Problem:
Score : 500 points

Problem Statement

Takahashi has come to a party as a special guest.
There are N ordinary guests at the party. The i-th ordinary guest has a power of A_i.

Takahashi has decided to perform M handshakes to increase the happiness of the party (let the current happiness be 0).
A handshake will be performed as follows:

Takahashi chooses one (ordinary) guest x for his left hand and another guest y for his right hand (x and y can be the same).

Then, he shakes the left hand of Guest x and the right hand of Guest y simultaneously to increase the happiness by A_x+A_y.

However, Takahashi should not perform the same handshake more than once. Formally, the following condition must hold:

Assume that, in the k-th handshake, Takahashi shakes the left hand of Guest x_k and the right hand of Guest y_k. Then, there is no pair p, q (1 \leq p < q \leq M) such that (x_p,y_p)=(x_q,y_q).

What is the maximum possible happiness after M handshakes?

Constraints

1 \leq N \leq 10^5

1 \leq M \leq N^2

1 \leq A_i \leq 10^5

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M
A_1 A_2 ... A_N

Output

Print the maximum possible happiness after M handshakes.

Sample Input 1

5 3
10 14 19 34 33

Sample Output 1

202

Let us say that Takahashi performs the following handshakes:

In the first handshake, Takahashi shakes the left hand of Guest 4 and the right hand of Guest 4.

In the second handshake, Takahashi shakes the left hand of Guest 4 and the right hand of Guest 5.

In the third handshake, Takahashi shakes the left hand of Guest 5 and the right hand of Guest 4.

Then, we will have the happiness of (34+34)+(34+33)+(33+34)=202.

We cannot achieve the happiness of 203 or greater, so the answer is 202.

Sample Input 2

9 14
1 3 5 110 24 21 34 5 3

Sample Output 2

1837

Sample Input 3

9 73
67597 52981 5828 66249 75177 64141 40773 79105 16076

Sample Output 3

8128170

Solution in C (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <stdio.h>
#include <stdlib.h>

long int n,m,used[100001]={0},a[100001]={0};

void quicksort(long int* number,long int first,long int last){
    long int i, j, pivot, temp;
    
    //randomly choose the pivot and move it to the first
    pivot=first+((last-first) * rand()/RAND_MAX);
    temp=number[first];
    number[first]=number[pivot];
    number[pivot]=temp;
                
    if(first<last){
        pivot=first;
        i=first;
        j=last;
        
        while(i<j){
            while(number[i]>=number[pivot]&&i<last)
                i++;
            while(number[j]<number[pivot])
                j--;
            if(i<j){
                temp=number[i];
                number[i]=number[j];
                number[j]=temp;
            };
        };
        
        temp=number[pivot];
        number[pivot]=number[j];
        number[j]=temp;
        quicksort(number,first,j-1);
        quicksort(number,j+1,last);
    };
};

/*void display_scores(void){
    int i,j;
    printf("   |");
    for(i=1;i<=n;i++){
        printf("%7d    ",i);
    };
    printf("\n---+");
    for(i=1;i<=n;i++){
        printf("-----------");
    };
    printf("\n");
    for(j=1;j<=n;j++){
        printf("%2d |",j);
        for(i=1;i<j;i++){
            printf("        ");
        };
        for(i=1;i<=n;i++){
            if(i<=used[j])putchar('*');else putchar(' ');
            printf("%-10d",a[i]+a[j]);
        };
        printf("\n");
    };
    return;
};*/

long int count_larger_combintion(long int x){
    long int low,high,mid,i,j,ans=0,prev_threshold;
    prev_threshold=n;
    for(i=1;i<=n;i++){
        low=1;
        high=prev_threshold;
        if(a[i]+a[1]<x){
            for(j=i;j<=n;j++) used[j]=0;
            return ans;
        };
        if(a[i]+a[high]>=x){
            used[i]=high;
            ans+=high;
            continue;
        };
        while(high-low>1){
            mid=(high+low)/2;
            if(a[i]+a[mid]>=x){
                low=mid;
            }else{
                high=mid;
            };
        };
        ans+=low;
        used[i]=low;
        prev_threshold=low;
    }
    return ans;
};


int main(void){
    long int i,xlow, xhigh, x,larger_num=0,threshold;
    long int sum[100001],ans=0;
    scanf("%ld %ld",&n,&m);
    for(i=1;i<=n;i++){
        scanf("%ld",&a[i]);
    };
    quicksort(a,1,n);
    xlow=2*a[n];
    xhigh=2*a[1];
    while(larger_num!=m && xhigh-xlow>1){
        x=xlow+(xhigh-xlow)/2;
        larger_num=count_larger_combintion(x);
        if(larger_num>=m) xlow=x;
        if(larger_num<m) xhigh=x;
        //printf("x=%d, num=%d\n",x,larger_num);
        //display_scores();
    };
    threshold=xlow;
    //printf("result: threshold=%d\n",threshold);
    sum[1]=a[1];
    for(i=2;i<=n;i++){
        sum[i]=sum[i-1]+a[i];
    };
    for(i=1;i<=n;i++){
        ans+=a[i]*used[i]+sum[used[i]];
    };
    ans-=(larger_num-m)*threshold;
    printf("%ld",ans);
    return 0;
};