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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;

public class Main{
	static FastReader input = new FastReader();
	static PrintWriter out = new PrintWriter(System.out);

	static int n, w;
	static int[][] wV;

	static long[][] memo;
	static final int _INF = (int) -1e9;
	static boolean[][] boolMemo;
	static boolean[][] visitiedBoolMemo;

	static boolean reachable(int sum, int w, int n) {

		if (w < 0 || sum < 0)
			return false;

		if (sum == 0)
			return true;

		if (n < 0)
			return false;

		if (visitiedBoolMemo[n][sum])
			return boolMemo[n][sum];

		visitiedBoolMemo[n][sum] = true;
		return boolMemo[n][sum] = reachable(sum - wV[n][1], w - wV[n][0], n - 1) || reachable(sum, w, n - 1);

	}

	public static void main(String[] args) throws NumberFormatException, IOException {

		n = input.nextInt();
		w = input.nextInt();

		wV = new int[n][2];

		for (int i = 0; i < n; i++) {
			wV[i][0] = input.nextInt();
			wV[i][1] = input.nextInt();
		}


		int i = (int) 1e3;
		for (; i >= 0; i--) {
			boolMemo = new boolean[n + 10][(int) 1e3 + 50];
			visitiedBoolMemo = new boolean[n + 10][(int) 1e3 + 50];
			if (reachable(i, w, n-1)) {
				break;
			}
		}
		
		System.out.println(i);
	}

	static class FastReader {
		BufferedReader br;
		StringTokenizer st;

		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

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

		int nextInt() throws NumberFormatException, IOException {
			return Integer.parseInt(next());
		}

		long nextLong() throws NumberFormatException, IOException {
			return Long.parseLong(next());
		}

		double nextDouble() throws NumberFormatException, IOException {
			return Double.parseDouble(next());
		}

		String nextLine() throws IOException {
			String str = "";
			str = br.readLine();
			return str;
		}
	}
}