Problem:
Score : 400 points

Problem Statement

You have N items and a bag of strength W.
The i-th item has a weight of w_i and a value of v_i.

You will select some of the items and put them in the bag.
Here, the total weight of the selected items needs to be at most W.

Your objective is to maximize the total value of the selected items.

Constraints

1 ≤ N ≤ 100

1 ≤ W ≤ 10^9

1 ≤ w_i ≤ 10^9

For each i = 2,3,...,N, w_1 ≤ w_i ≤ w_1 + 3.

1 ≤ v_i ≤ 10^7

W, each w_i and v_i are integers.

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 total value of the selected items.

Sample Input 1

4 6
2 1
3 4
4 10
3 4

Sample Output 1

11

The first and third items should be selected.

Sample Input 2

4 6
2 1
3 7
4 10
3 6

Sample Output 2

13

The second and fourth items should be selected.

Sample Input 3

4 10
1 100
1 100
1 100
1 100

Sample Output 3

400

You can take everything.

Sample Input 4

4 1
10 100
10 100
10 100
10 100

Sample Output 4

0

You can take nothing.

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)


import java.io.*;
import java.util.*;

/**
 * @author baito
 */
public class Main
{
    static StringBuilder sb = new StringBuilder();
    static FastScanner sc = new FastScanner(System.in);
    static int INF = 1234567890;
    static long MOD = 1000000007;
    static int[] y4 = {0, 1, 0, -1};
    static int[] x4 = {1, 0, -1, 0};
    static int[] y8 = {0, 1, 0, -1, -1, 1, 1, -1};
    static int[] x8 = {1, 0, -1, 0, 1, -1, 1, -1};
    static long[] F;//factorial
    static boolean[] isPrime;
    static int[] primes;

    static int N,W;
    static int[] w,v;
    static int[] ama;
    public static void main(String[] args)
    {
       N = sc.nextInt();
       W = sc.nextInt();
       w = new int[N];
       v = new int[N];
       ama = new int[N];
       for(int i = 0;i < N; i++){
           w[i] = sc.nextInt();
           v[i] = sc.nextInt();  
           ama[i] = w[i] -w[0];
       }
       long[][] dp = new long[101][30500];
       
       for(int i = 0;i<101;i++){
            Arrays.fill(dp[i],-1);
       }
       
       dp[0][0] = 0;
       for(int i = 0; i < N;i++){
           for(int j = 0 ; j < 30500;j++){
               if(dp[i][j] == -1)continue;
               dp[i+1][j] = Math.max(dp[i+1][j],dp[i][j]);
               
               dp[i+1][j+300 + ama[i]] = Math.max(dp[i+1][j +300+ ama[i]],dp[i][j] + v[i]);
           }
       }
       long max = 0;
       for(int i = 1; i < 30500;i++){
           int amari = (i-1) % 300;
           long ko = (i-1)/300;
           long omo = ko * w[0] + amari;
           if(omo > 1000000000)continue;
           max = Math.max(max,dp[100][i]);
       }
       for(int i = 0 ;i < 101;i++){
           for(int j = 0; j<40;j++){
               System.out.print(dp[i][j] + " ");
           }
           System.out.println();
       }
        System.out.println(max);
    }

    public static long sumMod(long... lar)
    {
        long sum = 0;
        for (long l : lar)
            sum = (sum + l % MOD) % MOD;
        return sum;
    }

    /**
     * <h1>指定した値以上の先頭のインデクスを返す</h1>
     * <p>配列要素が０のときは、０が返る。</p>
     *
     * @return<b>int</b> ： 探索した値以上で、先頭になるインデクス
     */
    public static int lowerBound(final int[] arr, final int value)
    {
        int low = 0;
        int high = arr.length;
        int mid;
        while (low < high)
        {
            mid = ((high - low) >>> 1) + low;    //(low + high) / 2 (オーバーフロー対策)
            if (arr[mid] < value)
            {
                low = mid + 1;
            }
            else
            {
                high = mid;
            }
        }
        return low;
    }

    /**
     * <h1>指定した値より大きい先頭のインデクスを返す</h1>
     * <p>配列要素が０のときは、０が返る。</p>
     *
     * @return<b>int</b> ： 探索した値より上で、先頭になるインデクス
     */
    public static int upperBound(final int[] arr, final int value)
    {
        int low = 0;
        int high = arr.length;
        int mid;
        while (low < high)
        {
            mid = ((high - low) >>> 1) + low;    //(low + high) / 2 (オーバーフロー対策)
            if (arr[mid] <= value)
            {
                low = mid + 1;
            }
            else
            {
                high = mid;
            }
        }
        return low;
    }

    //次の順列に書き換える、最大値ならfalseを返す
    public static boolean nextPermutation(int A[])
    {
        int len = A.length;
        int pos = len - 2;
        for (; pos >= 0; pos--)
        {
            if (A[pos] < A[pos + 1]) break;
        }
        if (pos == -1) return false;

        //posより大きい最小の数を二分探索
        int ok = pos + 1;
        int ng = len;
        while (Math.abs(ng - ok) > 1)
        {
            int mid = (ok + ng) / 2;
            if (A[mid] > A[pos]) ok = mid;
            else ng = mid;

        }

        swap(A, pos, ok);
        reverse(A, pos + 1, len - 1);


        return true;
    }

    //次の順列に書き換える、最小値ならfalseを返す
    public static boolean prevPermutation(int A[])
    {
        int len = A.length;
        int pos = len - 2;
        for (; pos >= 0; pos--)
        {
            if (A[pos] > A[pos + 1]) break;
        }
        if (pos == -1) return false;

        //posより小さい最大の数を二分探索
        int ok = pos + 1;
        int ng = len;
        while (Math.abs(ng - ok) > 1)
        {
            int mid = (ok + ng) / 2;
            if (A[mid] < A[pos]) ok = mid;
            else ng = mid;

        }

        swap(A, pos, ok);
        reverse(A, pos + 1, len - 1);


        return true;
    }

    //↓nCrをmod計算するために必要。　***factorial(N)を呼ぶ必要がある***
    static long ncr(int n, int r)
    {
        factorial(n);
        return F[n] / (F[n - r] * F[r]);
    }

    static long modNcr(int n, int r)
    {
        long result = F[n];
        result = result * modInv(F[n - r]) % MOD;
        result = result * modInv(F[r]) % MOD;
        return result;
    }

    static long modInv(long n)
    {
        return modPow(n, MOD - 2);
    }

    static void factorial(int n)
    {
        F = new long[n + 1];
        F[0] = F[1] = 1;
        for (int i = 2; i <= n; i++)
        {
            F[i] = (F[i - 1] * i) % MOD;
        }
    }

    static long modPow(long x, long n)
    {
        long res = 1L;
        while (n > 0)
        {
            if ((n & 1) == 1)
            {
                res = res * x % MOD;
            }
            x = x * x % MOD;
            n >>= 1;
        }
        return res;
    }

    //↑nCrをmod計算するために必要

    static int gcd(int n, int r)
    {
        return r == 0 ? n : gcd(r, n % r);
    }

    static long gcd(long n, long r)
    {
        return r == 0 ? n : gcd(r, n % r);
    }

    static <T> void swap(T[] x, int i, int j)
    {
        T t = x[i];
        x[i] = x[j];
        x[j] = t;
    }

    static void swap(int[] x, int i, int j)
    {
        int t = x[i];
        x[i] = x[j];
        x[j] = t;
    }

    public static void reverse(int[] x)
    {
        int l = 0;
        int r = x.length - 1;
        while (l < r)
        {
            int temp = x[l];
            x[l] = x[r];
            x[r] = temp;
            l++;
            r--;
        }
    }

    public static void reverse(int[] x, int s, int e)
    {
        int l = s;
        int r = e;
        while (l < r)
        {
            int temp = x[l];
            x[l] = x[r];
            x[r] = temp;
            l++;
            r--;
        }
    }

    static int length(int a)
    {
        int cou = 0;
        while (a != 0)
        {
            a /= 10;
            cou++;
        }
        return cou;
    }

    static int length(long a)
    {
        int cou = 0;
        while (a != 0)
        {
            a /= 10;
            cou++;
        }
        return cou;
    }

    static int countC2(char[][] a, char c)
    {
        int co = 0;
        for (int i = 0; i < a.length; i++)
            for (int j = 0; j < a[0].length; j++)
                if (a[i][j] == c) co++;
        return co;
    }

    static void fill(int[][] a, int v)
    {
        for (int i = 0; i < a.length; i++)
            for (int j = 0; j < a[0].length; j++)
                a[i][j] = v;
    }

    static int max(int a, int b, int c)
    {
        return Math.max(a, Math.max(b, c));
    }

    static int max(int[] ar)
    {
        int res = Integer.MIN_VALUE;
        for (int i : ar)
            res = Math.max(res, i);
        return res;
    }

    static int max(int[][] ar)
    {
        int res = Integer.MIN_VALUE;
        for (int i[] : ar)
            res = max(i);
        return res;
    }

    static int min(int a, int b, int c)
    {
        return Math.min(a, Math.min(b, c));
    }

    static int min(int[] ar)
    {
        int res = Integer.MAX_VALUE;
        for (int i : ar)
            res = Math.min(res, i);
        return res;
    }

    static int min(int[][] ar)
    {
        int res = Integer.MAX_VALUE;
        for (int i[] : ar)
            res = min(i);
        return res;
    }

    static int abs(int a)
    {
        return Math.abs(a);
    }

    static class FastScanner
    {

        private BufferedReader reader = null;
        private StringTokenizer tokenizer = null;

        public FastScanner(InputStream in)
        {
            reader = new BufferedReader(new InputStreamReader(in));
            tokenizer = null;
        }

        public String next()
        {
            if (tokenizer == null || !tokenizer.hasMoreTokens())
            {
                try
                {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e)
                {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        /*public String nextChar(){
            return (char)next()[0];
        }*/
        public String nextLine()
        {
            if (tokenizer == null || !tokenizer.hasMoreTokens())
            {
                try
                {
                    return reader.readLine();
                } catch (IOException e)
                {
                    throw new RuntimeException(e);
                }
            }

            return tokenizer.nextToken("\n");
        }

        public long nextLong()
        {
            return Long.parseLong(next());
        }

        public int nextInt()
        {
            return Integer.parseInt(next());
        }

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

        public int[] nextIntArray(int n)
        {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
            {
                a[i] = nextInt();
            }
            return a;
        }

        public int[][] nextIntArray2(int h, int w)
        {
            int[][] a = new int[h][w];
            for (int hi = 0; hi < h; hi++)
            {
                for (int wi = 0; wi < w; wi++)
                {
                    a[hi][wi] = nextInt();
                }
            }
            return a;
        }

        public int[] nextIntArray21(int n, int scalar)
        {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt() * scalar + nextInt();
            return a;
        }

        public Integer[] nextIntegerArray(int n)
        {
            Integer[] a = new Integer[n];
            for (int i = 0; i < n; i++)
            {
                a[i] = nextInt();
            }
            return a;
        }

        public char[] nextCharArray(int n)
        {
            char[] a = next().toCharArray();

            return a;
        }

        public char[][] nextCharArray2(int h, int w)
        {
            char[][] a = new char[h][w];
            for (int i = 0; i < h; i++)
            {
                a[i] = next().toCharArray();
            }
            return a;
        }

        //スペースが入っている場合
        public char[][] nextCharArray2s(int h, int w)
        {
            char[][] a = new char[h][w];
            for (int i = 0; i < h; i++)
            {
                a[i] = nextLine().replace(" ", "").toCharArray();
            }
            return a;
        }

        public char[][] nextWrapCharArray2(int h, int w, char c)
        {
            char[][] a = new char[h + 2][w + 2];
            //char c = '*';
            int i;
            for (i = 0; i < w + 2; i++)
                a[0][i] = c;
            for (i = 1; i < h + 1; i++)
            {
                a[i] = (c + next() + c).toCharArray();
            }
            for (i = 0; i < w + 2; i++)
                a[h + 1][i] = c;
            return a;
        }

        //スペースが入ってる時用
        public char[][] nextWrapCharArray2s(int h, int w, char c)
        {
            char[][] a = new char[h + 2][w + 2];
            //char c = '*';
            int i;
            for (i = 0; i < w + 2; i++)
                a[0][i] = c;
            for (i = 1; i < h + 1; i++)
            {
                a[i] = (c + nextLine().replace(" ", "") + c).toCharArray();
            }
            for (i = 0; i < w + 2; i++)
                a[h + 1][i] = c;
            return a;
        }

        public long[] nextLongArray(int n)
        {
            long[] a = new long[n];
            for (int i = 0; i < n; i++)
            {
                a[i] = nextLong();
            }
            return a;
        }

        public long[][] nextLongArray2(int h, int w)
        {
            long[][] a = new long[h][w];
            for (int hi = 0; hi < h; hi++)
            {
                for (int wi = 0; wi < h; wi++)
                {
                    a[h][w] = nextLong();
                }
            }
            return a;
        }
    }
}