Yo-Yo#421

Yo-Yo

1 second

128 megabytes

Very easy

The yo-yo toy consists of a spool wound with a string. If, while holding the end of the string, you release the spool, it will rotate, first descending, and then, due to inertia, rising back up. However, the height to which the spool rises on each ascent will be $k$ times less than the height from which it descended. The spool is considered to have stopped if the height of its next ascent is less than or equal to $1$ .

Write a program that, given the length of the string $l$ and the coefficient $k$ , calculates the number of ascents the spool makes before stopping. For example, if $l = 17$ l = 17 and $k = 2$ k = 2, then the ascents will be to the heights of $8.5$ , $4.25$ , $2.125$ , $1.0625$ , and then it will stop. Thus, the answer would be $4$ ascents.

Input

Two integers $l$ $(1 \leq l \leq 1 0^{9})$ (1 \leq l \leq 10^9) and $k$ $(2 \leq k \leq 100)$ (2 \leq k \leq 100).

Output

Print one integer — the number of ascents.

Examples

Example 1

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Example 2

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Example 3

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l = 17

k = 2

(1 \leq l \leq 1 0^{9})

(2 \leq k \leq 100)