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>
#pragma GCC optimize("O3")
using namespace std;
const long long INF = 2e18;
const long long MOD = 998244353;
const long long MB = 20;
void solve() {
  long long n, k;
  cin >> n >> k;
  vector<long long> a(n + 1);
  for (long long i = 1; i <= n; i++) {
    for (long long j = i * 2; j <= n; j += i) {
      a[j]++;
    }
  }
  long long sum = 0;
  for (long long i = 1; i <= n; i++) {
    sum += a[i];
  }
  if (sum < k) {
    cout << "No";
    return;
  }
  long long m = n;
  while (sum - a[m] >= k) {
    sum -= a[m];
    m--;
  }
  vector<bool> good(m + 1, true);
  vector<pair<long long, long long>> b;
  for (long long i = m / 2 + (m % 2 == 0 ? 1 : 0); i <= m; i++) {
    b.push_back({a[i], i});
  }
  sort(b.rbegin(), b.rend());
  long long count = m;
  for (auto& p : b) {
    if (sum - p.first >= k) {
      sum -= p.first;
      good[p.second] = false;
      count--;
    }
  }
  cout << "Yes\n";
  cout << count << '\n';
  for (long long i = 1; i <= m; i++) {
    if (good[i]) cout << i << " ";
  }
}
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  cout.precision(12);
  solve();
}