fhc2016r1_c.cpp

#include <queue>
#include <bitset>
#include <algorithm>
#include <iostream>
#include <set>
#include <map>
#include <iterator>
#include <cmath>
#include <tuple>
#include <stack>
#include <iomanip>
#include <string>
#include <vector>
#include <limits>
using namespace std;

long double solve(){
	long long n,a,b;
	cin >> n >> a >> b;
	vector<int> c(n);
	long long sum = 0;
	for(int i = 0; i < n; ++i){
		cin >> c[i];
		sum += c[i];
	}
	long double cycle = 0;
	for(int i = 0; i < n; ++i){
		cycle += c[i]*c[i]/2.0;
	}

	auto calc = [&](long long max){
		long double ret = max/sum*cycle;
		long long mod = max%sum;
		for(int i = 0; i < n; ++i){
			if(mod<=c[i]){
				ret += mod*mod/2.0;
				break;
			}else{
				ret += c[i]*c[i]/2.0;
				mod -= c[i];
			}
		}
		return ret;
	};
	long double ret = (calc(b)-calc(a))/(b-a);
	
	return ret;
}

int main() {
	cin.tie(nullptr); ios::sync_with_stdio(false);
	cout << fixed << setprecision(20);

	int t;
	cin >> t;
	for(int i = 0; i < t; ++i){
		cout << "Case #" << i+1 << ": " << solve() << endl;
	}
  return 0;
}