Jump King Choi Junmin

Junmin likes to jump. To test his jumping power, Changyoung laid out a number line and placed one chocolate on every integer coordinate from $a$ to $b$.

Junmin always starts at coordinate $0$. If his jumping power is $k$, one jump takes him from his current coordinate to the coordinate $-k$ or $+k$ away. Every jump covers exactly $k$. If a chocolate sits at coordinate $0$, he eats it before he starts jumping.

Junmin is addicted to chocolate, so he stepped onto the number line to collect all of it. He ate a huge breakfast, so he can jump an unlimited number of times. Find the largest number of chocolates Junmin can collect with jumping power $k$.

The input is a single line. It contains the jumping power $k$ ($1 \le k \le 10^{18}$) and the start coordinate $a$ and end coordinate $b$ of the chocolate range ($-10^{18} \le a \le b \le 10^{18}$), given as integers separated by spaces.

Print the largest number of chocolates Junmin can collect on one line.

The input values and the answer go past the 32 bit integer range. In C or C++, use the 64 bit type long long (format string %lld).