B. Our Tanya is Crying Out Loudtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputRight now she actually isn't. But she will be, if you don't solve this problem.You are given integers n, k, A and B. There is a number x, which is initially equal to n. You are allowed to perform two types of operations:   Subtract 1 from x. This operation costs you A coins.  Divide x by k. Can be performed only if x is divisible by k. This operation costs you B coins.  What is the minimum amount of coins you have to pay to make x equal to 1?InputThe first line contains a single integer n (1 ≤ n ≤ 2·109).The second line contains a single integer k (1 ≤ k ≤ 2·109).The third line contains a single integer A (1 ≤ A ≤ 2·109).The fourth line contains a single integer B (1 ≤ B ≤ 2·109).OutputOutput a single integer — the minimum amount of coins you have to pay to make x equal to 1.ExamplesInput9231Output6Input55220Output8Input19342Output12NoteIn the first testcase, the optimal strategy is as follows:   Subtract 1 from x (9 → 8) paying 3 coins.  Divide x by 2 (8 → 4) paying 1 coin.  Divide x by 2 (4 → 2) paying 1 coin.  Divide x by 2 (2 → 1) paying 1 coin. The total cost is 6 coins.In the second test case the optimal strategy is to subtract 1 from x 4 times paying 8 coins in total.
Input9231
Output6
['dp', 'greedy', '*1400']