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 Python (3.4.3) (judge verdict: Accepted)

n, m = map(int, input().split())
A = list(map(int, input().split()))
A.sort(reverse=True)
cumsumA = []

total = 0
for a in A:
    total += a
    cumsumA.append(total)
cumsumA.append(0)

l = 0
r = 10 ** 6
while l + 1 < r:
    num = (l+r)//2
    pair_idx = n-1
    count = 0
    for a in A:
        while a + A[pair_idx] < num and pair_idx >= 0:
            pair_idx -= 1

        count += pair_idx+1

    if count < m:
        r = num
        continue
    elif count >= m:
        l = num


ans = 0
count = 0
num = l
pair_idx = n-1
for a in A:
    while a + A[pair_idx] < num and pair_idx >= 0:
        pair_idx -= 1

    count += pair_idx+1
    ans += cumsumA[pair_idx] + a*(pair_idx+1)

diff = count - m
ans -= num * diff
print(ans)