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 N = 1e6 + 7;
const int inf = 0x3f3f3f3f;
const long long INF = 0x3f3f3f3f3f3f3f3f;
const int mod = 1e9 + 7;
const double eps = 1e-9;
const double PI = acos(-1);
int n;
long long k;
int rel[N];
bool vis[N];
int now;
vector<int> vc;
set<int> Set;
vector<int> fac[N];
void print() {
  cout << now << "!!!" << endl;
  for (auto& t : Set) printf("%d ", t);
  puts("");
}
int check(int v) {
  int cnt = 0;
  for (auto& t : Set) {
    if (v != t) {
      if (v % t == 0 || t % v == 0) {
        cnt++;
      }
    }
  }
  return cnt;
}
void calc() {
  int cnt = 0;
  vector<int> gg;
  for (auto& t : Set) gg.push_back(t);
  for (int i = 0; i < ((int)gg.size()); i++)
    for (int j = i + 1; j < ((int)gg.size()); j++)
      if (gg[j] % gg[i] == 0) cnt++;
  cout << now << " " << cnt << "~~~~" << endl;
}
int judge() {
  for (auto& t : Set) {
    if (rel[t] != check(t)) {
      return t;
    }
  }
  return -1;
}
int main() {
  scanf("%d%lld", &n, &k);
  if (n <= 16) {
    vector<int> ret;
    for (int S = 1; S < (1 << n); S++) {
      ret.clear();
      for (int i = 0; i < n; i++)
        if (S >> i & 1) ret.push_back(i + 1);
      int cnt = 0;
      for (int i = 0; i < ((int)ret.size()); i++) {
        for (int j = i + 1; j < ((int)ret.size()); j++) {
          if (ret[j] % ret[i] == 0) {
            cnt++;
          }
        }
      }
      if (cnt == k) {
        puts("Yes");
        printf("%d\n", ((int)ret.size()));
        for (auto& t : ret) printf("%d ", t);
        puts("");
        return 0;
      }
    }
    puts("No");
  } else {
    for (int i = 2; i <= n; i++) {
      for (int j = i + i; j <= n; j += i) vis[j] = true;
    }
    for (int i = 1; i <= n; i++) Set.insert(i);
    for (int i = 1; i <= n; i++) {
      for (int j = i + i; j <= n; j += i) {
        now++;
        rel[j]++;
        rel[i]++;
        fac[j].push_back(i);
      }
    }
    if (now < k) {
      puts("No");
      return 0;
    }
    if (now == k) {
      puts("Yes");
      printf("%d\n", ((int)Set.size()));
      for (auto& t : Set) printf("%d ", t);
      puts("");
      return 0;
    }
    for (int i = n / 2 + 1; i <= n; i++) {
      if (!vis[i]) {
        vc.push_back(i), now--, Set.erase(i);
        rel[1]--;
        if (now == k) {
          puts("Yes");
          printf("%d\n", ((int)Set.size()));
          for (auto& t : Set) printf("%d ", t);
          puts("");
          return 0;
        }
      }
    }
    while (now > k) {
      int v = *Set.rbegin();
      if (rel[v] <= now - k) {
        now -= rel[v];
        Set.erase(v);
        for (auto& t : fac[v]) rel[t]--;
      } else {
        int who = v;
        for (auto& t : Set)
          if (now - rel[t] <= k && rel[t] < rel[who]) who = t;
        now -= rel[who];
        Set.erase(who);
        for (auto& t : fac[who]) rel[t]--;
        while (now < k && ((int)vc.size())) {
          now++;
          Set.insert(vc.back());
          vc.pop_back();
        }
      }
    }
    if (now == k) {
      puts("Yes");
      printf("%d\n", ((int)Set.size()));
      for (auto& t : Set) printf("%d ", t);
      puts("");
      return 0;
    } else {
      puts("No");
    }
  }
  return 0;
}