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 a1,a2,...,an, where ai 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 b1,b2,...,bn (bi≥ai), where bi 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 a1,a2,...,an (0≤ai≤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 b1,b2,...,bn, where bi− the total number of walks on the i-th day according to the found solutions (ai≤bi for all i from 1 to n). If there are multiple solutions, print any of them.
3 5
2 0 1
4
2 3 2
3 1
0 0 0
1
0 1 0
4 6
2 4 3 5
0
2 4 3 5