A10581. Cormen — The Best Friend Of a Man

Recently a dog was bought for Polycarp. The dog's name is Cormen. Now Polycarp has a lot of troubles. For example, Cormen likes going for a walk.

Empirically Polycarp learned that the dog needs at least $k$ walks for any two consecutive days in order to feel good. For example, if $k=5$ and yesterday Polycarp went for a walk with Cormen $2$ times, today he has to go for a walk at least $3$ times.

Polycarp analysed all his affairs over the next $n$ days and made a sequence of $n$ integers $a_{1},a_{2},...,a_{n}$ , where $a_{i}$ is the number of times Polycarp will walk with the dog on the $i$ -th day while doing all his affairs (for example, he has to go to a shop, throw out the trash, etc.).

Help Polycarp determine the minimum number of walks he needs to do additionaly in the next $n$ days so that Cormen will feel good during all the $n$ days. You can assume that on the day before the first day and on the day after the $n$ -th day Polycarp will go for a walk with Cormen exactly $k$ times.

Write a program that will find the minumum number of additional walks and the appropriate schedule — the sequence of integers $b_{1},b_{2},...,b_{n}$ ( $b_{i}>=a_{i}$ ), where $b_{i}$ means the total number of walks with the dog on the $i$ -th day.

The first line contains two integers $n$ and $k$ ( $1<=n,k<=500$ ) — the number of days and the minimum number of walks with Cormen for any two consecutive days.

The second line contains integers $a_{1},a_{2},...,a_{n}$ ( $0<=a_{i}<=500$ ) — the number of walks with Cormen on the $i$ -th day which Polycarp has already planned.

In the first line print the smallest number of additional walks that Polycarp should do during the next $n$ days so that Cormen will feel good during all days.

In the second line print $n$ integers $b_{1},b_{2},...,b_{n}$ , where $b_{i}$ — the total number of walks on the $i$ -th day according to the found solutions ( $a_{i}<=b_{i}$ for all $i$ from 1 to $n$ ). If there are multiple solutions, print any of them.