//#pragma GCC target("avx2") //#pragma GCC optimize("O3") //#pragma GCC optimize("unroll-loops") #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using ll = long long; using pii = pair; using pll = pair; using pli = pair; #define TEST cerr << "TEST" << endl #define AMARI 998244353 //#define AMARI 1000000007 #define el '\n' #define El '\n' #define eps 1e-6 //r位を取った時スコアはいくつになるか ll func(ll score,int r,ll s){ ll ans = 500 * s / (8 + 2 * r); ans += 50 * s; ans += score; return ans; } #define MULTI_TEST_CASE false void solve(void){ int n; ll s; int id; cin >> n >> s >> id; vector a(n); for(int i = 0; i < n; i++)cin >> a[i]; swap(a[id],a[n - 1]); ll writer_score = a.back() + 100LL * s; a.pop_back(); n--; sort(a.rbegin(),a.rend()); long double ans = 1; cout << fixed << setprecision(15); int bunbo = n; for(int i = 0; i < n; i++){ //もし(N-i)位をとっても writer_score をオーバーするなら0を出力 if(func(a[i],n - i,s) > writer_score){ cout << 0 << el; return; } //cerr << func(a[i],1,s) << el; //もし1位をとっても writer_score をオーバーしないならそのまま if(func(a[i],1,s) <= writer_score)continue; //何位以下じゃないといけないかにぶたん int l = 0,r = n - i + 1; while(r - l >= 2){ int c = (r + l) / 2; if(func(a[i],c,s) <= writer_score)r = c; else l = c; } //cerr << l << ' ' << r << el; for(int j = r; j >= l - 1; j--){ if(func(a[i],j,s) > writer_score){ //j-1位がギリギリOKで、j位はダメ //一番下の取りうる順位はn int bunsi = 0,bunbo = 0; bunsi = n - j; bunbo = n - i; //cerr << bunsi << ' ' << bunbo << el; ans *= (long double)bunsi / (long double)bunbo; break; } } } cout << ans << El; return; } void calc(void){ return; } signed main(void){ cin.tie(nullptr); ios::sync_with_stdio(false); calc(); int t = 1; if(MULTI_TEST_CASE)cin >> t; while(t--){ solve(); } return 0; }