Double Dealing

You are given a deck of $n$ distinct cards. Deal the entire deck to $k$ players in the usual way: the top card goes to player 1, the next to player 2, the $k$-th to player $k$, the $(k+1)$-th back to player 1, and so on until the deck runs out.

Then gather the cards back up. Place player 1's pile on top, player 2's pile beneath it, and so on, so that player $k$'s pile ends up on the bottom. Within each player's pile the cards are in reverse order of dealing: the last card that player was dealt is on top, and the first is on the bottom.

Counting the first deal, how many times must this whole process be repeated before the deck returns to its original order?

The input contains multiple test cases. Each case is a single line with two integers $n$ and $k$ ($1 \le n \le 800$, $1 \le k \le 800$). The input ends with a line containing two zeros.

For each test case, print a single integer: the number of deals needed to return the deck to its original order. Print each integer on its own line, with no extra spaces and no blank lines between answers. For every possible input the answer fits in a signed 64-bit integer.