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



Sample input:
5 3
10 14 19 34 33


Sample output:
202

Submission status: Runtime Error

Solution code:
import numpy as np

N, M = map(int, input().split())
A = input().split()

A_sum = np.zeros((N, N))
for i in range(N):
  for j in range(N):
    A_sum[i,j] = int(A[i]) + int(A[j])

A_sum = A_sum.flatten()
A_sum = np.sort(A_sum)[::-1]
A_sum_can = A_sum[:M]

power_sum = np.sum(A_sum_can).astype(np.int)

print(power_sum)

Submission status: Runtime Error

Solution code:
import sys
input = sys.stdin.readline

def main():
    n,m=map(int,input().split())
    a=sorted(list(map(int,input().split())))
    a.reverse()
    l,r=2*a[-1],2*a[0]
    x=(l+r)//2
    while l+1<r:
        s=0
        cnt,cnt2=0,0
        for i,A in enumerate(a):
            if A>=x:
                cnt+=2*(n-i)
                s+=2*(sum(a[i+1:])+(n-i-1)*A)+A*2
                cnt2+=1
            else:
                if A*2>=x:
                    cnt2+=1
                    s+=A*2
                for B in a[i+1:]:
                    if A+B>=x:
                        cnt+=2
                        s+=2*(A+B)
                    else:
                        break
        cnt+=cnt2
        if cnt>=m:
            l=x
        else:
            r=x
        x=(l+r)//2
    if cnt>m:
        print(s-(m-cnt)*l)
    else:
        print(s)
    
if __name__ == '__main__':
    main()

Submission status: Runtime Error

Solution code:
import sys
input = sys.stdin.readline

def main():
    n,m=map(int,input().split())
    a=sorted(list(map(int,input().split())))
    a.reverse()
    l,r=2*a[-1],2*a[0]
    x=(l+r)//2
    while l+1<r:
        cnt=0
        s=0
        for A in a:
            for B in a:
                if A+B>=x:
                    cnt+=1
                    s+=A+B
                else:
                    break
        if cnt>=m:
            l=x
        else:
            r=x
        x=(l+r)//2
    print(s+(m-cnt)*l)
    
if __name__ == '__main__':
    main()