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.


-----Input-----

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. 


-----Output-----

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. 


-----Examples-----
Input
3 5
2 0 1

Output
4
2 3 2

Input
3 1
0 0 0

Output
1
0 1 0

Input
4 6
2 4 3 5

Output
0
2 4 3 5