Josephus Problem

Question

Description

Josephus Problem is an ancient problem named for Flavius Josephus. There are people standing in a circle waiting to be executed. The counting out begins at the first point in the circle and proceeds around the circle in a fixed direction. In each step, one person is skipped and the next person is executed. The elimination proceeds around the circle (which is becoming smaller and smaller as the executed people are removed), until only the last person remains, who is given freedom.

For example, if there are 10 people in the circle, the executed order is 2, 4, 6, 8, 10, 3, 7, 1, 9. So the 5th person survives.

Now we define a function J(n) to be the survivor’s number when there are n person in the circle, and J^2(n)=J(J(n)), for instance J^2(10)=J(J(10))=J(5)=3, and J^3(n)=J(J(J(n))), and so on. Could you calculate J^m(n)?

输入格式

The input consists of a number of cases.
Each case contains integers n and m. 0<n, m<=10^9
The input is terminated by a case with m=n=0

输出格式

For each case, print the number J^m(n)

输入样例

10 2
10 1
20 1
0 0

输出样例

3
5
9