CF732B.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.

最近，波利卡普买了一只狗。这只狗的名字叫科门。现在波利卡普遇到了很多麻烦。例如，科门很喜欢散步。

根据经验，波利卡普发现：为了让科门感觉良好，任意连续两天内，狗至少需要散步 $k$ 次。例如，若 $k = 5$，而昨天波利卡普带科门散步了 $2$ 次，则今天他至少还需再带科门散步 $3$ 次。

波利卡普分析了接下来 $n$ 天内自己的所有事务，并列出了一个长度为 $n$ 的整数序列 $a_1,\,a_2,\,\dots,\,a_n$，其中 $a_i$ 表示在第 $i$ 天，在完成所有事务（例如购物、倒垃圾等）的前提下，波利卡普计划带狗散步的次数。

请帮助波利卡普确定：在接下来的 $n$ 天中，他最少需要额外增加多少次散步，才能保证科门在这 $n$ 天内每天都感觉良好。你可以假设：在第 $1$ 天之前的那一天，以及在第 $n$ 天之后的那一天，波利卡普都会恰好带科门散步 $k$ 次。

请编写一个程序，求出最少额外散步次数，以及对应的安排方案——即一个整数序列 $b_1,\,b_2,\,\dots,\,b_n$（满足 $b_i \ge a_i$），其中 $b_i$ 表示第 $i$ 天实际带狗散步的总次数。

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.

第一行包含两个整数 $n$ 和 $k$（$1 \leq n, k \leq 500$）——分别表示天数，以及任意连续两天中与Cormen散步次数的最小值。

第二行包含 $n$ 个整数 $a_1,\ a_2,\ \dots,\ a_n$（$0 \leq a_i \leq 500$）——表示 Polycarp 已经计划好的第 $i$ 天与 Cormen 散步的次数。

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.

第一行输出 Polycarp 在接下来的 $n$ 天内需要额外进行的最少散步次数，使得 Cormen 在所有天数内都感觉良好。

第二行输出 $n$ 个整数 $b_1,\,b_2,\,...,\,b_n$，其中 $b_i$ 表示根据所求方案第 $i$ 天的总散步次数（对所有 $i$ 从 $1$ 到 $n$ 均满足 $a_i\,\leq\,b_i$）。若存在多种解，输出任意一种即可。