Description

After Tesla’s six-digit passcode was easily cracked, people began to doubt the security of electric vehicles. Upon hearing this, Li Hua designed his own passcode system:

• Suppose the security system has $n$ storage units. Each storage unit can hold up to 2 different types of signals (it may also hold none). There are two types of signals, $0$ and $1$, with $a$ copies of $0$ and $b$ copies of $1$ available. A single $0$ or $1$ counts as one signal. We need to store these signals in the storage units. The $0$ and $1$ signals do not have to be all stored; a storage unit may contain any number of $0$’s and any number of $1$’s. Every distinct storage plan, after Li Hua’s processing, will correspond to a distinct passcode.

Given $n,a,b$, find the number of possible distinct storage plans.

Input Format

The first line contains 3 integers, $n,a,b$.

Output Format

The first line contains an integer, the number of plans.

2 1 1

9

Hint

All 9 plans are as follows:

Constraints: For all testdata, $a,b \le 50$, $n+a \le 50$, $n+b \le 50$.

$\text{upd 2022.10.22}$: A new set of Hack testdata was added.

Translated by ChatGPT 5