Problem:
Score : 700 points

Problem Statement

You are given N integers A_1, A_2, ..., A_N.

Consider the sums of all non-empty subsequences of A. There are 2^N - 1 such sums, an odd number.

Let the list of these sums in non-decreasing order be S_1, S_2, ..., S_{2^N - 1}.

Find the median of this list, S_{2^{N-1}}.

Constraints

1 \leq N \leq 2000

1 \leq A_i \leq 2000

All input values are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the median of the sorted list of the sums of all non-empty subsequences of A.

Sample Input 1

3
1 2 1

Sample Output 1

2

In this case, S = (1, 1, 2, 2, 3, 3, 4). Its median is S_4 = 2.

Sample Input 2

1
58

Sample Output 2

58

In this case, S = (58).

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <algorithm>

int main()
{
	int k;
	long long int a[100010];
	std::cin >> k;
	
	for (int i = 0; i < k; ++i)
	{
		std::cin >> a[i];
		if (i == k - 1 && a[i] != 2)
		{
			std::cout << -1;
			return 0;
		}
	}
	
	long long int max = 3, min = 2;
	for (int i = k - 2; i >= 0; --i)
	{
		long long int check = (max / a[i]) * a[i];
		if (check >= min && check <= max)
		{
			if (min % a[i] == 0)
				min = a[i];
			else
				min = ((min / a[i]) + 1) * a[i];
			
			max = (((max / a[i]) * a[i]) + a[i]) - 1;
		}
		else
		{
			std::cout << -1;
			return 0;
		}
		
//		std::cout << min << " " << max << "\n";
	}
	
	if (min < 0)
		a[12312321321] = 2;
	else if (max < 0)
		while(1)
		{
			a[2] = 2;
		}
	
	std::cout << min << " " << max << "\n";
}