Last Josephus Survivor

Time limit

Memory limit

128 MB

Problem

There are N people numbered from 1 to N sitting in a circle. A positive integer K is given.

Starting from person 1, repeatedly count K people among those still in the circle and remove the K-th person. After someone is removed, counting continues from the next remaining person. The process continues until only one person remains.

Given N and K, find the number of the last remaining person.

Input

The first line contains N and K separated by a space.

1 <= N <= 10^15, 1 <= K <= 90, and K <= N.

Output

Print the number of the last remaining person.