Problem:
Score : 400 points

Problem Statement

You have N items and a bag of strength W.
The i-th item has a weight of w_i and a value of v_i.

You will select some of the items and put them in the bag.
Here, the total weight of the selected items needs to be at most W.

Your objective is to maximize the total value of the selected items.

Constraints

1 ≤ N ≤ 100

1 ≤ W ≤ 10^9

1 ≤ w_i ≤ 10^9

For each i = 2,3,...,N, w_1 ≤ w_i ≤ w_1 + 3.

1 ≤ v_i ≤ 10^7

W, each w_i and v_i are integers.

Input

Input is given from Standard Input in the following format:

N W
w_1 v_1
w_2 v_2
:
w_N v_N

Output

Print the maximum possible total value of the selected items.

Sample Input 1

4 6
2 1
3 4
4 10
3 4

Sample Output 1

11

The first and third items should be selected.

Sample Input 2

4 6
2 1
3 7
4 10
3 6

Sample Output 2

13

The second and fourth items should be selected.

Sample Input 3

4 10
1 100
1 100
1 100
1 100

Sample Output 3

400

You can take everything.

Sample Input 4

4 1
10 100
10 100
10 100
10 100

Sample Output 4

0

You can take nothing.

Solution in Go (1.6) (judge verdict: Wrong Answer)

package main

import "fmt"

type item struct {
	w int
	v int
}

type ValueWeight struct {
	valueSum  int
	itemCount int
}

var n, w int

func main() {
	fmt.Scan(&n, &w)
	items := make([]item, n)

	var firstWeight int
	for i := 0; i < n; i++ {
		if i == 0 {
			fmt.Scan(&firstWeight, &(items[i].v))
			firstWeight = firstWeight - 1
			items[i].w = 1
			continue
		}
		fmt.Scan(&(items[i].w), &(items[i].v))
		items[i].w = items[i].w - firstWeight
	}

	weightSumMax := 3 * n

	// dp[i][j]はi番目までのitemを最適にpickした際、各weightにおけるvalueの最大値
	dp := make([][]ValueWeight, n)
	for i := 0; i < n; i++ {
		dp[i] = make([]ValueWeight, weightSumMax+1)
		for j := 0; j <= weightSumMax; j++ {
			dp[i][j].valueSum = -1
		}
	}

	dp[0][0] = ValueWeight{0, 0}
	dp[0][1] = ValueWeight{items[0].v, 1}
	//fmt.Println(dp[0])
	for i := 1; i < n; i++ {
		for j := 0; j <= weightSumMax; j++ {
			if j-items[i].w < 0 {
				dp[i][j].valueSum = dp[i-1][j].valueSum
				dp[i][j].itemCount = dp[i-1][j].itemCount
				continue
			}

			v1 := dp[i-1][j].valueSum
			i1 := dp[i-1][j].itemCount
			v2 := dp[i-1][j-items[i].w].valueSum
			i2 := dp[i-1][j-items[i].w].itemCount

			if v1 == -1 && v2 == -1 {
				dp[i][j].valueSum = v1
				dp[i][j].itemCount = i1
			} else if v1 == -1 {
				v2 = v2 + items[i].v
				dp[i][j].valueSum = v2
				dp[i][j].itemCount = i2 + 1
			} else if v2 == -1 {
				dp[i][j].valueSum = v1
				dp[i][j].itemCount = i1
			} else {
				v2 = v2 + items[i].v
				if v1 > v2 {
					dp[i][j].valueSum = v1
					dp[i][j].itemCount = i1
				} else {
					dp[i][j].valueSum = v2
					dp[i][j].itemCount = i2 + 1
				}
			}
		}

		//fmt.Println(dp[i])
	}

	max := 0
	for j := weightSumMax; j >= 0; j-- {
		item := dp[n-1][j]
		value := item.valueSum
		weight := j + (firstWeight)*item.itemCount

		//fmt.Printf("%v: value=%v weight=%v\n", j, value, weight)
		if value == -1 || weight > w {
			continue
		}
		if value > max {
			max = value
		}
	}
	fmt.Println(max)
}