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)

# D - Floor Function

from math import floor

A, B, N = map(int, input().split())

if B < N:
    mx = floor(A * (B - 1) / B) - A * floor((B - 1) / B)
else:
    mx = floor(A * N / B) - A * floor(N / B)

# mx = -1 * float('inf')
# i = 0

# for i in range(N + 1):
#     result = floor(A * i / B) - A * floor(i / B)
#     print(i, result)
#     if mx <= result:
#         mx = result

print(mx)