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;
const int maxn = 3e5 + 100;
int d[maxn], t[maxn];
vector<int> v[maxn];
int main() {
  int n, k;
  cin >> n >> k;
  for (int i = 1; i < maxn; ++i) {
    for (int j = i * 2; j < maxn; j += i) {
      d[j]++;
    }
  }
  int num = 0;
  for (int i = 1; i <= n; ++i) {
    num += d[i];
  }
  if (num < k) {
    cout << "No" << endl;
    return 0;
  }
  cout << "Yes" << endl;
  if (k == 0) {
    cout << "1\n1\n";
    return 0;
  }
  int m = 0;
  num = 0;
  while (num < k) {
    m++;
    num += d[m];
  }
  num -= k;
  set<int> st;
  for (int i = 1; i <= m; ++i) {
    st.insert(i);
  }
  set<int> s;
  for (int i = 1; i <= m; ++i) {
    if (d[i] == 1) {
      t[m / i]++;
      s.insert(m / i);
      v[m / i].push_back(i);
    }
  }
  while (num) {
    auto it = s.upper_bound(num);
    it--;
    int a = *it;
    t[a]--;
    if (!t[a]) {
      s.erase(a);
    }
    num -= a;
    st.erase(v[a].back());
    v[a].pop_back();
  }
  cout << st.size() << endl;
  for (auto x : st) {
    cout << x << ' ';
  }
  cout << endl;
}