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)

from math import floor, gcd

def lcm(x, y):
    return (x * y) // gcd(x, y)

def main():
    A, B, N = list(map(int, input().split(' ')))
    
    tmp = 0
    
    mods = []
    # print([A * x % B for x in range(B)])
    for x in range(N):
        m = A * x % B
        if m >= 1:
            mods.append(m)
        else:
            if A < B:
                mods.append(1000000000000000000000)
            else:
                mods.append(0)
        
    
    print(mods)
    if A < B:
        index = mods.index(min(mods))
    else:
        index = mods.index(max(mods))
    print(index+1)

    # for x in range(1, N+1):
    #     out = floor(A * x / B) - floor(x / B)
    #     tmp = max(tmp, out)
    # print(tmp)
    
    
main()