Problem: A positive integer x is called a power of two if it can be represented as x = 2^y, where y is a non-negative integer. So, the powers of two are 1, 2, 4, 8, 16, ....

You are given two positive integers n and k. Your task is to represent n as the sum of exactly k powers of two.

Input

The only line of the input contains two integers n and k (1 ≤ n ≤ 10^9, 1 ≤ k ≤ 2 ⋅ 10^5).

Output

If it is impossible to represent n as the sum of k powers of two, print NO.

Otherwise, print YES, and then print k positive integers b_1, b_2, ..., b_k such that each of b_i is a power of two, and ∑ _{i = 1}^{k} b_i = n. If there are multiple answers, you may print any of them.

Examples

Input


9 4


Output


YES
1 2 2 4 


Input


8 1


Output


YES
8 


Input


5 1


Output


NO


Input


3 7


Output


NO

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
template <typename T>
T min(T a, T b, T c) {
  return min(a, min(b, c));
}
template <typename T>
T max(T a, T b, T c) {
  return max(a, max(b, c));
}
template <typename T>
T max(T a, T b, T c, T d) {
  return max(a, max(b, max(c, d)));
}
template <typename T>
T min(T a, T b, T c, T d) {
  return min(a, min(b, min(c, d)));
}
template <typename t1>
void fill(vector<t1> &arr, t1 val) {
  for (long long i = 0; i < (long long)arr.size(); i++) arr[i] = val;
}
template <typename t1>
void fill(vector<vector<t1>> &arr, t1 val) {
  for (long long i = 0; i < (long long)arr.size(); i++) {
    for (long long j = 0; j < (long long)arr[i].size(); j++) arr[i][j] = val;
  }
}
template <typename T>
void read(vector<T> &arr, long long N) {
  arr.clear();
  arr.resize(N);
  for (long long i = 0; i < N; i++) cin >> arr[i];
}
template <typename T>
void read(vector<pair<T, T>> &arr, long long N) {
  arr.clear();
  arr.resize(N);
  for (long long i = 0; i < (long long)arr.size(); i++)
    cin >> arr[i].first >> arr[i].second;
}
template <typename T>
void read(vector<vector<T>> &arr, long long N, long long M) {
  arr.clear();
  arr.resize(N, vector<T>(M));
  for (long long i = 0; i < N; i++) {
    for (long long j = 0; j < M; j++) cin >> arr[i][j];
  }
}
template <typename T, size_t N>
long long SIZE(const T (&t)[N]) {
  return N;
}
template <typename T>
long long SIZE(const T &t) {
  return t.size();
}
string to_string(const string s, long long x1 = 0, long long x2 = 1e9) {
  return '"' + ((x1 < s.size()) ? s.substr(x1, x2 - x1 + 1) : "") + '"';
}
string to_string(const char *s) { return to_string((string)s); }
string to_string(const bool b) { return (b ? "true" : "false"); }
string to_string(const char c) { return string({c}); }
template <size_t N>
string to_string(const bitset<N> &b, long long x1 = 0, long long x2 = 1e9) {
  string t = "";
  for (long long __iii__ = min(x1, SIZE(b)), __jjj__ = min(x2, SIZE(b) - 1);
       __iii__ <= __jjj__; ++__iii__) {
    t += b[__iii__] + '0';
  }
  return '"' + t + '"';
}
template <typename A, typename... C>
string to_string(const A(&v), long long x1 = 0, long long x2 = 1e9,
                 C... coords);
long long l_v_l_v_l = 0, t_a_b_s = 0;
template <typename A, typename B>
string to_string(const pair<A, B> &p) {
  l_v_l_v_l++;
  string res = "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
  l_v_l_v_l--;
  return res;
}
template <typename A, typename... C>
string to_string(const A(&v), long long x1, long long x2, C... coords) {
  long long rnk = rank<A>::value;
  string tab(t_a_b_s, ' ');
  string res = "";
  bool first = true;
  if (l_v_l_v_l == 0) res += '\n';
  res += tab + "[";
  x1 = min(x1, SIZE(v)), x2 = min(x2, SIZE(v));
  auto l = begin(v);
  advance(l, x1);
  auto r = l;
  advance(r, (x2 - x1) + (x2 < SIZE(v)));
  for (auto e = l; e != r; e = next(e)) {
    if (!first) {
      res += ", ";
    }
    first = false;
    l_v_l_v_l++;
    if (e != l) {
      if (rnk > 1) {
        res += '\n';
        t_a_b_s = l_v_l_v_l;
      };
    } else {
      t_a_b_s = 0;
    }
    res += to_string(*e, coords...);
    l_v_l_v_l--;
  }
  res += "]\n";
  if (l_v_l_v_l == 0) res += '\n';
  return res;
}
void printm() { ; }
template <typename Heads, typename... Tails>
void printm(Heads H, Tails... T) {
  cout << to_string(H) << " | ";
  printm(T...);
}
static bool comp(pair<long long, long long> &a, pair<long long, long long> &b) {
}
const long long Max = 2 * 1e17, Min = -2 * 1e17, mod = 1e9 + 7;
long long N, M, K;
const long long P = 31;
long long fastpow(long long a, long long p) {
  long long res = 1;
  while (p) {
    if (p % 2 == 0) {
      a = (a * a);
      p = p / 2;
    } else {
      res = (res * a);
      p--;
    }
  }
  return res;
}
void solve() {
  cin >> N >> K;
  map<long long, long long> has;
  multiset<long long> freq;
  for (long long i = 0; i <= 30; i++) {
    if (N & (1 << i)) {
      if (i > 0) freq.insert(i);
      has[i]++;
    }
  }
  if ((long long)has.size() > K) {
    cout << "NO" << '\n';
    return;
  }
  long long ans = (long long)has.size();
  while (ans < K and freq.empty() == false) {
    auto it = freq.rbegin();
    long long val = *it;
    freq.erase(--(freq.end()));
    has[val]--;
    has[val - 1] += 2;
    if (val - 1 > 0) {
      freq.insert(val - 1);
      freq.insert(val - 1);
    }
    ans++;
  }
  if (ans < K) {
    cout << "NO" << '\n';
    return;
  }
  cout << "YES" << '\n';
  for (auto it = (has).begin(); it != (has).end(); it++) {
    for (long long i = 0; i < it->second; i++)
      cout << fastpow(2, it->first) << ' ';
  }
  cout << '\n';
}
signed main() {
  bool testcases = 0;
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  if (testcases) {
    long long tt;
    cin >> tt;
    while (tt--) solve();
  } else
    solve();
}