#abc165d. [abc165_d]Floor Function

[abc165_d]Floor Function

Problem Statement

Given are integers AA, BB, and NN.

Find the maximum possible value of floor(Ax/B)A×floor(x/B)floor(Ax/B) - A × floor(x/B) for a non-negative integer xx not greater than NN.

Here floor(t)floor(t) denotes the greatest integer not greater than the real number tt.

Constraints

  • 1A1061 ≤ A ≤ 10^{6}
  • 1B10121 ≤ B ≤ 10^{12}
  • 1N10121 ≤ N ≤ 10^{12}
  • All values in input are integers.

Input

Input is given from Standard Input in the following format:

AA BB NN

Output

Print the maximum possible value of floor(Ax/B)A×floor(x/B)floor(Ax/B) - A × floor(x/B) for a non-negative integer xx not greater than NN, as an integer.


Sample Input 1

5 7 4

Sample Output 1

When x=3x=3, floor(Ax/B)A×floor(x/B)=floor(15/7)5×floor(3/7)=2floor(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