Problem:
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.

Sample Input 1

5 7 4

Sample Output 1

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 Input 2

11 10 9

Sample Output 2

9

Solution in Python (3.8.2) (judge verdict: Runtime Error)

import math
A, B, N = map(int, input().split())
 
if N <B:
	print(math.floor(A*N/B))
	exit()
 
k = [0]*(math.floor(N/B)+1)
 
for i in range (1, math.floor(N/B)+2):
	k[i-1] = i*B-1
 
for i in range (0, len(k)):
	if k[i] > N:
		k[i]=0
 
p=[0]*len(k)
 
for i in range (0, len(k)):
	p[i] = math.floor(A*k[i]/B)-A*math.floor(k[i]/B)
 
print(max(p))