CodeForces - 557B Pasha and Tea （模拟）

CodeForces - 557B

Pasha and Tea

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Description

Pasha decided to invite his friends to a tea party. For that occasion, he has a large teapot with the capacity of w milliliters and 2n tea cups, each cup is for one of Pasha's friends. The i-th cup can hold at most a_i

It turned out that among Pasha's friends there are exactly n boys and exactly n

• Pasha can boil the teapot exactly once by pouring there at most w
• Pasha pours the same amount of water to each girl;
• Pasha pours the same amount of water to each boy;
• if each girl gets x milliliters of water, then each boy gets 2x

In the other words, each boy should get two times more water than each girl does.

Pasha is very kind and polite, so he wants to maximize the total amount of the water that he pours to his friends. Your task is to help him and determine the optimum distribution of cups between Pasha's friends.

Input

The first line of the input contains two integers, n and w (1 ≤ n ≤ 10⁵, 1 ≤ w ≤ 10⁹) — the number of Pasha's friends that are boys (equal to the number of Pasha's friends that are girls) and the capacity of Pasha's teapot in milliliters.

The second line of the input contains the sequence of integers a_i (1 ≤ a_i ≤ 10⁹, 1 ≤ i ≤ 2n) — the capacities of Pasha's tea cups in milliliters.

Output

Print a single real number — the maximum total amount of water in milliliters that Pasha can pour to his friends without violating the given conditions. Your answer will be considered correct if its absolute or relative error doesn't exceed 10^- 6.

Sample Input

Input

2 41 1 1 1

Output

3

Input

3 184 4 4 2 2 2

Output

18

Input

1 52 3

Output

4.5

Hint

Pasha also has candies that he is going to give to girls but that is another task...

Source

Codeforces Round #311 (Div. 2)

//题意：输入n，w；

表示你有n个女同学，n个男同学，一个茶壶的容量为w，有n个茶杯，它们的容量已经给出，现在要给他们倒茶，倒茶有以下要求：

1、男生茶水是女生的二倍；

2、要求倒的茶水尽量多；

问最多到多少茶水？

#include<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
using namespace std;
const int MAXN = 2e5 + 100;
double a[MAXN];
int main()
{
	int n;
	double w;
	while(scanf("%d%lf",&n,&w)!=EOF)
	{
		
		for(int i=0;i<2*n;i++)
		{
			scanf("%lf",a + i);
		}
		sort(a, a + 2 * n);
		if(a[0] * 2 <= a[n]){
			if(w >= a[0]*3*n){
				printf("%lf\n", a[0] * 3 * n);
			}
			else{
				printf("%lf\n", w);
			}
		}
		else{
			double v = a[n] / 2;
			if(w >= v * 3 * n){
				printf("%lf\n", v * 3 * n);
			}
			else{
				printf("%lf\n", w);
			}
		}
	}
	return 0;
}