Alice and Bob decide to share a chocolate bar, which is an
rectangular grid of chocolate cells. They decide that Alice should
$a < n \cdot m$ pieces and that Bob should get
$b = n \cdot m -
a$ pieces. To split the chocolate bar, they repeatedly take a single piece of
chocolate and break it either horizontally or vertically, creating two
smaller pieces of chocolate.
What is the minimum number of splits that Alice and Bob need to
perform in order to split the
$m$ chocolate bar into two piles
$b$ chocolate cells?
Illustration of a solution to Sample Input 2, showing the original
$10$ chocolate bar split three times into pieces of size
$3$. Giving Alice the
$3$ pieces, she gets a total of
$50 + 21 = 71$ chocolate cells.
The input consists of a single line, containing the three integers
$1 \le n, m \le 10^6$,
$1 \le a < n \cdot m$).
Output the minimum number of splits needed to achieve the desired division of chocolate.
3 10 9
10 10 71