Mutation

Scientists on planet Olympia investigate various mutations in the genomes of primitive organisms every year. The genome of such an organism can be represented as a sequence of $n$ integers, each in the range from $1$ to $n$, inclusive. Genomes are subject to constant mutations. At each stage of mutation, the genome changes as follows:

• The number of $1$'s in the current genome is written to the first position;

• The number of $2$'s in the current genome is written to the second position;

• ...

• The number of $n$'s in the current genome is written to the $n$th position.

For example, the genome [1, 2, 3], consisting of three numbers, after one mutation becomes [1, 1, 1] — one $1$, one $2$, and one $3$. Other examples:

• [1, 2, 2, 3, 3, 3] becomes [1, 2, 3, 0, 0, 0]

• [7, 7, 7, 4, 7, 4, 4] becomes [0, 0, 0, 3, 0, 0, 4]

The genome continues to change according to the same rule in each subsequent mutation.

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

\InputFileThe first line contains two integers $n$ and $k$ (1 \leq n \leq 10^5, 1 \leq k \leq 10^9) — the initial genome length and the number of mutations. The second line contains $n$ integers, each between $1$ and $n$, representing the initial genome sequence.

\OutputFilePrint the genome after $k$ mutations as a sequence of $n$ space-separated integers.