SubdividedSlimes

The idols Ami and Mami like playing games. Today they bought a new game. At the beginning of the game a single slime appears on the screen. You are given an int S: the size of the slime.

The game consists of K turns. In each turn of the game the player must choose a single slime and cut it into two smaller parts. More precisely, suppose that the player chose a slime of size z. When cutting this slime, the player must choose two positive integers x and y such that x+y = z. The player will then cut the slime into two smaller slimes. The sizes of those smaller slimes will be x and y, respectively. Note that the player must always choose a slime of size 2 or more, as it is not possible to cut a slime of size 1.

The player gets a reward for making each cut: whenever you cut a slime of size x+y into slimes of sizes x and y, the player is awarded x*y mascots.

Ami and Mami have just started a new game. You are given two ints S and M. Calculate and return the smallest possible K (the number of turns in the game) such that Ami and Mami can get at least M mascots in the game. If there exists no such K, return -1 instead.