Problem: You have N items that you want to put them into a knapsack. Item i has value vi and weight wi.

You want to find a subset of items to put such that:

* The total value of the items is as large as possible.
* The items have combined weight at most W, that is capacity of the knapsack.



Find the maximum total value of items in the knapsack.

Constraints

* 1 ≤ N ≤ 100
* 1 ≤ vi ≤ 100
* 1 ≤ wi ≤ 10,000,000
* 1 ≤ W ≤ 1,000,000,000

Input


N W
v1 w1
v2 w2
:
vN wN


The first line consists of the integers N and W. In the following N lines, the value and weight of the i-th item are given.

Output

Print the maximum total values of the items in a line.

Examples

Input

4 5
4 2
5 2
2 1
8 3


Output

13


Input

2 20
5 9
4 10


Output

9

Solution (in JAVA):

Solution:
import java.io.IOException;
import java.io.InputStream;
import java.math.BigDecimal;
import java.util.*;
import java.util.function.IntFunction;
import java.util.function.Supplier;
import java.util.stream.Collectors;
import java.util.stream.IntStream;
import java.util.stream.Stream;


public class Main {

    public static void main(String[] args) {
        Scanner scanner = new Scanner();
        int n=scanner.nextInt();
        int W=scanner.nextInt();
        int[] v=new int[n];
        int[] w=new int[n];
        for(int i=0;i<n;i++){
            v[i]=scanner.nextInt();
            w[i]=scanner.nextInt();
        }
        int[][] dp=new int[n+1][10_000+1];
        for(int i=0;i<n+1;i++){
            for(int j=0;j<dp[0].length;j++){
                dp[i][j]=Integer.MAX_VALUE;
            }
        }
        dp[0][0]=0;
        for(int i=1;i<n+1;i++){
            for(int j=0;j<dp[0].length;j++){
                dp[i][j]=dp[i-1][j];
                if(j-v[i-1]>=0){
                    if(dp[i-1][j-v[i-1]]!=Integer.MAX_VALUE){
                        dp[i][j]=min(dp[i][j],dp[i-1][j-v[i-1]]+w[i-1]);
                    }
                }
            }
            //put(Arrays.toString(dp[i]));
        }
        int ans=0;
        for(int i=0;i<dp[0].length;i++){
            if(dp[n][i]<=W) ans=i;
        }
        put(ans);







    }

    public static int upper_bound(int[] a,int val){
        return upper_bound(a,0,a.length,val);
    }
    public static int upper_bound(int[] a,int l,int r,int val){
        if(r-l==1){
            if(a[l]>val) return l;
            return r;
        }
        int mid=(l+r)/2;
        if(a[mid]>val){
            return upper_bound(a,l,mid,val);
        }else{
            return upper_bound(a,mid,r,val);
        }
    }
    public static int lower_bound(int[] a,int val){
        return lower_bound(a,0,a.length,val);
    }
    public static int lower_bound(int[] a,int l,int r,int val){
        if(r-l==1){
            if(a[l]<val) return r;
            return l;
        }
        int mid=(l+r)/2;
        if(a[mid]<val){
            return lower_bound(a,mid,r,val);
        }else{
            return lower_bound(a,l,mid,val);
        }

    }


    public static int max(int a,int b){
        return Math.max(a,b);
    }
    public static long max(long a,long b){
        return Math.max(a,b);
    }
    public static int min(int a,int b){
        return Math.min(a,b);
    }
    public static long min(long a,long b){
        return Math.min(a,b);
    }
    public static int abs(int a){
        return Math.abs(a);
    }
    public static long abs(long a){
        return Math.abs(a);
    }
    public static void print(Object object){
        System.out.print(object);
    }
    public static void put(Object object) {
        System.out.println(object);
    }
    public static void put(){
        System.out.println();
    }
    public static String format(String string, Object... args) {
        return String.format(string, args);
    }
}

final class Scanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;

    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        } else {
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }

    private int readByte() {
        if (hasNextByte())
            return buffer[ptr++];
        else
            return -1;
    }

    private boolean isPrintableChar(int c) {
        return 33 <= c && c <= 126;
    }

    public boolean hasNext() {
        while (hasNextByte() && !isPrintableChar(buffer[ptr]))
            ptr++;
        return hasNextByte();
    }

    public String next() {
        if (!hasNext())
            throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while (isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    public long nextLong() {
        if (!hasNext())
            throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while (true) {
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            } else if (b == -1 || !isPrintableChar(b)) {
                return minus ? -n : n;
            } else {
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }

    public int nextInt() {
        long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE)
            throw new NumberFormatException();
        return (int) nl;
    }

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