bzoj1010

#include<cstdio>
#include<algorithm>
using namespace std;
#define maxn 50002
long long s[maxn],q[maxn],f[maxn];
double Y(long long j){return f[j]+s[j]*s[j];}
double X(long long j){return s[j];}
double slop(long long j,long long k){return(Y(k)-Y(j))/(X(k)-X(j));}
int main(){
    long long n,L,i,x,head,tail;
    scanf("%lld%lld",&n,&L);L++;s[0]=0;
    for(i=1;i<=n;i++){scanf("%lld",&s[i]);s[i]+=s[i-1];}
    for(i=1;i<=n;i++)s[i]+=i;
    head=tail=1;q[1]=0;
    for(i=1;i<=n;i++){
        while(head<tail && slop(q[head],q[head+1])<=2*(s[i]-L))head++;
        int j=q[head];
        f[i]=f[j]+(s[i]-s[j]-L)*(s[i]-s[j]-L);
        while(head<tail && slop(q[tail-1],q[tail])>slop(q[tail],i))tail--;
        q[++tail]=i;
    }
    printf("%lld\n",f[n]);
    return 0;
}