Problem: Imp is really pleased that you helped him. But it you solve the last problem, his gladness would raise even more.

<image> Let's define <image> for some set of integers <image> as the number of pairs a, b in <image>, such that:

  * a is strictly less than b; 
  * a divides b without a remainder. 



You are to find such a set <image>, which is a subset of {1, 2, ..., n} (the set that contains all positive integers not greater than n), that <image>. 

Input

The only line contains two integers n and k <image>.

Output

If there is no answer, print "No".

Otherwise, in the first line print "Yes", in the second — an integer m that denotes the size of the set <image> you have found, in the second line print m integers — the elements of the set <image>, in any order.

If there are multiple answers, print any of them.

Examples

Input

3 3


Output

No


Input

6 6


Output

Yes
5
1 2 4 5 6 

Input

8 3


Output

Yes
4
2 4 5 8

Note

In the second sample, the valid pairs in the output set are (1, 2), (1, 4), (1, 5), (1, 6), (2, 4), (2, 6). Thus, <image>.

In the third example, the valid pairs in the output set are (2, 4), (4, 8), (2, 8). Thus, <image>.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
template <typename T, typename U>
inline void smin(T &a, U b) {
  if (a > b) a = b;
}
template <typename T, typename U>
inline void smax(T &a, U b) {
  if (a < b) a = b;
}
template <class T>
inline void gn(T &first) {
  char c, sg = 0;
  while (c = getchar(), (c > '9' || c < '0') && c != '-')
    ;
  for ((c == '-' ? sg = 1, c = getchar() : 0), first = 0; c >= '0' && c <= '9';
       c = getchar())
    first = (first << 1) + (first << 3) + c - '0';
  if (sg) first = -first;
}
template <class T, class T1>
inline void gn(T &first, T1 &second) {
  gn(first);
  gn(second);
}
template <class T, class T1, class T2>
inline void gn(T &first, T1 &second, T2 &z) {
  gn(first);
  gn(second);
  gn(z);
}
template <class T>
inline void print(T first) {
  if (first < 0) {
    putchar('-');
    return print(-first);
  }
  if (first < 10) {
    putchar('0' + first);
    return;
  }
  print(first / 10);
  putchar(first % 10 + '0');
}
template <class T>
inline void printsp(T first) {
  print(first);
  putchar(' ');
}
template <class T>
inline void println(T first) {
  print(first);
  putchar('\n');
}
int power(int a, int b, int m, int ans = 1) {
  for (; b; b >>= 1, a = 1LL * a * a % m)
    if (b & 1) ans = 1LL * ans * a % m;
  return ans;
}
vector<int> d[303030], ans;
int cnt[303030], vst[303030];
set<pair<int, int> > s;
set<pair<int, int> >::iterator it;
int main() {
  int n, k, m, tot = 0;
  cin >> n >> k;
  for (int i = 1; i <= n; i++)
    for (int j = i + i; j <= n; j += i) d[j].push_back(i);
  for (int i = 1; i <= n; i++) {
    for (int j = 0; j < d[i].size(); j++) {
      int u = d[i][j];
      cnt[u]++;
      cnt[i]++;
    }
    tot += d[i].size();
    if (tot >= k) n = i;
  }
  for (int i = 1; i <= n; i++) s.insert(make_pair(cnt[i], i)), vst[i] = 1;
  if (k > tot)
    puts("No");
  else {
    m = tot - k;
    puts("Yes");
    while (m) {
      it = s.upper_bound(make_pair(m, n + 1));
      it--;
      int u = it->second;
      s.erase(it);
      m -= cnt[u];
      vst[u] = 0;
      for (int i = 0; i < d[u].size(); i++) {
        int v = d[u][i];
        if (!vst[v]) continue;
        s.erase(make_pair(cnt[v], v));
        cnt[v]--;
        if (cnt[v]) s.insert(make_pair(cnt[v], v));
      }
      for (int i = u * 2; i <= n; i += u) {
        if (!vst[i]) continue;
        s.erase(make_pair(cnt[i], i));
        cnt[i]--;
        if (cnt[i]) s.insert(make_pair(cnt[i], i));
      }
    }
    println(s.size());
    for (it = s.begin(); it != s.end(); it++) printsp(it->second);
  }
  return 0;
}