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: Time Limit Exceeded)

def fun(a,b,x)
  return ((a * x)/b) - a * (x/b)
end

arr = gets.chomp.split(' ').map{|j| j.to_i}
a = arr[0]
b = arr[1]
num = arr[2]
max = 0
i = 0
while i <= num
  # if max < fun(arr[0] , arr[1] , num)
  #   max = fun(arr[0],arr[1],num)
  # end
  if max < fun(a,b,i)
    max = fun(a,b,i)
  end
  i += 1 
end

print max