D - Floor Function

Score : $400$ points

Problem Statement

Given are integers $A$, $B$, and $N$.

Find the maximum possible value of $floor(Ax/B) - A × floor(x/B)$ for a non-negative integer $x$ not greater than $N$.

Here $floor(t)$ denotes the greatest integer not greater than the real number $t$.

Constraints

• $1 ≤ A ≤ 10^{6}$
• $1 ≤ B ≤ 10^{12}$
• $1 ≤ N ≤ 10^{12}$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$A$ $B$ $N$

Output

Print the maximum possible value of $floor(Ax/B) - A × floor(x/B)$ for a non-negative integer $x$ not greater than $N$, as an integer.

5 7 4

2

When $x=3$, $floor(Ax/B)-A×floor(x/B) = floor(15/7) - 5×floor(3/7) = 2$. This is the maximum value possible.

11 10 9

9