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: Runtime Error)

import java.util.Arrays;
import java.util.Scanner;

class Main{
    static int KnapSack(int val[], int wt[], int n, int W) {
        // array to store final result
        // dp[i] stores the profit with KnapSack capacity "i"
        int[] dp = new int[W + 1];

        // initially profit with 0 to W KnapSack capacity is 0
        Arrays.fill(dp, 0);

        // iterate through all items
        for (int i = 0; i < n; i++)

            // traverse dp array from right to left
            for (int j = W; j >= wt[i]; j--)
                dp[j] = Math.max(dp[j], val[i] + dp[j - wt[i]]);

        /*
         * above line finds out maximum of dp[j](excluding ith element value) and val[i]
         * + dp[j-wt[i]] (including ith element value and the profit with
         * "KnapSack capacity - ith element weight")
         */
        return dp[W];
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int w = sc.nextInt();
        int m = (int)1e3+10;
        int[] wi = new int[m],vi = new int[m];

        int V = 0;
        for (int i = 1; i <= n; i++) {
            wi[i] =sc.nextInt();
            vi[i] = sc.nextInt() ;
            // V+= vi[i];
        }

        int ret = KnapSack(vi,wi, n, w);
        System.out.println(ret);
        // long dp[] = new long[m];
        // long inf =(long) 1e13+10;
        // Arrays.fill(dp, inf);

        // dp[0] =0 ;
        // for(int item =1;item<=n;item++)
        // {
        //     int wt = wi[item], v = vi[item];
        //     for(int i =V;i>=v;i--)
        //     {
        //         dp[i] = Math.min(dp[i],dp[i-v]+wt);
        //     }
        // }
        // for(int i = V;i>=0;i--){
		// if(dp[i] <= w){
        //     // cout << i << endl;
        //     System.out.println(i);
		// 	break;
		// }
	// }
    }
}