CF351C Jeff and Brackets

Jeff loves regular bracket sequences. Today Jeff is going to take a piece of paper and write out the regular bracket sequence, consisting of $ nm $ brackets. Let's number all brackets of this sequence from $ 0 $ to $ nm $ - $ 1 $ from left to right. Jeff knows that he is going to spend $ a_{i\ mod\ n} $ liters of ink on the $ i $ -th bracket of the sequence if he paints it opened and $ b_{i\ mod\ n} $ liters if he paints it closed. You've got sequences $ a $ , $ b $ and numbers $ n $ , $ m $ . What minimum amount of ink will Jeff need to paint a regular bracket sequence of length $ nm $ ? Operation $ x\ mod\ y $ means taking the remainder after dividing number $ x $ by number $ y $ .

The first line contains two integers $ n $ and $ m $ ( $ 1

In a single line print the answer to the problem — the minimum required amount of ink in liters.

In the first test the optimal sequence is: $ ()()()()()() $ , the required number of ink liters is $ 12 $ .