#ifdef LOCAL111 #define _GLIBCXX_DEBUG #else #define NDEBUG #endif #define _USE_MATH_DEFINES #ifndef _GLIBCXX_NO_ASSERT #include #endif #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #if __cplusplus >= 201103L #include #include #include #include #include #include #include #include #endif // C++ #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #if __cplusplus >= 201103L #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #endif const int INF = 1e9; using namespace std; template ostream& operator<< (ostream& os, const pair& p) { os << '(' << p.first << ' ' << p.second << ')'; return os; } #define endl '\n' #define ALL(a) (a).begin(),(a).end() #define SZ(a) int((a).size()) #define FOR(i,a,b) for(int i=(a);i<(b);++i) #define RFOR(i,a,b) for (int i=(b)-1;i>=(a);i--) #define REP(i,n) FOR(i,0,n) #define RREP(i,n) for (int i=(n)-1;i>=0;i--) #ifdef LOCAL111 #define DEBUG(x) cout<<#x<<": "<<(x)< void dpite(T a, T b){ for(T ite = a; ite != b; ite++) cout << (ite == a ? "" : " ") << *ite; cout << endl;} #else #define DEBUG(x) true template void dpite(T a, T b){ return; } #endif #define F first #define S second #define SNP string::npos #define WRC(hoge) cout << "Case #" << (hoge)+1 << ": " template void pite(T a, T b){ for(T ite = a; ite != b; ite++) cout << (ite == a ? "" : " ") << *ite; cout << endl;} template bool chmax(T& a, T b){if(a < b){a = b; return true;} return false;} template bool chmin(T& a, T b){if(a > b){a = b; return true;} return false;} typedef long long int LL; typedef unsigned long long ULL; typedef pair P; void ios_init(){ cout.setf(ios::fixed); cout.precision(12); #ifdef LOCAL111 return; #endif ios::sync_with_stdio(false); cin.tie(0); } int main() { ios_init(); int f, n, k; while(cin >> f >> n >> k) { k = n-k+1; auto solve = [&](int x) -> double { vector> dp(n+1, vector(n+1)); dp[0][0] = 1.; double p1 = (x-1.) / f; double p2 = double(f-x) / f; DEBUG(x); DEBUG(p1); DEBUG(p2); REP(_, n) { DEBUG(_); RREP(i, n+1) { RREP(j, n+1) { dp[i][j] *= 1./f; if(i > 0) { dp[i][j] += dp[i-1][j] * p1; } if(j > 0) { dp[i][j] += dp[i][j-1] * p2; } } } REP(i, n+1) dpite(ALL(dp[i])); } double ans = 0; REP(x, k) REP(y, n-k+1) { DEBUG(x); DEBUG(y); DEBUG(dp[x][y]); ans += dp[x][y]; } DEBUG(ans); return ans; }; double ans = 0; FOR(x, 1, f+1) { ans += x * solve(x); } cout << ans << endl; } return 0; }