Problem Statement

This is a story about a certain RPG.
The enemy has $N$ HP. At first, you fight it as $1$ person, but if you request reinforcements, other online players come to help and multiple players can fight together.
In that case, the $K$ players who dealt the most damage become MVPs and obtain a special item.
In case of a tie (when the $K$-th player and the $K+1$-th player have dealt the same amount of damage), the MVPs are chosen at random.
Now, find the minimum amount of damage you should deal before requesting reinforcements in order to surely become an MVP.
Many of the other online players are strong, so after you request reinforcements, the enemy may be defeated before you deal any damage.
Also, if the number of players who dealt $1$ or more damage is less than $K$, all players who dealt damage become MVPs.

Input

$N$ $K$

$1 \leq N \leq 10^{18}$
$1 \leq K \leq 10^{18}$

Output

Output the answer.

Sample

15 1

8

1000000000000000000 2

333333333333333334