107B - Basketball Team - CodeForces Solution

// Problem: B. Basketball Team
// Contest: Codeforces - Codeforces Beta Round #83 (Div. 1 Only)
// URL: https://codeforces.com/problemset/problem/107/B
// Memory Limit: 256 MB
// Time Limit: 1000 ms
//
// Powered by CP Editor (https://cpeditor.org)

#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")

#include <bits/stdc++.h>

using namespace std;

void solve() {
    // READ QUESTION AGAIN 5 MINS AFTER YOU HAVE READ ONCE
    int N, M, H;
    cin >> N >> M >> H;
    int sum = 0;
    int curr = 0;
    for (int x = 0; x < M; x++) {
        int nb;
        cin >> nb;
        sum += nb;
        if (x == H - 1) curr = nb;
    }
    /*
    3 2 1
    2 2
    */
    if (sum < N) {
        cout << -1 << '\n';
        return;
    }
    if (sum - curr <= N - 2) {
        cout << 1 << '\n';
        return;
    }
    long double neg = 1;
    for (int x = 0; x + 1 < curr; x++) {
        neg *= (sum - N - x) / (long double)(sum - x - 1);
    }
    cout << fixed << setprecision(10) << 1 - neg << '\n';
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    int T = 1;
    // cin >> T;
    while (T--) {
        solve();
    }
    return 0;
}