Problem:
Score : 300 points

Problem Statement

There are N+1 towns. The i-th town is being attacked by A_i monsters.

We have N heroes. The i-th hero can defeat monsters attacking the i-th or (i+1)-th town, for a total of at most B_i monsters.

What is the maximum total number of monsters the heroes can cooperate to defeat?

Constraints

All values in input are integers.

1 \leq N \leq 10^5

1 \leq A_i \leq 10^9

1 \leq B_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_{N+1}
B_1 B_2 ... B_N

Output

Print the maximum total number of monsters the heroes can defeat.

Sample Input 1

2
3 5 2
4 5

Sample Output 1

9

If the heroes choose the monsters to defeat as follows, they can defeat nine monsters in total, which is the maximum result.

The first hero defeats two monsters attacking the first town and two monsters attacking the second town.

The second hero defeats three monsters attacking the second town and two monsters attacking the third town.

Sample Input 2

3
5 6 3 8
5 100 8

Sample Output 2

22

Sample Input 3

2
100 1 1
1 100

Sample Output 3

3

Solution in Haskell (GHC 7.10.3) (judge verdict: Accepted)

module Main where

import Data.List
import Control.Monad
import Debug.Trace
import qualified Data.ByteString.Char8 as BC
import Data.Maybe (fromJust)
import Control.Monad.ST (runST)
import qualified Data.Vector.Unboxed.Mutable as MV
import qualified Data.Vector.Unboxed as V
import Data.STRef.Strict



readTuple2 :: IO (Int, Int)
readTuple2 = do
    [a, b] <- map (fst . fromJust . BC.readInt) . BC.words <$> BC.getLine
    return (a, b)

readTuple3 :: IO (Int, Int, Int)
readTuple3 = do
    [a, b, c] <- map (fst . fromJust . BC.readInt) . BC.words <$> BC.getLine
    return (a, b, c)

readInt :: IO Int
readInt = fst . fromJust . BC.readInt <$> BC.getLine

readInts :: IO [Int]
readInts = map (fst . fromJust . BC.readInt) . BC.words <$> BC.getLine

split :: (a -> Bool) -> [a] -> [[a]]
split f [] = []
split f as = let
    (fo, la) = span f as
    las = case la of
        [] -> []
        xs -> split f $ tail xs
    in
        case fo of
            [] -> las
            xs -> xs : las

solve :: Int -> [Int] -> [Int] -> Int
solve n as bs = runST $ do
    av <- V.thaw $  V.fromList as
    bv <- V.thaw $  V.fromList bs
    ans <- newSTRef 0
    forM_ [0..n-1] $ \i -> 
        do
            b <- MV.read bv i
            a <- MV.read av i 
            a' <- MV.read av (i  + 1)
            let kill = min a b
            let remainB = b - kill
            modifySTRef ans (+kill)
            MV.write av i (a - kill)
            let kill' = min a' remainB
            modifySTRef ans (+kill')
            MV.write av (i + 1) (a' - kill')
    readSTRef ans


main = do
    n <- readInt
    as <- readInts
    bs <- readInts
    print $ solve n as bs