Reordering List to Avoid (i \bmod k) Conflicts

You are given an integer k and a list of n integers. Your task is to reorder the list so that for every index \(i\) (0-indexed) the following condition holds:

[ a_i \neq i \bmod k ]

If such a reordering is possible, output Yes on the first line and the valid reordered list (with elements separated by spaces) on the second line. Otherwise, output No Solution.

Note: In this problem, if k equals 1 and the list contains more than one element, you must output No Solution, even if the condition appears to hold.

inputFormat

The input is given from standard input and has the following format:

n k
a1 a2 ... an

where n is the number of integers in the list, k is the modulus parameter, and ai are the integers of the list.

outputFormat

If a valid reordering exists, print Yes on the first line, and on the second line print the reordered list (the integers separated by a single space). Otherwise, print No Solution.

## sample

5 3
1 2 3 4 5

Yes
1 2 3 4 5

</p>