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: Accepted)

# x = iB + j とすると
# floor(A(iB + j) / B) - A * floor((iB + j/)B)
#   = A * i + floor(A * j / B) - A * i - A * floor(j / B)
#   = floor(A * j / B)
# なので, A * j が最大の時, floor(Ax/B) - A * floor(x/B) は最大となる.
# 0 <= j < B なので, x の値は
#   N < B の時, x = N, N >= B の時 x = B - 1
# となる.


from math import floor


def solve():
    A, B, N = map(int, input().split())
    x = min(N, B - 1)
    print(floor(A * x / B) - A * floor(x / B))


if __name__ == '__main__':
    solve()