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感谢Orz大佬的斜率优化讲解
因为得分跟顺序无关，所以可以dp
令$f_{i,j}$表示第$i$次在$j$处分割的最大得分，$s_i$为$\sum \limits _{j=1}^{j\le i} a_j$，则有

代码如下：

#include<algorithm>
#include<ctype.h>
#include<cstdio>
#define INF 2147483647000000ll
#define N 100050
using namespace std;
inline int read()
{
    int x=0,f=1;char c;
    do c=getchar(),f=c=='-'?-1:f; while(!isdigit(c));
    do x=(x<<3)+(x<<1)+c-'0',c=getchar(); while(isdigit(c));
    return x*f;
}
typedef long long LL;
int n,k,l,r;
LL s[N],f[N],g[N],ans;
struct Point
{
    LL x,y;
    Point(){}
    Point(LL _,LL __):x(_),y(__){}
    double operator * (const Point &b)///算斜率
    {
        if(x==b.x) return y>b.y ?-INF:INF;
        return 1.0*(b.y-y)/(b.x-x);
    }
}q[N];
inline LL calc(int k)
{
    return g[k]-s[k]*s[n];
}
inline LL GetAns(int k)
{
    while(l<r && q[l].x+q[l].y*s[k]<q[l+1].x+q[l+1].y*s[k]) l++;
    return q[l].x-s[k]*s[k]+s[k]*s[n]+q[l].y*s[k];
}
inline void Add(Point k)
{
    while(l<r && q[r-1]*q[r]>q[r]*k) r--;
    q[++r]=k;
}
main()
{
    n=read();k=read();
    for(int i=1;i<=n;i++)
        s[i]=read()+s[i-1];
    for(int i=1;i<=k;i++)
    {
        l=r=1;
        for(int j=1;j<=n;j++)
        {
            f[j]=GetAns(j);
            Add(Point(calc(j),s[j]));
        }
        for(int j=1;j<=n;j++)
            g[j]=f[j];
    }
    for(int i=1;i<n;i++)
        ans=max(ans,g[i]);
    printf("%lld",ans);
    return 0;
}