Problem:
Score : 100 points

Problem Statement

There are N items, numbered 1, 2, \ldots, N.
For each i (1 \leq i \leq N), Item i has a weight of w_i and a value of v_i.

Taro has decided to choose some of the N items and carry them home in a knapsack.
The capacity of the knapsack is W, which means that the sum of the weights of items taken must be at most W.

Find the maximum possible sum of the values of items that Taro takes home.

Constraints

All values in input are integers.

1 \leq N \leq 100

1 \leq W \leq 10^5

1 \leq w_i \leq W

1 \leq v_i \leq 10^9

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 sum of the values of items that Taro takes home.

Sample Input 1

3 8
3 30
4 50
5 60

Sample Output 1

90

Items 1 and 3 should be taken.
Then, the sum of the weights is 3 + 5 = 8, and the sum of the values is 30 + 60 = 90.

Sample Input 2

5 5
1 1000000000
1 1000000000
1 1000000000
1 1000000000
1 1000000000

Sample Output 2

5000000000

The answer may not fit into a 32-bit integer type.

Sample Input 3

6 15
6 5
5 6
6 4
6 6
3 5
7 2

Sample Output 3

17

Items 2, 4 and 5 should be taken.
Then, the sum of the weights is 5 + 6 + 3 = 14, and the sum of the values is 6 + 6 + 5 = 17.

Solution in Go (1.6) (judge verdict: Accepted)

package main

import (
	"bufio"
	"errors"
	"fmt"
	"os"
	"strconv"
)

func lib_MaxInt64(values ...int64) (max int64, err error) {
	if len(values) == 0 {
		return 0, errors.New("empty slice is given")
	}
	max = values[0]
	for _, value := range values {
		if max < value {
			max = value
		}
	}
	return
}
func lib_MustMaxInt64(values ...int64) (max int64) {
	max, err := lib_MaxInt64(values...)
	if err != nil {
		panic(err)
	}
	return max
}
func lib_New2DimInt64Slice(row, col int) [][]int64 {
	ret := make([][]int64, row)
	for r := 0; r < row; r++ {
		ret[r] = make([]int64, col, col)
	}
	return ret
}
func main() {
	scanner := bufio.NewScanner(os.Stdin)
	const initialBufSize = 4096
	const maxBufSize = 1000000
	scanner.Buffer(make([]byte, initialBufSize), maxBufSize)
	scanner.Split(bufio.ScanWords)
	var N int64
	scanner.Scan()
	N, _ = strconv.ParseInt(scanner.Text(), 10, 64)
	var W int64
	scanner.Scan()
	W, _ = strconv.ParseInt(scanner.Text(), 10, 64)
	w := make([]int64, N)
	v := make([]int64, N)
	for i := int64(0); i < N; i++ {
		scanner.Scan()
		w[i], _ = strconv.ParseInt(scanner.Text(), 10, 64)
		scanner.Scan()
		v[i], _ = strconv.ParseInt(scanner.Text(), 10, 64)
	}
	fmt.Println(solve(N, W, w, v))
}
func solve(N int64, W int64, w []int64, v []int64) int64 {
	dp := lib_New2DimInt64Slice(int(N)+1, int(W+1))
	for i := 0; i < int(N); i++ {
		for j := int64(0); j <= W; j++ {
			newW := j + w[i]
			if newW <= W {
				dp[i+1][newW] = lib_MustMaxInt64(dp[i+1][newW], dp[i][j]+v[i])
			}
			dp[i+1][j] = lib_MustMaxInt64(dp[i+1][j], dp[i][j])
		}
	}
	return lib_MustMaxInt64(dp[N]...)
}