Flavius Josephus was a roman historian of Jewish origin. During the Jewish-Roman wars of the first century AD, he was in a cave with fellow soldiers, 40 men in all, surrounded by enemy Roman troops. They decided to commit suicide by standing in a ring and counting off each third man. Each man so designated was to commit suicide…​Josephus, not wanting to die, managed to place himself in the position of the last survivor. In the general version of the problem, there are n soldiers numbered from 1 to n and each k-th soldier will be eliminated. The count starts from the first soldier. What is the number of the last survivor?