codeforces 732B Cormen — The Best Friend Of a Man

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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 = 5and 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

3 52 0 1

output

42 3 2

input

3 10 0 0

output

10 1 0

input

4 62 4 3 5

output

02 4 3 5

题意：最近的两个的和要大于或者等于k，不够的补充，输出补充的数的和，和改变之后的数。参考了别人的想法。

#include<stdio.h>int main(){    int n,k,s[510];    scanf("%d%d",&n,&k);    for(int i=0;i<n;i++)    {        scanf("%d",&s[i]);    }    int cnt=0;    for(int i=1;i<n;i++)    {        if(s[i]+s[i-1]<k)        {            cnt+=k-(s[i]+s[i-1]);            s[i]=k-s[i-1];        }    }    printf("%d\n",cnt);    for(int i=0;i<n;i++)    {        if(i==n-1)            printf("%d\n",s[i]);        else            printf("%d ",s[i]);    }    return 0;}