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)

a, b, n= gets.chomp.split.map(&:to_i)

# 1.upto(n) do |x|
#   f = (a*x/b).floor - a*(x/b).floor
#   p "xが#{x}のとき"
#   p f
# end

if b == 1
  puts 0
  exit
end

if a % b == 0
  c = a / b

  puts c * (b-1)

  # puts n * (a/b)
  exit
end

if n > b-1
  # if a % b ==0
    # puts a - 2
  # else
    puts a - 1
  # end
else
  f = ((a*n)/b).floor - a * (n/b).floor
  puts f
end