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 long long int N = 3e5 + 100;
long long int n, k, d[N], e[N], dp[N], m = 0;
vector<long long int> v;
int main() {
  ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
  cin >> n >> k;
  for (int i = 2; i <= n; i++) d[i]++;
  for (int i = 2; i <= n; i++) {
    e[i] = e[i - 1] + d[i];
    for (int j = i + i; j <= n; j += i) {
      d[j]++;
      dp[j] = 1;
    }
  }
  if (e[n] < k) {
    cout << "No" << endl;
    return 0;
  }
  cout << "Yes" << endl;
  for (int i = n; i >= 1; i--)
    if (e[i] >= k) m = i;
  k = e[m] - k;
  for (int i = m; i > m / 2 && k > 0; i--) {
    if (dp[i] != 0 && k - d[i] >= 0 && d[i] > 1) {
      dp[i] = 2;
      k -= d[i];
    }
  }
  for (int i = m; i > m / 2 && k > 0; i--) {
    if (dp[i] != 2 && k - d[i] >= 0) {
      dp[i] = 2;
      k -= d[i];
    }
  }
  for (int i = 1; i <= m; i++)
    if (dp[i] != 2) v.push_back(i);
  cout << v.size() << endl;
  for (auto y : v) cout << y << ' ';
  return 0;
}