 1; } return 0; } void fail() { cout << -1 << '\n'; exit(0); } inline int popcount(const int x) { return __builtin_popcount(x); } inline int popcount(const ll x) { return __builtin_popcountll(x); } template void debug(vector>&v,ll h,ll w){for(ll i=0;i void debug(vector&v,ll n){if(n!=0)cerr<> A >> B >> C >> N; auto dp = make_vec(N+1, A+1, B+1, C+1, 3, (double)0); auto check = make_vec(N+1, A+1, B+1, C+1, 3, false); auto rec = [&](auto self, ll n, ll a, ll b, ll c, ll idx) -> double{ if(check[n][a][b][c][idx]) return dp[n][a][b][c][idx]; if(n == 0) return 0; ll S = a + b + c; double res = 0; double pa = (double)a*(a-1)/(S*(S-1)); double pb = (double)b*(b-1)/(S*(S-1)); double pc = (double)c*(c-1)/(S*(S-1)); double ga = 0, gb = 0, gc = 0; if(idx == 0) ga = 1.0; if(idx == 1) gb = 1.0; if(idx == 2) gc = 1.0; if(a > 1) res += pa * (self(self, n-1, a-1, b, c, idx) + ga); if(b > 1) res += pb * (self(self, n-1, a, b-1, c, idx) + gb); if(c > 1) res += pc * (self(self, n-1, a, b, c-1, idx) + gc); res += (1.0 - pa - pb - pc) * self(self, n-1, a, b, c, idx); dp[n][a][b][c][idx] = res; check[n][a][b][c][idx] = true; return res; }; cout << rec(rec, N, A, B, C, 0) spa rec(rec, N, A, B, C, 1) spa rec(rec, N, A, B, C, 2)<< endl; return 0; }