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)

s = input().split(' ')
a = int(s[0])
b = int(s[1])
i = int(s[2])

ans = 0
eps = 0.000000001
if(a * i < b):
    d1 = 0
else:
    d1 = (a * i) / b
    if(d1 < eps):
        d1 = 0
    else:
        d1 = int(d1+eps)
if(i < b):
    d2 = 0
else:
    d2 = (i // b)
    if(d2 < eps):
        d2 = 0
    else:
        d2 = int(d2+eps)
ansi = int(d1 - (a * d2))
ans = max(ans, ansi) 
print(ans)