Problem Statement

In Finite Encyclopedia of Integer Sequences (FEIS), all integer sequences of lengths between $1$ and $N$ (inclusive) consisting of integers between $1$ and $K$ (inclusive) are listed.

Let the total number of sequences listed in FEIS be $X$. Among those sequences, find the $(X/2)$-th (rounded up to the nearest integer) lexicographically smallest one.

Constraints

• $1 \leq N,K \leq 3 × 10^5$
• $N$ and $K$ are integers.

Input

Input is given from Standard Input in the following format:

K N

Output

Print the $(X/2)$-th (rounded up to the nearest integer) lexicographically smallest sequence listed in FEIS, with spaces in between, where $X$ is the total number of sequences listed in FEIS.