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=$stdin.read.chomp.split(" ").map(&:to_i)

def f(x)
  (A*x/B) - A * (x/B)
end

l = 0
r = [B+1, N].min
result = 0

mxl = 0
pl = 0
while l < r - 1
  xl = f(l)
  xr = f(r)
  mxl = [xl, mxl].max
  pl = l
  if xl < mxl
    while true
      res = f(pl)
      if res >= result
        result = res
      end
      pl += 1
    end
    break
  else
    l = (l + r) / 2
  end
  result = [xl,xr].max
end

puts result