Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

D. Equalize the Remainders

time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given an array consisting of $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$, and a positive integer $$$m$$$. It is guaranteed that $$$m$$$ is a divisor of $$$n$$$.

In a single move, you can choose any position $$$i$$$ between $$$1$$$ and $$$n$$$ and increase $$$a_i$$$ by $$$1$$$.

Let's calculate $$$c_r$$$ ($$$0 \le r \le m-1)$$$ — the number of elements having remainder $$$r$$$ when divided by $$$m$$$. In other words, for each remainder, let's find the number of corresponding elements in $$$a$$$ with that remainder.

Your task is to change the array in such a way that $$$c_0 = c_1 = \dots = c_{m-1} = \frac{n}{m}$$$.

Find the minimum number of moves to satisfy the above requirement.

Input

The first line of input contains two integers $$$n$$$ and $$$m$$$ ($$$1 \le n \le 2 \cdot 10^5, 1 \le m \le n$$$). It is guaranteed that $$$m$$$ is a divisor of $$$n$$$.

The second line of input contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$0 \le a_i \le 10^9$$$), the elements of the array.

Output

In the first line, print a single integer — the minimum number of moves required to satisfy the following condition: for each remainder from $$$0$$$ to $$$m - 1$$$, the number of elements of the array having this remainder equals $$$\frac{n}{m}$$$.

In the second line, print any array satisfying the condition and can be obtained from the given array with the minimum number of moves. The values of the elements of the resulting array must not exceed $$$10^{18}$$$.

Examples

Input

6 3

3 2 0 6 10 12

Output

3

3 2 0 7 10 14

Input

4 2

0 1 2 3

Output

0

0 1 2 3

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Sep/19/2018 11:03:22 (d1).

Desktop version, switch to mobile version.

User lists

Name |
---|