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: Time Limit Exceeded)

import math
a,b,n = map(int,input().split())
c = 0
for i in range(1,n+1):
    # tmp = (math.floor(a*i/b)-a*math.floor(i/b))
    if c < (math.floor(a*i/b)-a*math.floor(i/b)):
        c = (math.floor(a*i/b)-a*math.floor(i/b))
    elif c > 0 and c > (math.floor(a*i/b)-a*math.floor(i/b)):
        print(c)
        exit()
print(c)