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: Accepted)

{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TupleSections #-}
import qualified Data.ByteString.Lazy.Char8 as B
import Data.Maybe
import Data.List
import qualified Data.Vector.Unboxed as VU
-- import qualified Data.Vector.Unboxed.Mutable as VUM
-- import Control.Monad
-- import Control.Monad.ST
-- import Debug.Trace

solve :: Int -> Int -> [(Int,Int)] -> Int
solve bN bW wvs = vecFin VU.! bW
  where
  vecFin = foldl' op (VU.replicate (bW+1) 0) wvs
  op vec (w,v) =
    VU.zipWith max vec (VU.replicate w 0 VU.++ VU.map (+ v) vec)

readBInt :: B.ByteString -> Int
readBInt = fst . fromJust . B.readInt

tmain :: B.ByteString -> Int
tmain cont =
  let remLines0 = map B.words (B.lines cont)
      [bs_bN,bs_bW]:remLines1 = remLines0
      bN = readBInt bs_bN
      bW = readBInt bs_bW
      wvs = map (\[x1,x2] -> (readBInt x1,readBInt x2)) remLines1
  in solve bN bW wvs

outAnswer :: Int -> IO ()
outAnswer = putStrLn . show

main :: IO ()
main = outAnswer . tmain =<< B.getContents