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)

from math import floor
A, B, N = map(int, input().split())
dic = {}
if N <= 10**6:
    for i in range(1, N+1):
        tmp = floor(A*i/B) - A*floor(i/B)
        if tmp in dic:
            dic[tmp] += 1
        else:
            dic[tmp] = 1
else:
    for i in range(1, 10**6+1):
        tmp = floor(A*i/B) - A*floor(i/B)
        if tmp in dic:
            dic[tmp] += 1
        else:
            dic[tmp] = 1
ans = -1
for k, v in dic.items():
    if k > ans:
        ans = k
print(ans)