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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.Scanner;
import java.util.stream.IntStream;
import java.util.stream.LongStream;

/**
 * 解説どおりに作成したソースコード
 */
public class Main {

	private static final int N = 3;

	public static void main(String[] args) {
		try (Scanner scanner = new Scanner(System.in)) {
			long k = scanner.nextLong();
			long[] a = new long[N];
			IntStream.range(0, N).forEach(i -> a[i] = k / N + i);
			LongStream.range(0, k % N).forEach(l -> calcReverse(a, (int) (l % N)));
			System.out.println(N);
			IntStream.range(0, N - 1).forEach(i -> System.out.print(a[i] + " "));
			System.out.println(a[N - 1]);
		}
	}

	/**
	 * 指定された操作の逆操作を実施
	 * 
	 * @param a     操作対象の配列
	 * @param index 足し算をするindex
	 */
	private static void calcReverse(final long[] a, final int index) {
		a[index] += N + 1;
		IntStream.range(0, N).forEach(i -> a[i]--);
	}
}