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)

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

# y1 = (a * x1 / b).to_i   # 普通の直線の切り捨てまたは切り上げられる
# y2 = (x2 / b).to_i * a   # bの倍数になった時に固定値が変化する

result = 0
for i in  0..(n-1) do
  x = n -i
  y1 = (a * x / b).to_i
  y2 = (x / b).to_i * a
  result = (y1 - y2).to_i if  (y1 - y2).to_i > result

  if x == n
    y1_max = y1
    y2_max = y2
  else
    # どちらも短調増加
    # 最初離れていて近づくことはありえない
    if y1_max - y1 > 1 &&  y2_max - y2 > 1
      break
    end
  end
end

puts result