Finite Encyclopedia of Integer Sequences

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.

Examples

Input

3 2

Output

2 1

Input

2 4

Output

1 2 2 2

Input

5 14

Output

3 3 3 3 3 3 3 3 3 3 3 3 2 2

inputFormat

Input

Input is given from Standard Input in the following format:

K N

outputFormat

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.

Examples

Input

3 2

Output

2 1

Input

2 4

Output

1 2 2 2

Input

5 14

Output

3 3 3 3 3 3 3 3 3 3 3 3 2 2

样例

2 4

1 2 2 2