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: Wrong Answer)

import math 
 
a,b,n = map(int,input().split())

if b > n:
    if b%n !=0:
        ans = math.floor(a*n/b) - a*math.floor(n/b)
    else:
        n -= 1
        ans = math.floor(a*n/b) - a*math.floor(n/b)
    print(ans)
    exit()

M = 0
for i in range(b-1,n,b):
    temp = ans = math.floor(a*n/b) - a*math.floor(n/b)
    M = max(temp,M)

print(M)