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: Wrong Answer)

#include<stdio.h>
long long int gcd(long long int a,long long int b){
  long long int i;
  while(a!=0 && b!=0){
    i=b;
    b=a%b;
    a=i;
  }
  return a;
}


int main(){
  long long a,b,n,x,i,max=0;
  scanf("%lld%lld%lld",&a,&b,&n);
  if(a%b==0){
    if(b-1<=n)
      printf("%lld",b-1);
    else
      printf("%lld",n);
    return 0;
  }
  x=b/gcd(a,b);
  if(x<=n)
    printf("%lld\n",a/gcd(a,b));
  else{
    for(i=0;i<=n;i++)
      if(i%b>max)
        max=i%b;
    printf("%lld\n",(max*a)/b);
  }
  return 0;
}