CF940B Our Tanya is Crying Out Loud

Right 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: 1. Subtract 1 from $ x $ . This operation costs you $ A $ coins. 2. 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 $ ?

The first line contains a single integer $ n $ ( $ 1

Output a single integer — the minimum amount of coins you have to pay to make $ x $ equal to $ 1 $ .

In 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.