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 solve(x):
    return math.floor(a * x / b) - a * math.floor(x / b)

def isIncrease(x):
    # math.floor(a * x / b) - a * math.floor(x / b)
    if solve(x) > solve(x-1):
        return True
    else:
        return False

ans = 0

l = 0
# r = 10**12
r = n


while l <= r:
    m = (l+r)//2

    if isIncrease(m):
        l = m + 1
    else:
        r = m - 1

print(solve(m))