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: Runtime Error)

def f(A,B,x):
    return (((A*x)//B)-(A*(x//B)))
def main():
    A,B,N=map(int,input().split())
    lb=1
    ub=min(B-1,N)
    while(lb<=ub):
        mid=(lb+ub)//2
        if f(A,B,mid)<N:
            lb=mid+1
        elif f(A,B,mid)>N:
            ub=mid-1
        else:
            break
    print(f(A,B,mid))
if __name__=='__main__':
    main()