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: Wrong Answer)

import math


A, B, N = map(lambda x: int(x), input().split(" "))

result = 0
candidate = -1
for i in reversed(range(0, N+1, B)):
    if i % B == 0:
        candidate= i-1
        break
print(candidate)
if candidate > 0:
    i = candidate
    temp = math.floor(A*i/B) - A*math.floor(i/B)
    result = max(result, temp)

temp = math.floor(A*N/B) - A*math.floor(N/B)
result = max(result, temp)

print(result)