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 10^9

1 \leq w_i \leq W

1 \leq v_i \leq 10^3

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

1 1000000000
1000000000 10

Sample Output 2

10

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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;
import java.io.*;

//atcoder need change class name to Main
//E - Knapsack 2
//stand dp 
//this time Weight is to big, can not use it as lenght of dp
//loop from right to left

//https://atcoder.jp/contests/dp/tasks/dp_c

public class Main {
    static StringTokenizer st;
    static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

 
    public static void main(String[] args) throws IOException {
  
        int N = nextInt(); 
        int W = nextInt(); 
 
        //no need calc sum, use max 100* 1000
        int maxValue = 100000;
        long[] dp = new long[maxValue+1];
        Arrays.fill(dp, Integer.MAX_VALUE);
        dp[0] = 0;

        for (int i=1; i<=N;  i++) {
            int w = nextInt();
            int v = nextInt();
            for (int j=maxValue; j>=v; j--) {// from right to left
                //from right to left,  make usue only use 1
                //this can be use limit item
                //use count array 
                dp[j] = Math.min(dp[j], dp[j-v] + w); 
            }
        }

        for (int i = maxValue; i>=0; i--){
            if (dp[i] <=W) {
                System.out.println(i);
                return;
            }
        }
    }
    

    public static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }
    public static long nextLong() throws IOException {
        return Long.parseLong(next());
    }

    public static double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }

    static String next() throws IOException {
        while (st == null || !st.hasMoreTokens())
            st = new StringTokenizer(br.readLine().trim());
        return st.nextToken();
    }
}