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: Wrong Answer)

import java.io.*;
import java.math.BigInteger;
import java.util.*;


public class  Main{
	static int inf=(int)2e9;
	static long[][]memo;
	static int[]v;
	static int[]ws;
	static long dp(int i,int val) {
		if(i>=v.length) {
			if(val==0)return 0;
			return inf;
		}
		if(val<0)return inf;
		if(memo[i][val]!=-1)return memo[i][val];
		
		return memo[i][val]=Math.min(dp(i+1,val-v[i])+ws[i],dp(i+1,val));
	}
    public static void main(String[] args) throws Exception{
    	MScanner sc = new MScanner(System.in);
        //MScanner sc = new MScanner("reduce.in");
        PrintWriter pw=new PrintWriter(System.out);
        int n=sc.nextInt();int w=sc.nextInt();
        v=new int[n];ws=new int[n];
        memo=new long[n][100001];
        for(int i=0;i<n;i++) {
        	ws[i]=sc.nextInt();v[i]=sc.nextInt();
        }
        
        for(long[]a:memo)Arrays.fill(a,-1);
        int ans=-1;
        for(int i=1;i<100001;i++) {
        	dp(0,i);
        }
       // System.out.println(memo[0][17]);
        for(int i=0;i<n;i++) {
        	for(int j=0;j<100000;j++) {
        		if(memo[i][j]!=-1) {
        			if(memo[i][j]<=w) {
        				ans=Math.max(ans,j);
        			}
        		}
        	}
        }
        pw.println(ans);
        pw.flush();
    }
    
    static class MScanner {
		StringTokenizer st;
		BufferedReader br;
 
		public MScanner(InputStream system) {
			br = new BufferedReader(new InputStreamReader(system));
		}
 
		public MScanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}
 
		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}
 
		public String nextLine() throws IOException {
			return br.readLine();
		}
 
		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}
 
		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}
 
		public char nextChar() throws IOException {
			return next().charAt(0);
		}
 
		public Long nextLong() throws IOException {
			return Long.parseLong(next());
		}
 
		public boolean ready() throws IOException {
			return br.ready();
		}
 
		public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}
	}
}