All problems

Seedling Weeks

Easy · math

Isla runs a small plant nursery. She starts with a single seedling. At the end of every week, each seedling is split into k new seedlings, so the number of seedlings is multiplied by k each week.

She needs at least n seedlings for a big order. Return the number of weeks she has to wait. If she already has enough at the start, that is 0 weeks.

For example, with k = 3 the counts at the end of the weeks are 3, 9, 27, 81 and so on.

Examples

Example 1

Input: n = 20, k = 3

Output: 3

After 2 weeks she has 9 seedlings, which is not enough. After 3 weeks she has 27, which is.

Example 2

Input: n = 8, k = 2

Output: 3

The counts are 2, 4, 8. Exactly 8 is enough.

Example 3

Input: n = 1, k = 5

Output: 0

She already has 1 seedling at the start.

Constraints