#pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #include using namespace std; typedef long long ll; typedef long double ld; #define REP(i, n) for (int i = 0; i < (n); ++i) #define REPR(i, n) for (int i = n - 1; i >= 0; --i) #define FOR(i, m, n) for (int i = m; i < n; ++i) #define FORR(i, m, n) for (int i = m; i >= n; --i) #define ALL(v) (v).begin(),(v).end() #define ALLR(v) (v).rbegin(),(v).rend() #define SORT(v) sort(ALL(v)) #define RSORT(v) sort(ALLR(v)) #define REV(v) reverse(ALL(v)) #define UNIQUE(x) SORT(x), x.erase(unique(ALL(x)), x.end()) #define fi first #define se second #define PB push_back #define EB emplace_back using pii = pair; using pll = pair; template using vc = vector; template using vvc = vector>; template using vvvc = vector>; using vi = vc; using vl = vc; using vpi = vc; using vpl = vc; // noimi #define INT(...) int __VA_ARGS__;IN(__VA_ARGS__) #define LL(...) ll __VA_ARGS__;IN(__VA_ARGS__) #define STR(...) string __VA_ARGS__;IN(__VA_ARGS__) #define DBL(...) double __VA_ARGS__;IN(__VA_ARGS__) #define VEC(type, name, size) vector name(size);IN(name) #define VEC2(type, name1, name2, size) vector name1(size), name2(size);for(int i = 0; i < size; i++) IN(name1[i], name2[i]) #define VEC3(type, name1, name2, name3, size) vector name1(size), name2(size), name3(size);for(int i = 0; i < size; i++) IN(name1[i], name2[i], name3[i]) #define VEC4(type, name1, name2, name3, name4, size) vector name1(size), name2(size), name3(size), name4(size); for(int i = 0; i < size; i++) IN(name1[i], name2[i], name3[i], name4[i]); #define VV(type, name, h, w) vector> name(h, vector(w));IN(name) int scan() { return getchar(); } void scan(int &a) { cin >> a; } void scan(long long &a) { cin >> a; } void scan(char &a) { cin >> a; } void scan(double &a) { cin >> a; } void scan(string &a) { cin >> a; } template void scan(pair &p) { scan(p.first), scan(p.second); } template void scan(vector &); template void scan(vector &a) {for(auto &i : a) scan(i);} template void scan(T &a) { cin >> a; } void IN() {} template void IN(Head &head, Tail &...tail) {scan(head);IN(tail...);} // tute7627 template using PQ = priority_queue; template using QP = priority_queue,greater>; templatevoid stout(const T &v,ll h,ll w){for(ll i=0;ivoid stout(const T &v,ll n){for(ll i=0;ivoid stout(const vector&v){stout(v,v.size());} templatevoid stout(const vector>&v){for(auto &vv:v)stout(vv,vv.size());} templatevoid debug(const T &v,ll h,ll w){for(ll i=0;ivoid debug(const T &v,ll n){for(ll i=0;ivoid 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()){cerr<void debug(queue st){while(!st.empty()){cerr<void debug(deque st){while(!st.empty()){cerr<void debug(PQ st){while(!st.empty()){cerr<void debug(QP st){while(!st.empty()){cerr<void debug(const set&v){for(auto z:v)cerr<void debug(const multiset&v){for(auto z:v)cerr<void debug(const array &a){for(auto z:a)cerr<void debug(const map&v){for(auto z:v)cerr<<"["<void OUT(Head&& head, Tail&&... tail){cout << head;if(sizeof...(tail)) cout << " ";OUT(move(tail)...);} void ERR() {cerr << "\n";} template void ERR(Head&& head, Tail&&... tail){cerr << head;if(sizeof...(tail)) cerr << " ";ERR(move(tail)...);} void fsp(int n){cout << fixed << setprecision(n);} templatebool chmax(T &a, const T &b) { if (abool chmin(T &a, const T &b) { if (b // using namespace atcoder; // using mint=modint998244353; // using mint=modint1000000007; int main(){ cin.tie(0); ios::sync_with_stdio(false); INT(a,b,c,n); vector dp(a+1,vector(b+1,vector(c+1,0.))); dp[a][b][c]=1; REP(_,n){ vector tp(a+1,vector(b+1,vector(c+1,0.))); REP(i,a+1) REP(j,b+1) REP(k,c+1){ if(i+j+k<=1) continue; double den=1.*(i+j+k)*(i+j+k-1)/2; double aa=1.*i*(i-1)/2/den; double bb=1.*j*(j-1)/2/den; double cc=1.*k*(k-1)/2/den; double rem=1.-aa-bb-cc; if(i>=2) tp[i-1][j][k]+=dp[i][j][k]*aa; if(j>=2) tp[i][j-1][k]+=dp[i][j][k]*bb; if(k>=2) tp[i][j][k-1]+=dp[i][j][k]*cc; tp[i][j][k]+=dp[i][j][k]*rem; } swap(tp,dp); } double ra=0,rb=0,rc=0; REP(i,a+1) REP(j,b+1) REP(k,c+1){ ra+=dp[i][j][k]*(a-i); rb+=dp[i][j][k]*(b-j); rc+=dp[i][j][k]*(c-k); } fsp(10); OUT(ra,rb,rc); }