Problem Description

You want to measure the weight of an object in 1 g units using a balance scale.

You can prepare $N$ types of weights, each in the quantity of $K$. Here, the $i$th ($1 \leq i \leq N$) type of weight has the same weight.

You can place these $N \times K$ weights on

• The right pan of the balance
• The left pan of the balance
• Neither pan

When you place the object to be weighed on the right pan,

(Total weight of weights on the left pan) = (Total weight of weights on the right pan) + (Weight of the object)

The balance will be balanced, and at this time, the weight of the object can be measured as (Total weight of weights on the left pan) - (Total weight of weights on the right pan) g.

You want to measure all weights from 1 g to $M$ g in 1 g units with the least number of weight types. Output the minimum number of weight types $N$ required.

Input Format

The input is given from the standard input in the following format:

$M$ $K$

Output Format

Output the minimum number of weight types $N$.

Sample Input and Output

Sample Input #1

5 1

Sample Output #1

3

Sample Input #2

8 2

Sample Output #2

2

Notes/Hints

Constraints

• $1 \leq M \leq 10^9$
• $1 \leq K \leq 10^5$
• All inputs are integers.

Sample Explanation 1

For example, if you prepare weights of 1 g, 2 g, and 3 g, you can measure:
- 1 g by placing a 1 g weight on the left pan
- 2 g by placing a 2 g weight on the left pan
- 3 g by placing a 3 g weight on the left pan
- 4 g by placing 2 g and 3 g weights on the left pan and a 1 g weight on the right pan
- 5 g by placing 2 g and 3 g weights on the left pan
It is not possible to measure 1 g to 5 g with only 2 types of weights, so this is the minimum.

Sample Explanation 2

For example, preparing weights of 1 g and 3 g is sufficient.

见题面 Input 部分

见题面 Output 部分