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 PyPy3 (7.3.0) (judge verdict: Wrong Answer)

import math

A, B, N = map(int, input().split())

temp = -1 * float('inf')
temp2 = -1 * float('inf')

if A > N or B > N:
    temp = math.floor(A*N/B) - A*math.floor(N/B)
if A > B  and B < N:
    temp = math.floor(A*(B-1)/B) - A*math.floor((B-1)/B)
elif A < B and B < N:
    temp = math.floor(A*(B-1)/B) - A*math.floor((B-1)/B)
else:
    x = A - 1
    while x <= N:
        if temp <= math.floor(A*x/B) - A*math.floor(x/B):
            temp = math.floor(A*x/B) - A*math.floor(x/B)
            x += A

print(temp)