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 Kotlin (1.0.0) (judge verdict: Wrong Answer)

import java.io.*
import java.lang.RuntimeException

val pw = PrintWriter(System.out)
const val MOD = 1000000007L
const val INF = 2147483647
const val LINF = 9223372036854775807L

fun main(args: Array<String>) {
    solve()
    pw.flush()
}

fun solve() {
    val k = nextLong()
    val n = 50L
    val ary = Array(n.toInt()) { k }
    var count = 0L
    for (i in ary.indices){
        val rest = max(0L, ary[i] - (n - 1))
        count += (rest + n) / (n + 1)
    }
    ary[0] += n * (k - count)
    for (i in ary.indices){
        ary[i] -= k
    }

    println(ary.joinToString(" "))


}


fun println(v: String) {
    pw.println(v)
}

fun print(v: String) {
    pw.print(v)
}

fun next() = readLine()!!
fun nextInt() = next().toInt()
fun nextLong() = next().toLong()
fun nextDouble() = next().toDouble()
fun nextList() = next().split(" ").toMutableList()
fun nextIntList(index: Int = 0) = next().split(" ").map { it.toInt() + index }.toMutableList()
fun nextLongList(index: Long = 0L) = next().split(" ").map { it.toLong() + index }.toMutableList()
fun nextDoubleList() = next().split(" ").map { it.toDouble() }.toMutableList()

fun ary(n: Int, init: String = "") = Array(n) { init }
fun intAry(n: Int, init: Int = 0) = IntArray(n) { init }
fun longAry(n: Int, init: Long = 0L) = LongArray(n) { init }
fun doubleAry(n: Int, init: Double = 0.0) = DoubleArray(n) { init }
fun ary2(n: Int, m: Int, init: String = "") = Array(n) { Array(m) { init } }
fun intAry2(n: Int, m: Int, init: Int = 0) = Array(n) { IntArray(m) { init } }
fun longAry2(n: Int, m: Int, init: Long = 0) = Array(n) { LongArray(m) { init } }
fun doubleAry2(n: Int, m: Int, init: Double = 0.0) = Array(n) { DoubleArray(m) { init } }
fun ary3(n: Int, m: Int, k: Int, init: String = "") = Array(n) { Array(m) { Array(k) { init } } }
fun intAry3(n: Int, m: Int, k: Int, init: Int = 0) = Array(n) { Array(m) { IntArray(k) { init } } }
fun longAry3(n: Int, m: Int, k: Int, init: Long = 0L) = Array(n) { Array(m) { LongArray(k) { init } } }
fun doubleAry3(n: Int, m: Int, k: Int, init: Double = 0.0) = Array(n) { Array(m) { DoubleArray(k) { init } } }

fun abs(n: Int): Int = Math.abs(n)
fun abs(n: Long): Long = Math.abs(n)
fun abs(n: Double): Double = Math.abs(n)
fun max(vararg values: Int) = if (values.isEmpty()) -INF else values.max()!!
fun max(vararg values: Long) = if (values.isEmpty()) -LINF else values.max()!!
fun min(vararg values: Int) = if (values.isEmpty()) INF else values.min()!!
fun min(vararg values: Long) = if (values.isEmpty()) LINF else values.min()!!
fun swap(a: String, b: String) = Pair<String, String>(b, a)
fun swap(a: Int, b: Int) = Pair<Int, Int>(b, a)
fun swap(a: Long, b: Long) = Pair<Long, Long>(b, a)
fun swap(a: Double, b: Double) = Pair<Double, Double>(b, a)