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)

# ABC 165 D
# https://atcoder.jp/contests/abc165/tasks/abc165_d

require 'bigdecimal'

a, b, n = gets.split(/ /).map(&:to_i)
if n < b
  x = n
  x_per_b = BigDecimal(x.to_s) * BigDecimal(1.0.to_s) / BigDecimal(b.to_s)
  puts (BigDecimal(a) * BigDecimal(x_per_b.to_s)).floor - BigDecimal(a) * BigDecimal(x_per_b.to_s).floor
else
  puts a - 1
end