After some thought on where to spend a holiday Vova decided to travel
around South China and visit Guangzhou, Shenzhen, Macau and Hong Kong.
Vova heard that South China speaks the Cantonese dialect of the Chinese
language. So before setting off he learned several simple phrases in
Cantonese. During his first walk around the Guangzhou center Vova said
hello to n passers-by and m of them responded.
Vova concluded that the other (n − m) passers-by, obviously, spoke the
Mandarin dialect of the Chinese language.
After Vova finished his walk, he decided to evaluate M, the number of
Guangzhou citizens who speak Cantonese. Wikipedia states that the city's
population is N people. Help Vova to find such M, which maximizes the
probability that exactly m out of n random passers-by speak Cantonese.
The single input line contains integers n, m and N
(1 ≤ n ≤ N ≤ 108; 0 ≤ m ≤ n). Each of the n
passers-by was a Guangzhou citizen and met Vova exactly once during the
Print the required M. If there are multiple values of M maximizing the
probability, print the largest of them.
Problem Author: Alexander Ipatov
Problem Source: Open Ural FU Personal Contest 2013