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 matplotlib.pyplot as plt

def main():
    a,b,n = map(int,input().split())
    mx = 0
    for x in range(1,min(b+1,n+1)):
        left = int(a*x/b)
        right = a * int(x/b)
        #print("x=",x,"floor(Ax/B)=",int(a*x//b),"A*floor(x/B)=",a * int(x // b),"answer=",left-right)
        #right.append(a * int(x/b))

        mx = max(left-right,mx)
    print(mx)


    #plt.plot(list(range(len(right))),right,label="test")


if __name__ == '__main__':
    main()