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++14 (Clang 3.8.0) (judge verdict: Wrong Answer)

//includes
#include<iostream>
#include<vector>
#include<set>
#include<tuple>
#include<algorithm>
#include<cmath>
#include<string>
#include<stack>
#include<map>
#include<queue>
#include<iomanip>
#include<numeric>
#include<assert.h>
#include<cstring>
#include<unordered_map>
#include<bitset>

//macros and consts
#define REP(i, n) for(int i = 0; i < (int)(n); i++)
#define all(a) (a).begin(),(a).end()
#define FOR(i,a,b) for(int i = (a); i < (b); i++)
#define FORE(i,a) for(auto &i : a)
#define pb push_back
#define mp make_pair
#define eb emplace_back
#define accm accumulate
#define Fi first
#define Se second
#define INF 1e9
#define mINF -1e9
#define endl "\n"
#define cont continue
#define brk break

//shorter types
using namespace std;
using ll = long long;
using vi = std::vector<int>;
using vc = std::vector<char>;
using vll = std::vector<long long>;
using vs = std::vector<string>;
using Mi = map<int,int>;
using Mll = map<ll,ll>;
using UMi = unordered_map<int,int>;
using UMll = unordered_map<ll,ll>;
using Pi = pair<int,int>;
using Pll = pair<ll,ll>;
using vPi = vector<Pi>;
using vPll = vector<Pll>;
using vvi = vector<vector<int>>;
using vvll = vector<vector<ll>>;
using vvc = vector<vector<char>>;
using vvs = vector<vector<string>>;
using pqgi = priority_queue<int,vector<int>,greater<int>>;
using pqsi = priority_queue<int,vector<int>,less<int>>;
using pqgll = priority_queue<int,vector<int>,greater<int>>;
using pssll = priority_queue<int,vector<int>,less<int>>;
template<class T>
using vec = vector<T>;

//frequent functions and data structures
class Cpmath{
  public:
    template<typename T>
    static T gcd(T a, T b){
      if (a == 0) 
        return b; 
      return gcd(b % a, a); 
    }
    template<typename T>
    static T findGCD(vector<T> &arr, size_t n){
      T result = arr[0]; 
      for (size_t i = 1; i < n; i++) 
        result = gcd(arr[i], result); 
      return result; 
    }
    template<typename T>
    static T findLCM(vector<T> &arr, size_t n){
      T lcm = arr[0];
      for(size_t i = 1; i < n ;i++){
        lcm = (lcm / gcd(arr[i],lcm)) * arr[i];
      }
      return lcm;
    }
    template<typename T>
    static bool is_prime(T n){
      if(n == 1){
        return false;
      }
      for(size_t i = 2 ; i <= pow(n,0.5) ; i++){
        if(n % i == 0){
          return false;
        }
      }
      return true;
    }
    static ll fact(ll n){
      if(n == 0){
        return 1LL;
      }
      else{
        return n * fact(n - 1);
      }
    }
    static ll permutation(int n, int r){
      assert(n >= r);
      ll ret = 1;
      for(int i = n ; i > n - r ; i--){
        ret *= i;
      }
      return ret;
    }
};

class NCR{
  private:
    static const int MAX = 210000;
    static const int MOD = 998244353;
    ll fac[MAX],finv[MAX],inv[MAX];
  public:
    void COMinit(){
      fac[0] = fac[1] = 1;
      finv[0] = finv[1] = 1;
      inv[1] = 1;
      for(int i = 2 ; i < MAX ; i++){
        fac[i] = fac[i-1] * i % MOD;
        inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
        finv[i] = finv[i-1] * inv[i] % MOD;
      }
    }
    ll COM(int n,int k){
      if(n < k) return 0;
      if(n < 0 || k < 0){
        return 0;
      }
      return fac[n] * (finv[k] * finv[n-k] % MOD) % MOD;
    }
};

struct BipartiteMatching {
    vector<vector<int>> E; int n, m; vector<int> match, dist;
    void init(int _n,int _m){n=_n,m=_m;E.resize(n+m+2);match.resize(n+m+2);dist.resize(n+m+2);}
    bool bfs() {
        queue<int> que;
        FOR(i, 1, n + 1) {
            if (!match[i]) dist[i] = 0, que.push(i);
            else dist[i] = INF;
        }
        dist[0] = INF;
        while (!que.empty()) {
            int u = que.front(); que.pop();
            if (u) for(auto &v : E[u]) if (dist[match[v]] == INF) {
                dist[match[v]] = dist[u] + 1;
                que.push(match[v]);
            }
        }
        return (dist[0] != INF);
    }
    bool dfs(int u) {
        if (u) {
            for(auto &v : E[u]) if (dist[match[v]] == dist[u] + 1) if (dfs(match[v])) {
                match[v] = u; match[u] = v;
                return true;
            }
            dist[u] = INF;
            return false;
        }
        return true;
    }
    void add(int a, int b) { b += n; E[a + 1].push_back(b + 1); E[b + 1].push_back(a + 1); }
    int whois(int x) { return match[x + 1] - 1; }
    int solve() {
        FOR(i, 0, n + m + 1) match[i] = 0;
        int res = 0;
        while (bfs()) FOR(i, 1, n + 1) if (!match[i] && dfs(i)) res++;
        return res;
    }
};

struct SegmentTree{
  private:
    int n;
    vector<int> node;
  public:
    SegmentTree(vector<int> v){
      int sz = v.size();
      n = 1;
      while(n < sz) n *= 2;
      node.resize(2 * n - 1 , INF);
      for(int i = 0 ; i < sz ; i++){
        node[i + n - 1] = v[i];
      }
      for(int i = n - 2 ; i >= 0 ; i--){
        node[i] = min(node[2*i+1],node[2*i+2]);
      }
    }
    void update(int x, int val){
      x += (n - 1);
      node[x] = val;
      while(x > 0){
        x = (x - 1) / 2;
        node[x] = min(node[2*x+1],node[2*x+2]);
      }
    }
    int getmin(int a, int b , int k = 0, int l = 0, int r = -1){
      if(r < 0){
        r = n;
      }
      if(r <= a || b <= l){
        return INF;
      }
      if(a <= l && r <= b){
        return node[k];
      }
      int vl = getmin(a,b,2*k+1,l,(l+r)/2);
      int vr = getmin(a,b,2*k+2,(l+r)/2,r);
      return min(vl,vr);
    }
};

template<class Abel> struct WUnionFind {
    vector<int> par;
    vector<int> rank;
    vector<Abel> diff_weight;

    WUnionFind(int n = 1, Abel SUM_UNITY = 0) {
        init(n, SUM_UNITY);
    }

    void init(int n = 1, Abel SUM_UNITY = 0) {
        par.resize(n); rank.resize(n); diff_weight.resize(n);
        for (int i = 0; i < n; ++i) par[i] = i, rank[i] = 0, diff_weight[i] = SUM_UNITY;
    }

    int root(int x) {
        if (par[x] == x) {
            return x;
        }
        else {
            int r = root(par[x]);
            diff_weight[x] += diff_weight[par[x]];
            return par[x] = r;
        }
    }

    Abel weight(int x) {
        root(x);
        return diff_weight[x];
    }

    bool issame(int x, int y) {
        return root(x) == root(y);
    }

    bool merge(int x, int y, Abel w) {
        w += weight(x); w -= weight(y);
        x = root(x); y = root(y);
        if (x == y) return false;
        if (rank[x] < rank[y]) swap(x, y), w = -w;
        if (rank[x] == rank[y]) ++rank[x];
        par[y] = x;
        diff_weight[y] = w;
        return true;
    }

    Abel diff(int x, int y) {
        return weight(y) - weight(x);
    }
};

struct UnionFind{
  vector<int> par;
  UnionFind(int n) : par(n,-1) {}
  void init(int n) {par.assign(n,-1);}
  int root(int x){
    if(par[x] < 0) return x;
    else return par[x] = root(par[x]);
  }
  bool issame(int x,int y){
    return root(x) == root(y);
  }
  bool merge(int x,int y){
    x = root(x);
    y = root(y);
    if (x == y) return false;
    if (par[x] > par[y]){
      swap(x,y);
    }
    par[x] += par[y];
    par[y] = x;
    return true;
  }
  int size(int x){
    return -par[root(x)];
  }
};

void YN(bool a){
  cout << (a?"YES":"NO") << endl;
}

void Yn(bool a){
  cout << (a?"Yes":"No") << endl;
}
void yn(bool a){
  cout << (a?"yes":"no") << endl;
}
template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }

int dx[4] = {1,0,-1,0};
int dy[4] = {0,1,0,-1};
template<typename T>
inline int digitsum(T num){
  int ret = 0;
  while(num){
    ret += num % 10;
    num /= 10;
  }
  return ret;
}
template<typename InputIt,typename T>
inline bool argexist(InputIt first,InputIt last,const T& x){
  if(std::find(first,last,x) != last){
    return true;
  }
  else{
    return false;
  }
}
template<typename InputIt,typename T>
inline int argfind(InputIt first, InputIt last, const T& x){
  auto it = find(first,last,x);
  return distance(first,it);
}
template<typename InputIt>
inline int argmax(InputIt first, InputIt last) {
    auto it = max_element(first, last);
    return distance(first, it);
}
template<typename InputIt>
inline int argmin(InputIt first, InputIt last) {
    auto it = min_element(first, last);
    return distance(first, it);
}
// you need sort before using this func
template<typename T>
inline void erasebv(vector<T>& c,T v){
  c.erase(remove(begin(c),end(c),v),end(c));
}
// you need sort before using this func
template<typename T>
inline void uniq(T& c) {
    c.erase(unique(begin(c), end(c)), end(c));
}
template<typename T>
inline T POP_BACK(vector<T>& que) {
    T x = que.back(); que.pop_back();
    return x;
}
template<typename T>
inline T POP_BACK(deque<T>& que) {
    T x = que.back(); que.pop_back();
    return x;
}
template<typename T>
inline T POP_FRONT(deque<T>& que) {
    T x = que.front(); que.pop_front();
    return x;
}
template<typename T, typename C>
inline T POP(stack<T,C>& stk) {
    T x = stk.top(); stk.pop();
    return x;
}
template<typename T, typename C>
inline T POP(queue<T,C>& que) {
    T x = que.front(); que.pop();
    return x;
}
template<typename T, typename Cont, typename Cmp>
inline T POP(priority_queue<T,Cont,Cmp>& que) {
    T x = que.top(); que.pop();
    return x;
}
template<typename T1, typename T2> ostream& operator<<(ostream& s, const pair<T1, T2>& p) {return s << "(" << p.first << ", " << p.second << ")";}
template<typename T> ostream& operator<<(ostream& s, const vector<T>& v) {
  int len = v.size();
  for (int i = 0; i < len; ++i) {
    s << v[i]; if (i < len - 1) s << "\t";
  }
  return s;
}
template<typename T> ostream& operator<<(ostream& s, const vector< vector<T> >& vv) {
  int len = vv.size();
  for (int i = 0; i < len; ++i) {
  s << vv[i] << endl;
  }
  return s;
}

//utils to solve graph chals easy
namespace GraphLib{
  using Weight = int;
  struct Edge{
    int src,dst;
    Weight weight;
    Edge(int src,int dst,Weight weight):
      src(src),dst(dst),weight(weight){}
  };
  bool operator < (const Edge &e, const Edge &f) {
    return e.weight != f.weight ? e.weight > f.weight :
      e.src != f.src ? e.src < f.src : e.dst < f.dst;
  }
  using Edges = vector<Edge>;
  using Graph = vector<Edges>;
  using Array = vector<Weight>;
  using Matrix = vector<Array>;
  
  void shortestPath(const Graph &g, int s,
      vector<Weight> &dist, vector<int> &prev) {
    int n = g.size();
    dist.assign(n, INF); dist[s] = 0;
    prev.assign(n, -1);
    priority_queue<Edge> Q; // "e < f" <=> "e.weight > f.weight"
    for (Q.push(Edge(-2, s, 0)); !Q.empty(); ) {
      Edge e = Q.top(); Q.pop();
      if (prev[e.dst] != -1) continue;
      prev[e.dst] = e.src;
      FORE(f,g[e.dst]) {
        if (dist[f.dst] > e.weight+f.weight) {
          dist[f.dst] = e.weight+f.weight;
          Q.push(Edge(f.src, f.dst, e.weight+f.weight));
        }
      }
    }
  }
  vector<int> DijkstraBuildPath(const vector<int> &prev, int t) {
    vector<int> path;
    for (int u = t; u >= 0; u = prev[u])
      path.push_back(u);
    reverse(path.begin(), path.end());
    return path;
  }
  void visit(const Graph & g, int v, int u,
      Edges& brdg, vector< vector<int> >& tecomp,
      stack<int>& roots, stack<int>& S, vector<bool>& inS,
      vector<int>& num, int& time) {
    num[v] = ++time;
    S.push(v); inS[v] = true;
    roots.push(v);
    FORE(e, g[v]) {
      int w = e.dst;
      if (num[w] == 0)
        visit(g, w, v, brdg, tecomp, roots, S, inS, num, time);
      else if (u != w && inS[w])
        while (num[roots.top()] > num[w]) roots.pop();
    }
    if (v == roots.top()) {
      brdg.push_back(Edge(u, v, 1)); // any weight will do
      tecomp.push_back(vector<int>());
      while (1) {
        int w = S.top(); S.pop(); inS[w] = false;
        tecomp.back().push_back(w);
        if (v == w) break;
      }
      roots.pop();
    }
  }
  void bridge(const Graph& g, Edges& brdg, vector< vector<int> >& tecomp) {
    const int n = g.size();
    vector<int> num(n);
    vector<bool> inS(n);
    stack<int> roots, S;
    int time = 0;
    REP(u, n) if (num[u] == 0) {
      visit(g, u, n, brdg, tecomp, roots, S, inS, num, time);
      brdg.pop_back();
    }
  }
}


//here begins your code
vi a;
int K;
signed main(){
  std::ios::sync_with_stdio(false);
  std::cin.tie(0);
  REP(i,50){
    a.eb(i);
  }
  cin >> K;
  REP(i,50){
    a[i] += (50-1) * (K / 50);
  }
  REP(i,K % 50){
    a[i] += 50;
    REP(j,50){
      if(i == j){
        cont;
      }
      a[j]--;
    }
  }
  cout << 50 << endl;
  REP(i,50){
    cout << a[i] << " ";
  }
  cout << endl;
  return 0;
}