Score : $300$ points
There is an iron bar of length $L$ lying east-west. We will cut this bar at $11$ positions to divide it into $12$ bars. Here, each of the $12$ resulting bars must have a positive integer length.
Find the number of ways to do this division. Two ways to do the division are considered different if and only if there is a position cut in only one of those ways.
Under the constraints of this problem, it can be proved that the answer is less than $2^{63}$.
Input is given from Standard Input in the following format:
$L$
Print the number of ways to do the division.
12
1
There is only one way: to cut the bar into $12$ bars of length $1$ each.
13
12
Just one of the resulting bars will be of length $2$. We have $12$ options: one where the westmost bar is of length $2$, one where the second bar from the west is of length $2$, and so on.
17
4368