5839: ABC165 —— D - Floor Function
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Description
Given are integers $A,\ B,\ N$.
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 $t$.
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 $t$.
Input
Input is given from Standard Input in the following format:
$A\ B\ N$
$A\ B\ N$
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.
Constraints
$1≤A≤10^6$
$1≤B≤10^{12}$
$1≤N≤10^{12}$
All values in input are integers.
$1≤B≤10^{12}$
$1≤N≤10^{12}$
All values in input are integers.
Sample 1 Input
5 7 4
Sample 1 Output
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.
Sample 2 Input
11 10 9
Sample 2 Output
9