\gdef\thisproblemauthor{Anton Maydell}
\gdef\thisproblemdeveloper{Anton Maydell}
\begin{problem}{Set Intersection}
{intset.in}{intset.out}
{2 seconds (\textsl{3 seconds for Java})}{256 mebibytes}{}

Vasya and Petya have two identical sets of cards.
Each set consists of $N$ cards.
Each card contains one integer written on it.
All integers from $1$ to $N$ are present in the set.

Vasya randomly chooses $L$ cards from the first set.
Petya randomly chooses $M$ cards from the second set.
Each choice is equally probable, and Vasya's and Petya's choices
are independent.
After choosing the cards, Vasya and Petya count the number of integers
which are present in both of their selections.
If this number is strictly less than $K$,
Petya is declared the winner.
Otherwise, Vasya wins.

Your task is to choose the number $K$ in such a way that the game is
the most fair.
Formally, you must find the maximal $K$ not exceeding $N$ such that
the probability of Vasya's victory is at least $0.5$.

\InputFile

The first line contains three positive integers $N$, $L$ and $M$
($1 \le L, M \le N \le 1\,000\,000$).

\OutputFile

Print the non-negative integer $K$.
You are allowed to solve the problem approximately:
your solution will be considered correct if the absolute value
of the difference between your answer and the jury's answer
does not exceed $10$.

\Example

\begin{example}
\exmp{
4 1 2
}{%
1
}%
\end{example}

\end{problem}
