**Josephus problem** is a theoretical problem related to a certain counting-out game. However, Narnal thought this problem is too easy for him, so he constructed a more complex Josephus problem as following.

There are \(n\) people standing in a circle indexing from \(1\) to \(n\), and each person in the circle holds a note marked with a positive integer. At first, given a positive integer \(m\), people count the number from one to the next starting from index \(1\) in clockwise (\(1, 2, \ldots, n, 1, 2, \ldots\)). When the counted number reaches \(m\), the corresponding person will be eliminated from the circle and yell the number in his/her note, denoted by \(k_{i}\), and then people restart counting from the next person targeting for number \(k_{i}\) until, eventually, only one person is left in the circle.