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 = gets.chomp.split(" ").map(&:to_i)

def calc(x)
  (A*x/B.to_f).floor - A * (x/B.to_f).floor
end

ans = [0]
ans << calc(N)
wk = (A*N/B * B) / A
ans << calc(wk)
ans << calc(wk+1)
wk = N/B * B
ans << calc(wk)
ans << calc(wk-1) if wk > 0

puts ans.max