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 Kotlin (1.0.0) (judge verdict: Accepted)

import java.math.BigInteger

fun main(args: Array<String>) {
    val n = readLine()!!.toInt()
    val aList = readLine()!!.split(" ").map(String::toInt)
    val aSum = aList.sum()
    var dpTable = BigInteger.ONE
    for (a in aList) {
        dpTable = dpTable.or(dpTable.shiftLeft(a))
    }
    val ans = (((aSum + 1) / 2)..aSum).filter { dpTable.testBit(it) }.first()
    println(ans)
}