# Mutation

# Mutation

The scientists of the planet Olympia each year investigate various mutations of the genomes of primitive organisms. The genome of such organisms can be represented as a sequence of n integers, numbered from left to right from one to n and does not exceed the number n. Genomes are subject to permanent mutations. At each stage of the mutation, the genome changes as follows:

the number of ones in the input genome is written to the first place;

the number of twos in the input genome is written to the second place;

...,

the number of n's in the input genome is written to the n's place;

For example, genome [1, 2, 3] with three integers after mutation transforms to [1, 1, 1] - one one, two and three. Another samples:

[1, 2, 2, 3, 3, 3] transforms into [1, 2, 3, 0, 0, 0]

[7, 7, 7, 4, 7, 4, 4] transforms into [0, 0, 0, 3, 0, 0, 4]

Further, the genome changes according to the same principle.

Write a program that, given the initial state of genome, determines its state after k mutations.

## Input data

First line contains two integers n and k (1 ≤ n ≤ `10^5`

, 1 ≤ k ≤ `10^9`

) giving the initial size of genome and number of genome mutations. Second line contains n nonnegative integers, not exceeding n, - the initial state of genome.

## Output data

Print the genome after k mutations in the input format: n space separated integers.

## Examples

4 2 1 3 1 4

2 1 0 0