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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <limits.h>
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <time.h>

// 内部定数
#define D_ARRAY_CNT		50										// 数列数

// 内部変数
static int siDCnt;												// 表示数

// 内部変数 - テスト用
#ifdef D_TEST
	static FILE *szpFpT;
#endif

// 表示
long long
fDsp(
	long long plVal				// <I> 値
)
{
	// スペース
	if (siDCnt > 0) {
		printf(" ");
	}

	// 表示
	printf("%lld", plVal);

	// 表示数
	siDCnt++;

	return 0;
}

// 実行メイン
int
fMain(
	int piTNo					// <I> テスト番号 1～
)
{
	int i;
	char lc1Buf[1024];

	// データ初期化
	siDCnt = 0;													// 表示数

	// テストファイルオープン
#ifdef D_TEST
	sprintf(lc1Buf, ".\\Test\\T%d.txt", piTNo);
	szpFpT = fopen(lc1Buf, "r");
#endif

	// 操作回数取得
	long long llOCnt;
#ifdef D_TEST
	fgets(lc1Buf, sizeof(lc1Buf), szpFpT);
#else
	fgets(lc1Buf, sizeof(lc1Buf), stdin);
#endif
	sscanf(lc1Buf, "%lld", &llOCnt);

	// 全数列加算値
	long long llAll = llOCnt / (long long)D_ARRAY_CNT;

	// 加算数
	int liACnt = (int)(llOCnt % (long long)D_ARRAY_CNT);

	// 数列数表示
	printf("%d\n", D_ARRAY_CNT);

	// 数列表示
	for (i = 0; i < liACnt; i++) {
		fDsp(llAll + (long long)D_ARRAY_CNT);
	}
	llAll--;
	for (i = liACnt; i < D_ARRAY_CNT; i++) {
		fDsp(llAll + (long long)D_ARRAY_CNT);
	}

	// 改行
	printf("\n");

	// テストファイルクローズ
#ifdef D_TEST
	fclose(szpFpT);
#endif

	return 0;
}

int
main()
{

#ifdef D_TEST
	int i;
	for (i = D_TEST_SNO; i <= D_TEST_ENO; i++) {
		fMain(i);
	}
#else
	fMain(0);
#endif

	return 0;
}