Legend has it that Josephus - a famous historian of the first century - survived and became famous mathematical genius. During the Jewish war, he in the squad of 41 Jewish warrior was driven by the Romans in a cave. Preferring suicide captivity, the soldiers decided to stand in a circle and consistently kill each third of the living until, until there is a single man. However, Joseph, along with one of his supporters felt like the end of the senseless - he quickly figured out the saving space in a vicious circle, which has placed himself and his companion. And just so we know its history.

In our version, we start with what is built in terms of N people, numbered from 1 to N, and will exclude every k-th until then, until only one person survives. (For example, if N = 10, k = 3, the first die third, then the 6-th and then 9-th, then 2-nd, then the 7-th, then the 1-st, then the 8-th, with the it - the 5-th, and then the 10-th. Thus, escape the 4-th.)

Input

In the input file are given positive integers N and k. 1 ≤ N ≤ 500, 1 ≤ k ≤ 100.

Output

The output file should contain a single number - the number of surviving humans.