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

• $0 \leq K \leq 50 \times 10^{16}$

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, $2 \leq N \leq 50$ and $0 \leq a_i \leq 10^{16} + 1000$ must hold.

0

4
3 3 3 3

1

3
1 0 3

2

2
2 2

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

3

7
27 0 0 0 0 0 0

1234567894848

10
1000 193 256 777 0 1 1192 1234567891011 48 425