409618: GYM103647 A Night Nesting

You've been birdwatching all day, and it's finally sunset!

Any second now, the $$$n$$$ pigeons will be flying home back to their nests. As you wait an anticipation, you realize something: there are only $$$m$$$ nests in the tree! Some of the pigeons will need to share a nest in order to have somewhere to sleep at night.

It would be quite uncomfortable to share a nest with other pigeons, so a natural question arises: if the pigeons rest optimally, how many pigeons must there be in the fullest nest?

There is only one line of input, which contains two integers, $$$n$$$ and $$$m$$$ ($$$1 \leq n, m \leq 10^{18}$$$). $$$n$$$ represents the number of pigeons returning home, and $$$m$$$ represents the number of nests.

Output a single integer, the number of pigeons in the fullest nest if the pigeons distribute among the nests optimally.

15 5

3

4 3

2

In the first test case, the pigeons can evenly distribute themselves, yielding 3 pigeons in each of the 5 nests.

In the second test case, no matter how they arrange themselves, there will always be a nest containing at least 2 pigeons.