## Algorithm

B. Cormen — The Best Friend Of a Man
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

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 a1, a2, ..., an (0 ≤ ai ≤ 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 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.

Examples
input
Copy
`3 52 0 1`
output
Copy
`42 3 2`
input
Copy
`3 10 0 0`
output
Copy
`10 1 0`
input
Copy
`4 62 4 3 5`
output
Copy
`02 4 3 5`

## Code Examples

### #1 Code Example with C++ Programming

```Code - C++ Programming```

``````#include <iostream>

using namespace std;

int arr[501];

int main() {
long long n, k, counter = 0;
cin >> n >> k;

for (int i = 0; i < n; i++) cin >> arr[i];

for (int i = 0; i < n - 1; i++)
if (arr[i] + arr[i + 1] < k) {
counter += k - (arr[i] + arr[i + 1]);
arr[i + 1] += k - (arr[i] + arr[i + 1]);
}

cout << counter << endl;
for (int i = 0; i < n; i++) cout << arr[i] << ' ';
cout << endl;

return 0;
}``````
Copy The Code &

Input

cmd
3 5
2 0 1

Output

cmd
4
2 3 2