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)

line = gets.split(' ').map(&:to_i)

a = line[0]
b = line[1]
n = line[2]

def culc(a,b,x)
  return (a * x / b).floor - a * (x / b).floor
end

if n > 1000000 then
  n = 50 * (n ** 0.5).floor
end

answer = 0

for x in 0..n
  result = culc(a,b,x)
  if result > answer then
    answer = result
  end
end
  
print answer