Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

The problem statement has recently been changed. View the changes.

×
C. Pashmak and Buses

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputRecently Pashmak has been employed in a transportation company. The company has *k* buses and has a contract with a school which has *n* students. The school planned to take the students to *d* different places for *d* days (each day in one place). Each day the company provides all the buses for the trip. Pashmak has to arrange the students in the buses. He wants to arrange the students in a way that no two students become close friends. In his ridiculous idea, two students will become close friends if and only if they are in the same buses for all *d* days.

Please help Pashmak with his weird idea. Assume that each bus has an unlimited capacity.

Input

The first line of input contains three space-separated integers *n*, *k*, *d* (1 ≤ *n*, *d* ≤ 1000; 1 ≤ *k* ≤ 10^{9}).

Output

If there is no valid arrangement just print -1. Otherwise print *d* lines, in each of them print *n* integers. The *j*-th integer of the *i*-th line shows which bus the *j*-th student has to take on the *i*-th day. You can assume that the buses are numbered from 1 to *k*.

Examples

Input

3 2 2

Output

1 1 2

1 2 1

Input

3 2 1

Output

-1

Note

Note that two students become close friends only if they share a bus each day. But the bus they share can differ from day to day.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Feb/25/2021 11:33:57 (f1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|