CoderForces999D-Equalize the Remainders

D. Equalize the Remainders

time limit per test

3 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

You are given an array consisting of n.

In a single move, you can choose any position 1.

Let's calculate a with that remainder.

Your task is to change the array in such a way that c0=c1=⋯=cm−1=nm.

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

Input

The first line of input contains two integers n.

The second line of input contains 0≤ai≤109), 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 nm.

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 1018.

Examples

input

Copy

6 3
3 2 0 6 10 12

output

Copy

3
3 2 0 7 10 14 

input

Copy

4 2
0 1 2 3

output

Copy

0
0 1 2 3