(This story is more or less based upon real facts.)

Some absent-minded professors
inadvertently make the statement of a problem available to everyone
the day before an exam.
One student notices this fact,
and in solidarity he warns *k* other students.
Each one of them warns *k* other students
(all different and who did not know yet),
and so on.
Knowing the total number of students *n* and the constant *k*,
when will all students be aware?

**Input**

Input consists of several cases,
each with two natural numbers *n* and *k*.
Assume 1 ≤ *n* ≤ 10^{6} and 1 ≤ *k* ≤ 1000.

**Output**

For every case, print the moment when all students will be aware. Suppose that the first student is aware at the moment 1, ant that transmitting the information requires one unit of time.

Public test cases

**Input**

1 3 2 3 4 3 5 3 13 3 14 3 524287 2 524288 2

**Output**

1 2 2 3 3 4 19 20

Information

- Author
- Salvador Roura
- Language
- English
- Translator
- Original language
- Catalan
- Other languages
- Catalan
- Official solutions
- C++
- User solutions
- C++
- Event
- Vuitè Concurs de Programació de la FME
- Date
- 2011-12-21