Problem:
Knapsack Problem with Limitations

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

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.

You can select at most mi items for ith item.

Find the maximum total value of items in the knapsack.

Input

N W
v1 w1 m1
v2 w2 m2
:
vN wN mN

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

Output

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

Constraints

1 ≤ N ≤ 100

1 ≤ vi ≤ 1,000

1 ≤ wi ≤ 1,000

1 ≤ mi ≤ 10,000

1 ≤ W ≤ 10,000

Sample Input 1

4 8
4 3 2
2 1 1
1 2 4
3 2 2

Sample Output 1

12

Sample Input 2

2 100
1 1 100
2 1 50

Sample Output 2

150

Solution in Haskell (judge verdict: Memory Limit Exceeded)

{-# OPTIONS_GHC -O2 #-}
import Control.Applicative
import Data.IORef
import qualified Data.Vector.Unboxed.Mutable as VM
import qualified Data.Vector.Unboxed as V
import Control.Monad

main = do
  [_,capa] <- map (read :: String -> Int) . words <$> getLine
  goods' <- map (map (read :: String -> Int) . words) . lines <$> getContents
  let goods = bunkai goods' []
  capaVM <- VM.replicate (capa+1) 0
  ans <- newIORef 0
  mapM_ (resolve capa capaVM ans) goods
  print =<< readIORef ans

bunkai ([x,y,n]:xs) ys
  | null xs = merge [x,y] n ys
  | otherwise = bunkai xs (merge [x,y] n ys)
  where
    merge xs n ys
      | n == 1 = xs:ys
      | otherwise = merge xs (n-1) (xs:ys)


resolve capa capaVM ans [v,w] =
  if capa < w
    then return ()
    else V.mapM_ (koushin [v,w]) (V.enumFromStepN (capa-w) (-1) (capa-w+1))
       where
         koushin [v,w] n = do
           oldValue <- VM.read capaVM n
           newValue <- VM.read capaVM (n+w)
           judge oldValue newValue
             where
               judge oldValue newValue
                 | n == 0 && newValue <= v  = kakikae
                 | n ==0                    = return ()
                 | newValue >= v + oldValue = return ()
                 | otherwise  = kakikae
                 where
                   kakikae = do
                     VM.write capaVM (n+w) (v + oldValue)
                     ans' <- readIORef ans
                     writeIORef ans (max ans' (v + oldValue))