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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.IO;
using System.Collections.Generic;
using System.Linq;
using System.Numerics;

namespace AtCoder.Contest.E
{
	static class Program
	{
		public static void Solve(Scanner cin)
		{
			var (n, m) = cin.ReadValue<int, long>();
			var a = cin.ReadLongArray(n);
			Array.Sort(a);
			long l = a[0] * 2 - 1;
			long r = a[n - 1] * 2 + 1;
			while (r - l > 1)
			{
				long mid = l + (r - l) / 2;
				if (CountSuitable(a, mid) >= m) l = mid;
				else r = mid;
			}
			var big = CountSuitable(a, l + 1);
			var ans = SumSuitable(a, l + 1);
			ans += (m - big) * l;
			Console.WriteLine(ans);
		}

		public static long CountSuitable(long[] a, long m)
		{
			long ret = 0;
			for (int i = 0; i < a.Length; i++)
			{
				ret += a.Length - BinarySearch.LowerBound(a, m - a[i]);
			}
			return ret;
		}

		public static long SumSuitable(long[] a, long m)
		{
			var n = a.Length;
			var sum = new long[n + 1];
			sum[0] = 0;
			for (int i = 0; i < n; i++)
			{
				sum[i + 1] = sum[i] + a[i];
			}
			long ret = 0;
			for (int i = 0; i < a.Length; i++)
			{
				var p = BinarySearch.LowerBound(a, m - a[i]);
				ret += (n - p) * a[i];
				ret += sum[n] - sum[p];
			}
			return ret;
		}

		public static void Main(string[] args)
		{
			var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
			Console.SetOut(sw);
			var cin = new Scanner();
			Solve(cin);
			Console.Out.Flush();
		}

		public static void YESNO(bool condition) => Console.WriteLine(condition ? "YES" : "NO");
		public static void YesNo(bool condition) => Console.WriteLine(condition ? "Yes" : "No");
		public static void yesno(bool condition) => Console.WriteLine(condition ? "yes" : "no");
	}

	static class BinarySearch
	{
		public static int UpperBound<T>(T[] array, T value) => UpperBound(array, 0, array.Length - 1, value, Comparer<T>.Default);

		public static int UpperBound<T>(T[] array, T value, Comparer<T> comparer) => UpperBound(array, 0, array.Length - 1, value, comparer);

		public static int UpperBound<T>(T[] array, int index, int length, T value) => UpperBound(array, index, length, value, Comparer<T>.Default);

		public static int UpperBound<T>(T[] array, int index, int length, T value, Comparer<T> comparer)
		{
			var l = index;
			var r = l + length;
			while (l <= r)
			{
				var mid = l + (r - l) / 2;
				var res = comparer.Compare(array[mid], value);
				if (res <= 0) l = mid + 1;
				else r = mid - 1;
			}
			return l;
		}

		public static int UpperBound<T>(this List<T> list, T item) => list.UpperBound(0, list.Count, item, Comparer<T>.Default);

		public static int UpperBound<T>(this List<T> list, T item, Comparer<T> comparer) => list.UpperBound(0, list.Count, item, comparer);

		public static int UpperBound<T>(this List<T> list, int index, int count, T item, Comparer<T> comparer)
		{
			var l = index;
			var r = l + count;
			while (l <= r)
			{
				var mid = l + (r - l) / 2;
				var res = comparer.Compare(list[mid], item);
				if (res <= 0) l = mid + 1;
				else r = mid - 1;
			}
			return l;
		}

		public static int LowerBound<T>(T[] array, T value) => LowerBound(array, 0, array.Length - 1, value, Comparer<T>.Default);

		public static int LowerBound<T>(T[] array, T value, Comparer<T> comparer) => LowerBound(array, 0, array.Length - 1, value, comparer);

		public static int LowerBound<T>(T[] array, int index, int length, T value) => LowerBound(array, index, length, value, Comparer<T>.Default);

		public static int LowerBound<T>(T[] array, int index, int length, T value, Comparer<T> comparer)
		{
			var l = index;
			var r = l + length;
			while (l <= r)
			{
				var mid = l + (r - l) / 2;
				var res = comparer.Compare(array[mid], value);
				if (res == -1) l = mid + 1;
				else r = mid - 1;
			}
			return l;
		}

		public static int LowerBound<T>(this List<T> list, T item) => list.LowerBound(0, list.Count, item, Comparer<T>.Default);

		public static int LowerBound<T>(this List<T> list, T item, Comparer<T> comparer) => list.LowerBound(0, list.Count, item, comparer);

		public static int LowerBound<T>(this List<T> list, int index, int count, T item, Comparer<T> comparer)
		{
			var l = index;
			var r = l + count;
			while (l <= r)
			{
				var mid = l + (r - l) / 2;
				var res = comparer.Compare(list[mid], item);
				if (res == -1) l = mid + 1;
				else r = mid - 1;
			}
			return l;
		}
	}

	static class Util
	{
		static string Join<T>(this IEnumerable<T> x, string separator = " ") => string.Join(separator, x);
	}

	class Scanner
	{
		string[] s;
		int i;

		char[] separator = new char[] { ' ' };

		public Scanner()
		{
			s = new string[0];
			i = 0;
		}

		public string Read() => ReadString();

		public string ReadString()
		{
			if (i < s.Length) return s[i++];
			string st = Console.ReadLine();
			while (st == "") st = Console.ReadLine();
			s = st.Split(separator, StringSplitOptions.RemoveEmptyEntries);
			if (s.Length == 0) return ReadString();
			i = 0;
			return s[i++];
		}

		public string[] ReadStringArray(int N)
		{
			string[] Array = new string[N];
			for (int i = 0; i < N; i++)
			{
				Array[i] = ReadString();
			}
			return Array;
		}

		public int ReadInt()
		{
			return int.Parse(ReadString());
		}

		public int[] ReadIntArray(int N, int add = 0)
		{
			int[] Array = new int[N];
			for (int i = 0; i < N; i++)
			{
				Array[i] = ReadInt() + add;
			}
			return Array;
		}

		public long ReadLong()
		{
			return long.Parse(ReadString());
		}

		public long[] ReadLongArray(int N, long add = 0)
		{
			long[] Array = new long[N];
			for (int i = 0; i < N; i++)
			{
				Array[i] = ReadLong() + add;
			}
			return Array;
		}

		public double ReadDouble()
		{
			return double.Parse(ReadString());
		}

		public double[] ReadDoubleArray(int N, double add = 0)
		{
			double[] Array = new double[N];
			for (int i = 0; i < N; i++)
			{
				Array[i] = ReadDouble() + add;
			}
			return Array;
		}

		public T1 ReadValue<T1>() => (T1)Convert.ChangeType(ReadString(), typeof(T1));

		public (T1, T2) ReadValue<T1, T2>()
		{
			var inputs = ReadStringArray(2);
			var v1 = (T1)Convert.ChangeType(inputs[0], typeof(T1));
			var v2 = (T2)Convert.ChangeType(inputs[1], typeof(T2));
			return (v1, v2);
		}

		public (T1, T2, T3) ReadValue<T1, T2, T3>()
		{
			var inputs = ReadStringArray(3);
			var v1 = (T1)Convert.ChangeType(inputs[0], typeof(T1));
			var v2 = (T2)Convert.ChangeType(inputs[1], typeof(T2));
			var v3 = (T3)Convert.ChangeType(inputs[2], typeof(T3));
			return (v1, v2, v3);
		}

		public (T1, T2, T3, T4) ReadValue<T1, T2, T3, T4>()
		{
			var inputs = ReadStringArray(4);
			var v1 = (T1)Convert.ChangeType(inputs[0], typeof(T1));
			var v2 = (T2)Convert.ChangeType(inputs[1], typeof(T2));
			var v3 = (T3)Convert.ChangeType(inputs[2], typeof(T3));
			var v4 = (T4)Convert.ChangeType(inputs[3], typeof(T4));
			return (v1, v2, v3, v4);
		}

		public (T1, T2, T3, T4, T5) ReadValue<T1, T2, T3, T4, T5>()
		{
			var inputs = ReadStringArray(5);
			var v1 = (T1)Convert.ChangeType(inputs[0], typeof(T1));
			var v2 = (T2)Convert.ChangeType(inputs[1], typeof(T2));
			var v3 = (T3)Convert.ChangeType(inputs[2], typeof(T3));
			var v4 = (T4)Convert.ChangeType(inputs[3], typeof(T4));
			var v5 = (T5)Convert.ChangeType(inputs[4], typeof(T5));
			return (v1, v2, v3, v4, v5);
		}

		public (T1, T2, T3, T4, T5, T6) ReadValue<T1, T2, T3, T4, T5, T6>()
		{
			var inputs = ReadStringArray(6);
			var v1 = (T1)Convert.ChangeType(inputs[0], typeof(T1));
			var v2 = (T2)Convert.ChangeType(inputs[1], typeof(T2));
			var v3 = (T3)Convert.ChangeType(inputs[2], typeof(T3));
			var v4 = (T4)Convert.ChangeType(inputs[3], typeof(T4));
			var v5 = (T5)Convert.ChangeType(inputs[4], typeof(T5));
			var v6 = (T6)Convert.ChangeType(inputs[5], typeof(T6));
			return (v1, v2, v3, v4, v5, v6);
		}

		public (T1, T2, T3, T4, T5, T6, T7) ReadValue<T1, T2, T3, T4, T5, T6, T7>()
		{
			var inputs = ReadStringArray(7);
			var v1 = (T1)Convert.ChangeType(inputs[0], typeof(T1));
			var v2 = (T2)Convert.ChangeType(inputs[1], typeof(T2));
			var v3 = (T3)Convert.ChangeType(inputs[2], typeof(T3));
			var v4 = (T4)Convert.ChangeType(inputs[3], typeof(T4));
			var v5 = (T5)Convert.ChangeType(inputs[4], typeof(T5));
			var v6 = (T6)Convert.ChangeType(inputs[5], typeof(T6));
			var v7 = (T7)Convert.ChangeType(inputs[6], typeof(T7));
			return (v1, v2, v3, v4, v5, v6, v7);
		}

		public T1[] ReadValueArray<T1>(int N)
		{
			var v1 = new T1[N];
			for (int i = 0; i < N; i++)
			{
				v1[i] = ReadValue<T1>();
			}
			return v1;
		}

		public (T1[], T2[]) ReadValueArray<T1, T2>(int N)
		{
			var (v1, v2) = (new T1[N], new T2[N]);
			for (int i = 0; i < N; i++)
			{
				var (t1, t2) = ReadValue<T1, T2>();
				v1[i] = t1;
				v2[i] = t2;
			}
			return (v1, v2);
		}

		public (T1[], T2[], T3[]) ReadValueArray<T1, T2, T3>(int N)
		{
			var (v1, v2, v3) = (new T1[N], new T2[N], new T3[N]);
			for (int i = 0; i < N; i++)
			{
				var (t1, t2, t3) = ReadValue<T1, T2, T3>();
				v1[i] = t1;
				v2[i] = t2;
				v3[i] = t3;
			}
			return (v1, v2, v3);
		}

		public (T1[], T2[], T3[], T4[]) ReadValueArray<T1, T2, T3, T4>(int N)
		{
			var (v1, v2, v3, v4) = (new T1[N], new T2[N], new T3[N], new T4[N]);
			for (int i = 0; i < N; i++)
			{
				var (t1, t2, t3, t4) = ReadValue<T1, T2, T3, T4>();
				v1[i] = t1;
				v2[i] = t2;
				v3[i] = t3;
				v4[i] = t4;
			}
			return (v1, v2, v3, v4);
		}

		public (T1[], T2[], T3[], T4[], T5[]) ReadValueArray<T1, T2, T3, T4, T5>(int N)
		{
			var (v1, v2, v3, v4, v5) = (new T1[N], new T2[N], new T3[N], new T4[N], new T5[N]);
			for (int i = 0; i < N; i++)
			{
				var (t1, t2, t3, t4, t5) = ReadValue<T1, T2, T3, T4, T5>();
				v1[i] = t1;
				v2[i] = t2;
				v3[i] = t3;
				v4[i] = t4;
				v5[i] = t5;
			}
			return (v1, v2, v3, v4, v5);
		}

		public (T1[], T2[], T3[], T4[], T5[], T6[]) ReadValueArray<T1, T2, T3, T4, T5, T6>(int N)
		{
			var (v1, v2, v3, v4, v5, v6) = (new T1[N], new T2[N], new T3[N], new T4[N], new T5[N], new T6[N]);
			for (int i = 0; i < N; i++)
			{
				var (t1, t2, t3, t4, t5, t6) = ReadValue<T1, T2, T3, T4, T5, T6>();
				v1[i] = t1;
				v2[i] = t2;
				v3[i] = t3;
				v4[i] = t4;
				v5[i] = t5;
				v6[i] = t6;
			}
			return (v1, v2, v3, v4, v5, v6);
		}

		public (T1[], T2[], T3[], T4[], T5[], T6[], T7[]) ReadValueArray<T1, T2, T3, T4, T5, T6, T7>(int N)
		{
			var (v1, v2, v3, v4, v5, v6, v7) = (new T1[N], new T2[N], new T3[N], new T4[N], new T5[N], new T6[N], new T7[N]);
			for (int i = 0; i < N; i++)
			{
				var (t1, t2, t3, t4, t5, t6, t7) = ReadValue<T1, T2, T3, T4, T5, T6, T7>();
				v1[i] = t1;
				v2[i] = t2;
				v3[i] = t3;
				v4[i] = t4;
				v5[i] = t5;
				v6[i] = t6;
				v7[i] = t7;
			}
			return (v1, v2, v3, v4, v5, v6, v7);
		}
	}
}