Problem:
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You are given $n$ packages of $w_i$ kg from a belt conveyor in order ($i = 0, 1, ... n-1$). You should load all packages onto $k$ trucks which have the common maximum load $P$. Each truck can load consecutive packages (more than or equals to zero) from the belt conveyor unless the total weights of the packages in the sequence does not exceed the maximum load $P$.

Write a program which reads $n$, $k$ and $w_i$, and reports the minimum value of the maximum load $P$ to load all packages from the belt conveyor.

Input

In the first line, two integers $n$ and $k$ are given separated by a space character. In the following $n$ lines, $w_i$ are given respectively.

Output

Print the minimum value of $P$ in a line.

Constraints

$1 \leq n \leq 100,000$

$1 \leq k \leq 100,000$

$1 \leq w_i \leq 10,000$

Sample Input 1

5 3
8
1
7
3
9

Sample Output 1

10

If the first truck loads two packages of $\{8, 1\}$, the second truck loads two packages of $\{7, 3\}$ and the third truck loads a package of $\{9\}$, then the minimum value of the maximum load $P$ shall be 10.

Sample Input 2

4 2
1
2
2
6

Sample Output 2

6

If the first truck loads three packages of $\{1, 2, 2\}$ and the second truck loads a package of $\{6\}$, then the minimum value of the maximum load $P$ shall be 6.

Solution in Haskell (judge verdict: Accepted)

{-# OPTIONS_GHC -O2 -funbox-strict-fields #-}
{-# OPTIONS_GHC -fno-warn-unused-imports #-}
{-# OPTIONS_GHC -fno-warn-missing-signatures #-}
{-# OPTIONS_GHC -fno-warn-unused-binds #-}
{-# OPTIONS_GHC -fno-warn-incomplete-patterns #-}
{-# OPTIONS_GHC -fno-warn-name-shadowing #-}
{-# LANGUAGE OverloadedStrings #-}
-- {-# LANGUAGE FlexibleContexts #-}
-- {-# LANGUAGE MultiWayIf #-}
-- {-# LANGUAGE BangPatterns #-}
-- {-# LANGUAGE ViewPatterns #-}
-- {-# LANGUAGE TupleSections #-}

import           System.IO hiding (char8)
import           Control.Applicative
import           Control.Monad
import           Data.List
import           Data.Tuple
import           Data.Int
import           Data.Char
import           Data.Function (on)
import           Data.Ord (comparing)
import           Data.Monoid (mappend)
import           Data.Array
-- import           Data.Array.Unboxed
-- import           Data.Array.IArray
-- import           Data.Array.ST
-- import           Data.Array.MArray
-- import           Data.Array.Unsafe
-- import           Data.Array.Base(unsafeRead, unsafeWrite)
-- import           Data.Array.IO
import           Data.Ix
import           Data.Maybe
-- import           Data.Monoid hiding ((<>))
import qualified Data.ByteString.Char8 as BS
import qualified Data.ByteString.Lazy.Char8 as BL
import           Data.ByteString.Builder
-- import           Data.Graph
-- import           Data.Vector.Unboxed ((//), (++), (!), (!?))
-- import qualified Data.Vector.Unboxed as U
-- import           Data.IntSet (IntSet)
-- import qualified Data.IntSet as IntSet
-- import           Data.IntMap.Strict (IntMap)
-- import qualified Data.IntMap.Strict as IntMap
-- import           Data.Sequence ((|>), (<|), (><),ViewR(..), ViewL(..), Seq)
-- import qualified Data.Sequence              as Seq
-- import           Data.Foldable (toList, minimumBy)
-- import           Debug.Trace

main = do
  (n, k) <- readInt2 <$> BS.getLine
  ws <- map readInt1 <$> replicateM n BS.getLine
  print $ solve k ws

solve k ws = binsearch (maximum ws, sum ws) (packable k ws)

packable :: Int -> [Int] -> Int -> Bool
packable k ws maxw = fst (foldl' f (1, 0) ws) <= k
  where
    f (c, sumw) w = if sumw + w > maxw then (c + 1, w) else (c, sumw + w)

binsearch :: (Int, Int) -> (Int -> Bool) -> Int
binsearch (l, h) p = f (l, h)
  where
    f (l, h)
      | l == m    = if p l then l else h
      | p m       = f (l, m)
      | otherwise = f (m + 1, h)
      where
        m = l + (h - l) `div` 2

--  --  --  --  --  --  --  --  --  --  --  --  --  --  --  --  --  --  --  --

format :: Show a => Maybe a -> IO ()
format Nothing = putStrLn "NO"
format (Just a) = putStrLn "YES" >> print a

-- [1,2,3] -> 1 2 3
putIntN :: [Int] -> IO ()
putIntN [] = return ()
putIntN xs = BL.putStrLn . toLazyByteString . foldl1 mappend . intersperse (char8 ' ') $ map intDec xs

readInt1 :: BS.ByteString -> Int
readInt1 = fst . fromJust . BS.readInt

readInt2 :: BS.ByteString -> (Int,Int)
readInt2 = toTuple . readIntN

readInt3 :: BS.ByteString -> (Int,Int,Int)
readInt3 = toTriple . readIntN

readIntN :: BS.ByteString -> [Int]
readIntN =  map readInt1 . BS.words

readInt641 :: BS.ByteString -> Int64
readInt641 = fromIntegral . fst . fromJust . BS.readInteger

readInt642 :: BS.ByteString -> (Int64,Int64)
readInt642 = toTuple . readInt64N

readInt643 :: BS.ByteString -> (Int64,Int64,Int64)
readInt643 = toTriple . readInt64N

readInt64N :: BS.ByteString -> [Int64]
readInt64N =  map readInt641 . BS.words

readInteger1 :: BS.ByteString -> Integer
readInteger1 = fst . fromJust . BS.readInteger

readInteger2 :: BS.ByteString -> (Integer,Integer)
readInteger2 = toTuple . readIntegerN

readInteger3 :: BS.ByteString -> (Integer,Integer,Integer)
readInteger3 = toTriple . readIntegerN

readIntegerN :: BS.ByteString -> [Integer]
readIntegerN =  map readInteger1 . BS.words

toTuple :: [a] -> (a, a)
toTuple [x, y] = (x, y)

toTriple :: [a] -> (a, a, a)
toTriple [x, y, z] =(x, y, z)

fromTuple :: (a, a) -> [a]
fromTuple (x, y) = [x, y]

fromTriple :: (a, a, a) -> [a]
fromTriple (x, y, z) = [x, y, z]

-- if not applying, use "const"

applyTuple :: (a -> a') -> (b -> b') -> (a, b) -> (a', b')
applyTuple f g (x, y) = (f x, g y)

applyTriple :: (a -> a') -> (b -> b') -> (c -> c') -> (a, b, c) -> (a', b', c')
applyTriple f g h (x, y, z) = (f x, g y, h z)

-- @since 4.8.0.0
sortOn' :: Ord b => (a -> b) -> [a] -> [a]
sortOn' f =
  map snd . sortBy (comparing fst) . map (\x -> let y = f x in y `seq` (y, x))