1043: Jump and Remove in a ring (Clockwise)

Memory Limit:128 MB Time Limit:1.000 S
Judge Style:Text Compare Creator:
Submit:138 Solved:37

Description

Suppose a set of N consecutive integers starting are arranged in a circle. 
0 1 2 3 4 5 ...... k
N-1 N-2 ...k+2  k+1

When the counting start at 1 and a number will be remove after p counts in a clockwise manner. The procedure does not stop until only a single integer remains.       


For example starting with 
0 1 2 3 4 
and let p=2. Numbers 2 4 1 0 will be removed sequentially and the number 3 remains.
Write a program to take input N and p and shows the set of numbers which are sequentially removed and the one remains at last in the following format.

Input:
N p
Output:
0 p ....
k

in which N is the number of integers, p number of counting operation and k is the number that remains at last.

Input

5 2

Output

2 4 1 0

3

Sample Input Copy

5 2

Sample Output Copy

2 4 1 0
3