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.*;
import java.math.BigInteger;
 
public class Main {
	static PrintWriter out;
	static StringBuilder sb;
	static final double EPS = 1e-9;
	static long mod = (int) 1e9 + 7;
	static int inf = (int) 1e9 + 2;
	static long[] fac;
	static int[] si;
	static ArrayList<Integer> primes;
	static ArrayList<Integer>[] ad;
	static ArrayList<pair>[] d;
	static edge[] ed;
	static boolean []vis;
	static int[] l, ch;
	static int[] occ;
	static Queue<Integer>[] can;
	static String s;
	static int n,m;
	static long [][]memo;
	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		out = new PrintWriter(System.out);
	    n=sc.nextInt();
	    long W=sc.nextLong();
	    memo=new long [n+1][100000+1];
	    long []w=new long [n];
	    int []v=new int [n];
	    for(int i=0;i<n;i++) {
	          w[i]=sc.nextLong();
	          v[i]=sc.nextInt();
	    }
	//    System.out.println(Arrays.toString(w)+" "+Arrays.toString(v));
	   for(long []h:memo)
		   Arrays.fill(h, 600000000000l);
	    int all=0;
	    for(int i=0;i<n;i++) {
	    	all+=v[i];
	      memo[i][0]=0;
	    }
	 //   for(int i=0;i<memo[0].length;i++)
	   // 	memo[n][i]=0;
	    
	//    for(long []h:memo)
		//	   System.out.println(Arrays.toString(h));
	    memo[n][0]=0;
	    for(int i=n-1;i>=0;i--) {
	    	memo[i][0]=0;
	    	for(int j=1;j<=100000;j++) {
	    	       long leave=memo[i+1][j];
	    	       long take=600000000000l;
	    	       if(j-v[i]>=0)
	    	         take=memo[i+1][j-v[i]]+w[i];
	    	       memo[i][j]=Math.min(leave,take);
	    	}
	    }
	    int ans=0;
	 //   for(long []h:memo)
		//	   System.out.println(Arrays.toString(h));
	    for(int i=0;i<=n;i++)
	    	for(int j=0;j<memo[0].length;j++) {
	    		if(memo[i][j]!=0 && memo[i][j]<=W)
	    			ans=Math.max(ans, j);
	    	}
	    out.println(ans);
		out.flush();
	}
	static long inver(long x,long kk) {
		int a = (int) x;
		long e = (kk - 2);
		long res = 1;
		while (e > 0) {
			if ((e & 1) == 1) {
				// System.out.println(res*a);
				res = (int) ((1l * res * a) % kk);
			}
			a = (int) ((1l * a * a) % kk);
			e >>= 1;
		}
		// out.println(res+" "+x);
		return res % kk;
	}
 
	static TreeSet<Integer> trr;

	static class qu  implements Comparable<qu>{
		int i,j;
		qu(int a, int s) {
			i=a;
			j=s;
		}
       public String toString() {
    	   return i+" "+j;
       }
       public int compareTo(qu o) {
    	   if(i==o.i)
    		   return j-o.j;
    	   return i-o.i;
       }
	}
    
	static class pair {
		int to;
		int number;
 
		pair(int t, int n) {
			number = n;
			to = t;
		}
 
		public String toString() {
			return to + " " + number;
		}
	}
 
	static double modPow(double a, int e)
 
	{
		double res = 1;
		while (e > 0) {
			if ((e & 1) == 1)
				res = (res * a);
			a = (a * a);
			e >>= 1;
		}
		return res;
	}
 
	static boolean[] in;
 
	/*
	 * static void mst() { Arrays.sort(ed); UnionFind uf=new UnionFind(n); for(int
	 * i=0;i<m;i++) { edge w=ed[i]; if(!uf.union(w.from, w.to)) continue;
	 * in[i]=true; } }
	 */
	static class edge implements Comparable<edge> {
		int from;
		int to;
		int number;
 
		edge(int f, int t, int n) {
			from = f;
			to = t;
			number = n;
		}
 
		public String toString() {
			return from + " " + to + " " + number;
		}
 
		public int compareTo(edge f) {
			return number - f.number;
		}
	}
 
	static class seg implements Comparable<seg> {
		int a;
		int b;
 
		seg(int s, int e) {
			a = s;
			b = e;
		}
 
		public String toString() {
			return a + " " + b;
		}
 
		public int compareTo(seg o) {
			// if(a==o.a)
			return o.b - b;
			// return
		}
	}
 
	static long power(int i) {
		// if(i==0)
		// return 1;
		long a = 1;
		for (int k = 0; k < i; k++)
			a *= i;
		return a;
	}
 
	static void seive(int N) {
		si = new int[N];
		primes = new ArrayList<>();
		si[1] = 1;
		for (int i = 2; i < N; i++) {
			if (si[i] == 0) {
				si[i] = i;
				primes.add(i);
			}
			for (int j = 0; j < primes.size() && primes.get(j) <= si[i] && (i * primes.get(j)) < N; j++)
				si[primes.get(j) * i] = primes.get(j);
 
		}
	}
	static long fac(int n) {
		if (n == 0)
			return fac[n] = 1;
		if (n == 1)
			return fac[n] = 1;
		long ans = 1;
		for (int i = 1; i <= n; i++)
			fac[i] = ans = (i % mod * ans % mod) % mod;
		return ans % mod;
	}
 
	static long gcd(long a, long b) {
 
		if (b == 0)
			return a;
		return gcd(b, a % b);
	}
 
	static class unionfind {
		int[] p;
		int[] size;
 
		unionfind(int n) {
			p = new int[n];
			size = new int[n];
 
			for (int i = 0; i < n; i++) {
				p[i] = i;
			}
			Arrays.fill(size, 1);
		}
 
		int findSet(int v) {
			if (v == p[v])
				return v;
			return p[v] = findSet(p[v]);
		}
 
		boolean sameSet(int a, int b) {
			a = findSet(a);
			b = findSet(b);
			if (a == b)
				return true;
			return false;
		}
 
		int max() {
			int max = 0;
			for (int i = 0; i < size.length; i++)
				if (size[i] > max)
					max = size[i];
			return max;
		}
 
		boolean combine(int a, int b) {
			a = findSet(a);
			b = findSet(b);
			if (a == b)
				return true;
			if (size[a] > size[b]) {
				p[b] = a;
				size[a] += size[b];
 
			} else {
				p[a] = b;
				size[b] += size[a];
			}
			return false;
		}
	}
 
	static class Scanner {
		StringTokenizer st;
		BufferedReader br;
 
		public Scanner(InputStream system) {
			br = new BufferedReader(new InputStreamReader(system));
		}
 
		public Scanner(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);
		}
	}
}