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)

a, b, n = map(int, input().split())
ans = 0
if b == 1:
    print(0)
else:
    if b > n:
        ans = (a*n)//b
        print(ans)
    else:
        c = n//b
        max_c = [0]*(c+1)
        for i in range(1, c+1):
            max_c[i] = (a * (b*(i+1) - 1))//b - a*i
        max_c[c] = (a*n)//b - a*c
        print(max(max_c))