Processing math: 100%

Problem D. Diversify start positions

Author:I. Tuphanov   Time limit:1 sec
Input file:input.txt   Memory limit:256 Mb
Output file:output.txt  

Statement

New Vasuki Challenge (NVC) is a race developed to make New Vasuki a new racing capital of the world. An outstanding feature of NVC is the distribution of start positions.

Let n be the number of cars taking place in NVC during the whole season. Each car has its id — integer number in range from 1 to n. A season consists of x races. Before a race each car takes a start position. There are n start positions, numbered from 1 to n.

In the beginning of a new season NVC director declares a permutation P=(p1,p2,,pn). Before the first race car number i takes start position number i for each i from 1 to n. Before each next race start positions are permuted according to P: car which was on start position pi in the last race now goes to start position i.

Say, n=6, x=3, P=(4,3,6,5,1,2). So, there will be three races and cars will stand in positions (1,2,3,4,5,6) before the first race, (4,3,6,5,1,2) before the second race, and (5,6,2,1,4,3) before the third race.

A permutation P of size n is called feasible for given x iff:

For the example given above, (4,3,6,5,1,2) is feasible because all three start position distributions are different, and if there were a forth race the distribution would be (1,2,3,4,5,6) which already met in the first race.

Your task is to find a feasible permutation P for given n and x. If there are multiple solutions, output any of them.

Input file format

Input file contains two integers n and x.

Output file format

Output file must contain a feasible permutation. If a feasible permutation doesn't exist, output a single integer 1.

Constraints

2n103

2x106

Sample tests

No. Input file (input.txt) Output file (output.txt)
1
6 3
4 3 6 5 1 2

0.069s 0.008s 13