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 10^5

1 \leq w_i \leq W

1 \leq v_i \leq 10^9

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

5 5
1 1000000000
1 1000000000
1 1000000000
1 1000000000
1 1000000000

Sample Output 2

5000000000

The answer may not fit into a 32-bit integer type.

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

{-# LANGUAGE OverloadedStrings #-}
module Main where

import           Data.List
import           Control.Monad
import           Debug.Trace
import qualified Data.ByteString.Char8         as BC
import           Data.Maybe                     ( fromJust )
import qualified Data.Set                      as S
import qualified Data.IntMap.Strict            as IM
import qualified Data.IntMap.Lazy            as IML
import qualified Data.Map.Strict               as M
import qualified Data.Map.Lazy               as ML
import           Data.Char
import qualified Data.Array.IArray as A
import qualified Data.Array.Unboxed as UA
import Data.Bits
import Control.Monad.State.Strict

modN = 1000000007


readTuple2 :: IO (Int, Int)
readTuple2 = do
    [a, b] <- map (fst . fromJust . BC.readInt) . BC.words <$> BC.getLine
    return (a, b)

readTuple3 :: IO (Int, Int, Int)
readTuple3 = do
    [a, b, c] <- map (fst . fromJust . BC.readInt) . BC.words <$> BC.getLine
    return (a, b, c)

readInt :: IO Int
readInt = fst . fromJust . BC.readInt <$> BC.getLine

readInts :: IO [Int]
readInts = map (fst . fromJust . BC.readInt) . BC.words <$> BC.getLine

split :: (a -> Bool) -> [a] -> [[a]]
split f [] = []
split f as =
    let (fo, la) = span f as
        las      = case la of
            [] -> []
            xs -> split f $ tail xs
    in  case fo of
            [] -> las
            xs -> xs : las

pow :: Int -> Int -> Int -> Int
pow base 1 modNum = base `mod` modNum
pow base time modNum
    | odd time = let 
        a = pow base (time `div` 2) modNum `mod` modNum
        in
        a * a * base `mod` modNum
    | otherwise = let
        a = pow base (time `div` 2) modNum `mod` modNum
        in
        a * a `mod` modNum

solve :: Int -> Int -> [(Int, Int)] -> Int
solve n w merchs = let
    valMap :: UA.Array Int (Int, Int)
    valMap = A.array (1, n) $ zip [1..] merchs
    getWV :: Int -> Int -> State (M.Map (Int, Int) Int) Int
    getWV 0 _ = pure 0
    getWV _ 0 = pure 0
    getWV w v = do
        memo <- get
        case M.lookup (w, v) memo of
            Just a -> pure a
            Nothing -> do
                let (wi, vi) = valMap A.! v
                nochoose <- getWV w (v - 1)
                ans <-  if wi > w then pure nochoose  
                        else do
                            v2 <- getWV (w - wi) (v - 1)
                            pure $ max nochoose $ v2  + vi
                modify' $ M.insert (w, v) ans
                pure ans
    in evalState (getWV w n) M.empty


main = do
    (n, w) <- readTuple2
    merchs <- replicateM n readTuple2
    print $ solve n w merchs