You are running a lottery, and have a number of different balls numbered 1 to N. Your job is to figure out how many different ways these balls can go into k different buckets. The only stipulation is that each bucket must have at least one ball in it.

For example, if you have 4 balls and 2 buckets, you can divide them up seven different ways:

• 123, 4
• 124, 3
• 134, 2
• 234, 1
• 12, 34
• 13, 24
• 14, 23

The order of the buckets does not matter, so (12, 34) is the same as (34, 12). Likewise, the order of the balls does not matter, so (12, 34) is the same as (21, 43). Good luck!