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: Accepted)

A,B,N = gets.split.map &:to_i
n = [N-1-N%B,1].max
m = N%B*A - A*N%B
x = n%B*A - A*n%B
m = x  if m < x
t = Time.now
c = 0
y = N%B
N.downto(1){|n|
  l = y*A
  r = A*n %B
  x = l - r
  m = x  if m < x
  c += 1
  y -= 1
  y += B  if y < 0
  break if 0 == c&0xffff && Time.now - t > 1.92
}
p m / B