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(int, input().split())

if a%b == 0:
    if b-1 <= n:
        print(b-1)
    else:
        print(n)
else:
    maxT = 0
    i = n
    while i >= n-1000000 and i>= 0:
        t = math.floor(a*i/b)-a*math.floor(i/b)
        if t > maxT:
            maxT = t
        i-=1
    wild = max(n//b, (n-1)//b)
    print(max(maxT, wild))