Problem Statement

yuki, the king of the Yuki Kingdom, has prepared $N$ presents for the coming Christmas.

Each present has a value called its "worth", and the worth of the $i~(1 \leq i \leq N)$-th present is $i$.

There are currently $K$ children in the Yuki Kingdom.

yuki wants to distribute the prepared presents to the children of the kingdom so that all of the following conditions are satisfied.

• Each child receives the same number of presents
• The sum of the worth of the presents received is the same for each child

yuki has asked you, the chancellor of the kingdom, whether such a distribution exists and, if it does, how the presents should be distributed.

Constraints

• $1 \leq N \leq 200000$
• $1 \leq K \leq N$
• $K$ is a divisor of $N$
• All inputs are integers

Input

The input is given from standard input in the following format.

$N$ $K$

Output

If no distribution of presents satisfying the conditions exists, print No.

If one exists, print Yes, then a newline, and then print $K$ more lines.

Here, on the $i + 1$-th line of the output, print the numbers of the presents received by the $i$-th child, separated by spaces.

If there are multiple distributions satisfying the conditions, any of them will be accepted.

Sample

4 2

Yes
2 3
1 4

6 2

No