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)

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

def fnc(x):
    return math.floor(A*x*1.0/B) - A*math.floor(x*1.0/B)

if N < B:
    print(fnc(N))
else:
    ans = 0
    for i in range(B-1, N+1, B):
        s = fnc(i)
        if s > ans:
            ans = s
    print(ans)