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AIO2010 Solution

Ninjas

You used to like ninjas. That was before the shadowy shiro-obi ninja clan moved in next door. They're mostly decent neighbours - they keep to themselves and never throw loud parties - but every few nights they sneak into your house and raid the kitchen. With no one else to turn to, you decide to take matters into your own hands and catch them in the act.

There are N ninjas trying to get inside, one at a time. You wait and watch carefully, grabbing the first one who comes past. However, in the time it takes you to securely tie up this first ninja, K other ninjas manage to sneak past you. Nevertheless, you persevere, grabbing the next ninja. Again, while you tie them up, K more ninjas sneak past. This continues until all of the ninjas have tried to get in.

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In the above example, K=2. That is, for each ninja you tie up, the following two ninjas will sneak past. You catch the first ninja who comes past, and then ninjas #2 and #3 sneak past you. You catch ninja #4, and then ninjas #5 and #6 sneak past you. This repeats until all N ninjas have either been caught or have snuck past you.

Your task is to write a program that reads in the values of N and K, and calculates the number of ninjas who sneak past you.

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