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 Ruby (2.7.1) (judge verdict: Wrong Answer)

#!/usr/bin/env ruby
a, b, n = gets.chomp.split(" ").map(&:to_i)

ans = - Float::INFINITY

# bの倍数だけ試せば十分

x = b

if x > n
  puts (a * n / b).floor - a * (n / b).floor
else
  while x < n
    x = b

    value = (a * x / b).floor - a * (x / b).floor

    ans = [ans, value].max

    x += b
  end

  puts ans
end




# n.downto(0) do |i|
#   value = (a * i / b).floor - a * (i / b).floor
#
#   break if ans > value
#   ans = value
# end
#
# puts ans