Problem: Recently 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 ≤ 109).

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.

Solution (in PYTHON3):

Solution:
from __future__ import division, print_function

import os
import sys
from io import BytesIO, IOBase


def main():
    # if numOfBuses >= numOfStudents: YES
    # if numOfPermutations (numOfDays**numOfStudents) >= numOfStudents: YES
        # at least one student will have a different permutation than
        # any other

    # for each student -> represent it in base numOfBuses and then
    # turn it into numOfBuses'ry (like binary)
    # loop -> get the mod of the number and divide it by numOfBuses
    # until the result is not integer
    # print the accumulated mods for each student
    numOfStudents, numOfBuses, numOfDays = [ int(x) for x in input().split() ]

    if numOfBuses**numOfDays >= numOfStudents:
        studentSequences = [
            [1] * numOfDays
            for student in range(numOfStudents)
        ]

        for student in range(numOfStudents):
            number = student

            for day in range(numOfDays):
                remainder = number % numOfBuses
                studentSequences[student][day] = remainder+1
                number //= numOfBuses

                if number == 0: break

        for day in range(numOfDays):
            print(' '.join(
                [ str(studentSequences[student][day])
                for student in range(numOfStudents)]
            ))

    else:
        print(-1)

BUFSIZE = 8192

class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)

class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")

input = lambda: sys.stdin.readline().rstrip("\r\n")

def print(*args, **kwargs):
    """Prints the values to a stream, or to sys.stdout by default."""
    sep = kwargs.pop("sep", " ")
    file = kwargs.pop("file", sys.stdout)

    atStart = True
    for x in args:
        if not atStart:
            file.write(sep)
        file.write(str(x))
        atStart = False
    file.write(kwargs.pop("end", "\n"))

    if kwargs.pop("flush", False):
        file.flush()

sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)

main()