Problem:
Score : 600 points

Problem Statement

We have a sequence of length N consisting of non-negative integers. Consider performing the following operation on this sequence until the largest element in this sequence becomes N-1 or smaller.

Determine the largest element in the sequence (if there is more than one, choose one). Decrease the value of this element by N, and increase each of the other elements by 1.

It can be proved that the largest element in the sequence becomes N-1 or smaller after a finite number of operations.

You are given an integer K. Find an integer sequence a_i such that the number of times we will perform the above operation is exactly K. It can be shown that there is always such a sequence under the constraints on input and output in this problem.

Constraints

0 ≤ K ≤ 50 \times 10^{16}

Input

Input is given from Standard Input in the following format:

K

Output

Print a solution in the following format:

N
a_1 a_2 ... a_N

Here, 2 ≤ N ≤ 50 and 0 ≤ a_i ≤ 10^{16} + 1000 must hold.

Sample Input 1

0

Sample Output 1

4
3 3 3 3

Sample Input 2

1

Sample Output 2

3
1 0 3

Sample Input 3

2

Sample Output 3

2
2 2

The operation will be performed twice: [2, 2] -> [0, 3] -> [1, 1].

Sample Input 4

3

Sample Output 4

7
27 0 0 0 0 0 0

Sample Input 5

1234567894848

Sample Output 5

10
1000 193 256 777 0 1 1192 1234567891011 48 425

Solution in C# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

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

namespace FertiLib.Contest.D
{
	static class Program
	{
		public static void Solve(Scanner cin)
		{
			long k = cin.ReadLong();
			int n = 50;
			var a = Enumerable.Repeat((long)(n - 1), n).ToArray();
			for (int i = 0; i < n; i++)
			{
				a[i] += k / n * n;
				if (i < k % n) a[i] += n;
			}

			Console.WriteLine(n);
			Console.WriteLine(a.Join(" "));
		}

		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");

		public static bool Chmax<T>(ref T a, T b) where T : IComparable<T>
		{
			if (a.CompareTo(b) >= 0) return false;
			a = b;
			return true;
		}
		public static bool Chmin<T>(ref T a, T b) where T : IComparable<T>
		{
			if (a.CompareTo(b) <= 0) return false;
			a = b;
			return true;
		}
	}

	static class Util
	{
		public 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);
		}
	}
}