Codeforces Round #311 (Div. 2)（B）排序

B. Pasha and Tea

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

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 ai milliliters of water.

It turned out that among Pasha's friends there are exactly n boys and exactly n girls and all of them are going to come to the tea party. To please everyone, Pasha decided to pour the water for the tea as follows:

• Pasha can boil the teapot exactly once by pouring there at most w milliliters of water;
• 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 milliliters of water.

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 ai (1 ≤ ai ≤ 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 test(s)

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

Note

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

题意：有n个男孩，n个女孩。有2*n个茶壶，一共有W毫升的茶水。当每个女孩得到x毫升的水，那么男孩就必须获得2*x的水，问最多可以倒出多少水

题解：先排序，求出这次倒水量的上界  男孩的最小容量和女孩的最小容量：max=min(a[n+1]/2,a[1])，最多只能倒出这么多的水（max*3*n），如果可以容下所有的水，那么直接输出w

#include <set>#include <map>#include <list> #include <cmath> #include <queue> #include <vector>#include <cstdio> #include <string> #include <cstring>#include <iomanip> #include <iostream> #include <sstream>#include <algorithm>#define LL long long using namespace std;#define N 200000double a[N<<1];int main(){#ifdef CDZSCfreopen("i.txt","r",stdin);#endifint mx[10],mn[10];int n;double w;while(~scanf("%d%lf",&n,&w)){for(int i=1;i<=2*n;i++){scanf("%lf",a+i);}sort(a+1,a+2*n+1);double mx=min(a[n+1]/2,a[1]);mx*=3;printf("%.10lf",n*mx>=w?w:(double(n)*mx));puts("");}return 0;}