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 C (GCC 9.2.1) (judge verdict: Time Limit Exceeded)

#include <stdio.h>

int main(void)
{
  long long int a, b, n, i, tmp=1, ans=0, ans_tmp;

  scanf("%lld%lld%lld", &a, &b, &n);

  for (i = 0; i <= n; i++) {
    if (b*tmp-1 <= n) i = b*tmp-1;
    ans_tmp = (long long int)(a*i/b) - a*(long long int)(i/b);
    if (ans < ans_tmp)
      ans = ans_tmp;
    tmp++;
  }

  printf("%lld", ans);

  return 0;
}