# 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

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

, ^{5}**1** ≤ **k** ≤ `10`

) giving the initial size of genome and number of genome mutations. Second line contains ^{9}**n** nonnegative integers, not exceeding **n**, - the initial state of genome.

#### Output

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

4 2 1 3 1 4

2 1 0 0

**Example description:**
First [1, 3, 1, 4] mutates into [2, 0, 1, 1], and then mutates into [2, 1, 0, 0].