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)

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

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

high = N
low = 0
while high - low > 1:
    mid_left = high / 3 + low * 2 / 3
    mid_right = high * 2 / 3 + low / 3
    # print(mid_left, mid_right)
    if f(mid_left) > f(mid_right):
        high = mid_right
    else:
        low = mid_left
print(f(high))