#pragma region Macros #include using namespace std; template inline bool chmax(T &a, T b) { if(a < b) { a = b; return 1; } return 0; } template inline bool chmin(T &a, T b) { if(a > b) { a = b; return 1; } return 0; } #ifdef DEBUG template ostream &operator<<(ostream &os, const pair &p) { os << '(' << p.first << ',' << p.second << ')'; return os; } template ostream &operator<<(ostream &os, const vector &v) { os << '{'; for(int i = 0; i < (int)v.size(); i++) { if(i) { os << ','; } os << v[i]; } os << '}'; return os; } void debugg() { cerr << endl; } template void debugg(const T &x, const Args &... args) { cerr << " " << x; debugg(args...); } #define debug(...) \ cerr << __LINE__ << " [" << #__VA_ARGS__ << "]: ", debugg(__VA_ARGS__) #define dump(x) cerr << __LINE__ << " " << #x << " = " << (x) << endl #else #define debug(...) (void(0)) #define dump(x) (void(0)) #endif struct Setup { Setup() { cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } __Setup; using ll = long long; #define ALL(v) (v).begin(), (v).end() #define RALL(v) (v).rbegin(), (v).rend() #define FOR(i, a, b) for(int i = (a); i < int(b); i++) #define REP(i, n) FOR(i, 0, n) const int INF = 1 << 30; const ll LLINF = 1LL << 60; constexpr int MOD = 1000000007; const int dx[4] = {1, 0, -1, 0}; const int dy[4] = {0, 1, 0, -1}; void Case(int i) { cout << "Case #" << i << ": "; } int popcount(int x) { return __builtin_popcount(x); } ll popcount(ll x) { return __builtin_popcountll(x); } #pragma endregion Macros int A, B, C, N; array memo[55][55][55][55]; bool seen[55][55][55][55]; array rec(int i, int a, int b, int c) { if(seen[i][a][b][c]) return memo[i][a][b][c]; if(i == N) { seen[i][a][b][c] = true; return (memo[i][a][b][c] = {0.0, 0.0, 0.0}); } array res = {0.0, 0.0, 0.0}; int sum = a + b + c; double pa = (double)(a * (a-1)) / (sum * (sum-1)); double pb = (double)(b * (b-1)) / (sum * (sum-1)); double pc = (double)(c * (c-1)) / (sum * (sum-1)); double other = 1.0 - (pa + pb + pc); // aa if(a >= 2) { auto tmp = rec(i+1, a-1, b, c); res[0] += pa * (tmp[0] + 1); res[1] += pa * tmp[1]; res[2] += pa * tmp[2]; } // bb if(b >= 2) { auto tmp = rec(i+1, a, b-1, c); res[0] += pb * tmp[0]; res[1] += pb * (tmp[1] + 1); res[2] += pb * tmp[2]; } // cc if(c >= 2) { auto tmp = rec(i+1, a, b, c-1); res[0] += pc * tmp[0]; res[1] += pc * tmp[1]; res[2] += pc * (tmp[2] + 1); } // other { auto tmp = rec(i+1, a, b, c); res[0] += other * tmp[0]; res[1] += other * tmp[1]; res[2] += other * tmp[2]; } seen[i][a][b][c] = true; return (memo[i][a][b][c] = res); } int main() { cin >> A >> B >> C >> N; auto res = rec(0, A, B, C); cout << res[0] << " " << res[1] << " " << res[2] << "\n"; }