Problem:
Score : 500 points

Problem Statement

We have N logs of lengths A_1,A_2,\cdots A_N.

We can cut these logs at most K times in total. When a log of length L is cut at a point whose distance from an end of the log is t (0<t<L), it becomes two logs of lengths t and L-t.

Find the shortest possible length of the longest log after at most K cuts, and print it after rounding up to an integer.

Constraints

1 \leq N \leq 2 \times 10^5

0 \leq K \leq 10^9

1 \leq A_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K
A_1 A_2 \cdots A_N

Output

Print an integer representing the answer.

Sample Input 1

2 3
7 9

Sample Output 1

4

First, we will cut the log of length 7 at a point whose distance from an end of the log is 3.5, resulting in two logs of length 3.5 each.

Next, we will cut the log of length 9 at a point whose distance from an end of the log is 3, resulting in two logs of length 3 and 6.

Lastly, we will cut the log of length 6 at a point whose distance from an end of the log is 3.3, resulting in two logs of length 3.3 and 2.7.

In this case, the longest length of a log will be 3.5, which is the shortest possible result. After rounding up to an integer, the output should be 4.

Sample Input 2

3 0
3 4 5

Sample Output 2

5

Sample Input 3

10 10
158260522 877914575 602436426 24979445 861648772 623690081 433933447 476190629 262703497 211047202

Sample Output 3

292638192

Solution in Haskell (GHC 8.8.3) (judge verdict: Time Limit Exceeded)

{-# LANGUAGE BangPatterns, OverloadedStrings #-}

import Control.Monad
import Data.Array.Unboxed
import Data.Bits
import Data.Bool
import Data.Char
import Data.Coerce
import Data.Function
import Data.Int 
import Data.IORef
import Data.List
import Data.Maybe
import qualified Data.Map.Strict as M
import qualified Data.Vector.Unboxed as V
import qualified Data.Vector.Unboxed.Mutable as MV
import qualified Data.ByteString.Char8 as BS

main :: IO ()
main = do
  (_, k) <- getIntPair
  ns <- getIntList
  print $ ceiling $ solve k ns

solve k ns = bisearchD check (0, fromIntegral (maximum ns))
  where
    check d = k < (sum $ map (subtract 1 . ceiling . (/d)) ds)
    ds = map fromIntegral ns

-- Input

getInt :: IO Int
getInt = readLn
second :: (b -> c) -> (a, b) -> (a, c)
second f (a, b) = (a, f b)

readInt :: BS.ByteString -> Maybe (Int, BS.ByteString)
readInt = fmap (second BS.tail) . BS.readInt

getIntVec :: Int -> IO (V.Vector Int)
getIntVec n = V.unfoldrN n readInt <$> BS.getLine
 
getIntList :: IO [Int]
getIntList = map (fst . fromJust . BS.readInt) . BS.words <$> BS.getLine

getIntegerList :: IO [Integer]
getIntegerList = map (fst . fromJust . BS.readInteger) . BS.words <$> BS.getLine

getIntPair :: IO (Int, Int)
getIntPair = do
  v <- getIntVec 2
  return (v V.! 0, v V.! 1)

-- Search

bisearch :: (Int -> Bool) -> (Int, Int) -> (Int, Int)
bisearch check = bis
  where
    bis (l, r)
      | l + 1 == r = (l, r)
      | check mid  = bis (mid, r)
      | otherwise  = bis (l, mid)
      where
        mid = l + (r - l) `div` 2
        
bisearchD :: (Double -> Bool) -> (Double, Double) -> Double
bisearchD check = bis 0
  where
    bis count (l, r)
      | count > (10^6) = l
      | check mid  = bis (count + 1) (mid, r)
      | otherwise  = bis (count + 1) (l, mid)
      where
        mid = l + (r - l) / 2

-- Modular Arithmetic
--
 
modulo :: Int64
modulo = 10^9+7
addMod, subMod, mulMod :: Int64 -> Int64 -> Int64
addMod !x !y | x + y >= modulo = x + y - modulo
             | otherwise = x + y
subMod !x !y | x >= y = x - y
             | otherwise = x - y + modulo
mulMod !x !y = (x * y) `rem` modulo

newtype N = N { unwrapN :: Int64 } deriving (Eq)
instance Show N where
  show (N x) = show x
instance Num N where
  (+) = coerce addMod
  (-) = coerce subMod
  (*) = coerce mulMod
  fromInteger n = N (fromInteger (n `mod` fromIntegral modulo))
  abs = undefined; signum = undefined
---
 
exEuclid :: (Eq a, Integral a) => a -> a -> (a, a, a)
exEuclid !f !g = loop 1 0 0 1 f g
  where loop !u0 !u1 !v0 !v1 !f 0 = (f, u0, v0)
        loop !u0 !u1 !v0 !v1 !f g =
          case divMod f g of
            (q,r) -> loop u1 (u0 - q * u1) v1 (v0 - q * v1) g r
 
recipM :: Int64 -> Int64
recipM !x = case exEuclid x modulo of
             (1,a,_) -> a `mod` modulo
             (-1,a,_) -> (-a) `mod` modulo
divM :: Int64 -> Int64 -> Int64
divM !x !y = x `mulMod` recipM y
 
instance Fractional N where
  (/) = coerce divM
  recip = coerce recipM
  fromRational = undefined

-- 組み合わせ
powerset :: [a] -> [[a]]  
powerset xs = filterM (\x -> [True, False]) xs