{-# OPTIONS_GHC -O2 #-}
{-# LANGUAGE BangPatterns          #-}
{-# LANGUAGE CPP                   #-}
{-# LANGUAGE LambdaCase            #-}
{-# LANGUAGE MagicHash             #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE MultiWayIf            #-}
{-# LANGUAGE OverloadedStrings     #-}
{-# LANGUAGE TupleSections         #-}
{-# LANGUAGE TypeFamilies          #-}
{-# LANGUAGE ViewPatterns          #-}

import           Control.Applicative
import           Control.Exception
import           Control.Monad
import           Control.Monad.Primitive
import           Control.Monad.ST
import           Control.Monad.State.Strict
import           Data.Bool
import qualified Data.ByteString             as B
import qualified Data.ByteString.Builder     as B
import qualified Data.ByteString.Char8       as C
import qualified Data.ByteString.Internal    as B
import qualified Data.ByteString.Unsafe      as B
import           Data.Char
import qualified Data.Foldable               as F
import           Data.Function
import qualified Data.IntMap.Strict          as IM
import qualified Data.IntSet                 as IS
import qualified Data.List                   as L
import qualified Data.Map.Strict             as M
import           Data.Monoid
import           Data.Ord
import           Data.Primitive.MutVar
import qualified Data.Set                    as S
import           Data.Tuple
import qualified Data.Vector                 as V
import qualified Data.Vector.Generic         as G
import qualified Data.Vector.Generic.Mutable as GM
import qualified Data.Vector.Unboxed         as U
import qualified Data.Vector.Unboxed.Mutable as UM
import           Debug.Trace
import           Foreign                     hiding (void)
import           GHC.Exts
import qualified System.IO                   as IO
import           Unsafe.Coerce

main :: IO ()
main = do
    [n, k] <- map read.words <$> getLine :: IO [Int]
    xs <- U.unfoldr parseInt <$> C.getLine
    print $ solve n k xs

solve :: Int -> Int -> U.Vector Int -> Int
solve n k xs = head $ filter validate ds
  where
    !s = U.sum xs
    ds = L.sortBy (flip compare) $ divisors s
    validate d = sum (take (n-quot ss d) xs') <= k
      where
        xs' = L.sort.U.toList $ U.map (flip rem d) xs
        !ss = sum xs'



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

smallPrimes :: [Int]
smallPrimes = 2 : [ n | n<-[3,5..46337], all ((>0).rem n) $ takeWhile (\x->x*x<=n) smallPrimes]

primeFactors :: Int -> [Int]
primeFactors n | n < 2 = []
primeFactors n = go n smallPrimes
  where
    go !n pps@(p:ps)
        | n < p * p = [n]
        | r > 0     = go n ps
        | otherwise = p : go q pps
      where
        (q, r) = quotRem n p
    go n [] = [n]

isPrime :: Int -> Bool
isPrime n = [n] == primeFactors n

totient :: Int -> Int
totient n = n `quot` product ps * product (map (subtract 1) ps)
  where
    ps = map head . L.group $ primeFactors n

divisors :: Int -> [Int]
divisors n = L.sort . map product . mapM (scanl (*) 1) . L.group $ primeFactors n

type Parser a = C.ByteString -> Maybe (a, C.ByteString)

parseInt :: Parser Int
parseInt = C.readInt . C.dropWhile isSpace

parseInt2 :: Parser (Int, Int)
parseInt2 = runStateT $
    (,) <$> StateT (C.readInt . C.dropWhile isSpace)
        <*> StateT (C.readInt . B.unsafeTail)

parseInt3 :: Parser (Int, Int, Int)
parseInt3 = runStateT $
    (,,) <$> StateT (C.readInt . C.dropWhile isSpace)
        <*> StateT (C.readInt . B.unsafeTail)
        <*> StateT (C.readInt . B.unsafeTail)

parseInt4 :: Parser (Int, Int, Int, Int)
parseInt4 = runStateT $
    (,,,) <$> StateT (C.readInt . C.dropWhile isSpace)
        <*> StateT (C.readInt . B.unsafeTail)
        <*> StateT (C.readInt . B.unsafeTail)
        <*> StateT (C.readInt . B.unsafeTail)

Measured memory_bytes: 1148