Polycarp's Practice(从一组数据中找出前n个最大的数的及其下标)

Polycarp is practicing his problem solving skill. He has a list of nn problems with difficulties a1,a2,…,ana1,a2,…,an, respectively. His plan is to practice for exactly kk days. Each day he has to solve at least one problem from his list. Polycarp solves the problems in the order they are given in his list, he cannot skip any problem from his list. He has to solve all nn problems in exactly kk days.

Thus, each day Polycarp solves a contiguous sequence of (consecutive) problems from the start of the list. He can't skip problems or solve them multiple times. As a result, in kk days he will solve all the nn problems.

The profit of the jj-th day of Polycarp's practice is the maximum among all the difficulties of problems Polycarp solves during the jj-th day (i.e. if he solves problems with indices from ll to rr during a day, then the profit of the day is maxl≤i≤raimaxl≤i≤rai). The total profit of his practice is the sum of the profits over all kk days of his practice.

You want to help Polycarp to get the maximum possible total profit over all valid ways to solve problems. Your task is to distribute all nnproblems between kk days satisfying the conditions above in such a way, that the total profit is maximum.

For example, if n=8,k=3n=8,k=3 and a=[5,4,2,6,5,1,9,2]a=[5,4,2,6,5,1,9,2], one of the possible distributions with maximum total profit is: [5,4,2],[6,5],[1,9,2][5,4,2],[6,5],[1,9,2]. Here the total profit equals 5+6+9=205+6+9=20.

Input

The first line of the input contains two integers nn and kk (1≤k≤n≤20001≤k≤n≤2000) — the number of problems and the number of days, respectively.

The second line of the input contains nn integers a1,a2,…,ana1,a2,…,an (1≤ai≤20001≤ai≤2000) — difficulties of problems in Polycarp's list, in the order they are placed in the list (i.e. in the order Polycarp will solve them).

Output

In the first line of the output print the maximum possible total profit.

In the second line print exactly kk positive integers t1,t2,…,tkt1,t2,…,tk (t1+t2+⋯+tkt1+t2+⋯+tk must equal nn), where tjtj means the number of problems Polycarp will solve during the jj-th day in order to achieve the maximum possible total profit of his practice.

If there are many possible answers, you may print any of them.

Examples

input

8 3
5 4 2 6 5 1 9 2

output

20
3 2 3

input

5 1
1 1 1 1 1

output

1
5

input

4 2
1 2000 2000 2

output

4000
2 2

题意：一个人需要在k天解决n个问题，现在把这些问题，分成k段，表示每一天解决的问题，然后有个最大解决问题，是每一段的最大解决问题的数的和。然后在输出每一段的长度。

题解：模拟 先找出里面最大的k个数存入一个数组，从左到右遍历，如果当前问题在最大问题数组里面，就把下标记录下来，或者直接计算长度，与上一个坐标差。

#include<cstdio>
#include<algorithm>
#include<stdlib.h>
#include<string.h>
#include<iostream>
using namespace std;
int n,m,a[2001],p[2001],k,s;
int main()
{
    scanf("%d%d",&n,&m);
    for(int i=1; i<=n; i++)scanf("%d",a+i);
    for(int j=2000; j; j--)
    {
        for(int i=1; i<=n; i++)
        {
            if(j==a[i])
            {
                p[++k]=i;
            }
        }
    }
    sort(p+1,p+1+m);
    for(int j=1; j<=m; j++)
        s+=a[p[j]];
    printf("%d\n",s);
    if(m>1)
        printf("%d ",p[1]);
    for(int j=2; j<m; j++)
        printf("%d ",p[j]-p[j-1]);
    printf("%d",n-p[m-1]);
    return 0;
}