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 Haskell (GHC 7.10.3) (judge verdict: Time Limit Exceeded)

import Control.Applicative( (<$>))
import Control.Monad( replicateM)
import Data.List( sortBy)
import Data.Function( on)
import Data.Ratio( (%))

main = do
    [n_, w_] <- map read . words <$> getLine
    let
	object = do
	    [w,v] <- map read . words <$> getLine
	    return (w,v)
    
    os_ <- replicateM n_ object
    let
	cosperOrder = sortBy compare' os_
	  where
	    compare' (w1,v1) (w2,v2) = let
				cosper1 = v1%w1
				cosper2 = v2%w2
			    in
				if cosper1==cosper2
				then w2 `compare` w1
				else cosper2 `compare` cosper1


	insert values 0 _ = [values]
	insert values _ [] = [values]
	insert values slack ((w,v):os)
	  | w<=slack =
			let
			    ins = insert (values+v) (slack-w) os
			    non = insert values slack os
			in
			    concat [ins,non]

	  | otherwise = insert values slack os
    
    print . maximum $ insert 0 w_ cosperOrder