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)

from collections import deque

def main():
    A,B,N=map(int,input().split())
    d=deque()
    
    for x in range(N+1):
        #tmp=((A*x)//B)-A*(x//B)
        if (A*x<B):
            tmp1=0
        if (x<B):
            tmp2=0
        tmp1=((A*x)//B)
        tmp2=A*(x//B)
        tmp=tmp1-tmp2
        
        if x>=1:
            if d[-1]>tmp:
                break
        
        d.append(tmp)
        
    print(d[-1])
    exit()
    
if __name__=="__main__":
    main()