Problem:
0-1 Knapsack Problem

You have N items that you want to put them into a knapsack. Item i has value vi and weight wi.

You want to find a subset of items to put such that:

The total value of the items is as large as possible.

The items have combined weight at most W, that is capacity of the knapsack.

Find the maximum total value of items in the knapsack.

Input

N W
v1 w1
v2 w2
:
vN wN

The first line consists of the integers N and W. In the following lines, the value and weight of the i-th item are given.

Output

Print the maximum total values of the items in a line.

Constraints

1 ≤ N ≤ 100

1 ≤ vi ≤ 1000

1 ≤ wi ≤ 1000

1 ≤ W ≤ 10000

Sample Input 1

4 5
4 2
5 2
2 1
8 3

Sample Output 1

13

Sample Input 2

2 20
5 9
4 10

Sample Output 2

9

Solution in Kotlin (judge verdict: Wrong Answer)

/**
 * ナップザック問題
 * @link http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DPL_1_B&lang=jp
 */
fun main(args: Array<String>) {
    Main.init()

    Main.execute()

    Main.display()
}

class Main {
    companion object {

        private val DEFAULT_VALUE = 0

        private val matrix = arrayListOf<IntArray>()

        private var maxWeight: Int = 0
        private var itemNum: Int = 0


        private lateinit var itemList: List<Item>

        fun init() {
            val (inputItemNum, inputMaxWeight) = readLine()!!.split(" ")
            itemNum = inputItemNum.toInt()
            maxWeight = inputMaxWeight.toInt()

            itemList = List(itemNum) {
                val (value, weight) = readLine()!!.split(" ")
                Item(weight = weight.toInt(), value = value.toInt())
            }

            // matrixを準備
            for (index in 1..itemNum) {
                matrix.add(this.getEmptyMatrixRow())
            }
        }

        fun getEmptyMatrixRow(): IntArray {
            return IntArray(maxWeight + 1) {
                DEFAULT_VALUE
            }
        }


        fun execute() {
            /**
             * matrixを走査
             */
            var round = 0
            while (itemList.lastIndex >= round) {
                val item = itemList[round]

                val currentRound = matrix[round]
                val previewRound =
                    if (round == 0) this.getEmptyMatrixRow() else matrix[round - 1]


                for (weight in 0 until currentRound.size) {

                    val valueWhenNone = previewRound[weight]

                    if (weight - item.weight < 0) {
                        currentRound[weight] = valueWhenNone
                        continue
                    }

                    val valueWhenAdded = currentRound[weight - item.weight] + item.value

                    if (valueWhenAdded > valueWhenNone) {
                        currentRound[weight] = valueWhenAdded
                    } else {
                        currentRound[weight] = valueWhenNone
                    }
                }
                round++
            }
        }

        fun display() {
            // 最大の値を出力
            println(matrix.last().max())
        }
    }
}

data class Item(val weight: Int, val value: Int)