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: Time Limit Exceeded)

#!/usr/bin/python
# -*- coding: utf-8 -*-

from math import floor,ceil

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

check_list1 = {B*n for n in range(0,ceil(N/B))}
check_list2 = {ceil((B/A)*n) for n in range(0,ceil(N/(B/A)))}
check_list3 = {floor((B/A)*n) for n in range(0,ceil(N/(B/A)))}

check_list = check_list1.union(check_list2,check_list3)

ans = 0

for n in check_list:
    ans = max(ans,floor(A*n/B)-A*floor(n/B))

print(ans)