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;
void Print(int _x) { printf("%d\n", _x); }
void Print(long long _x) { printf("%lld\n", _x); }
template <typename T>
void Print(T _a[], int _s, int _t) {
  for (int i = _s; i <= _t; i++) cout << _a[i] << " ";
  cout << endl;
}
struct InputReader {
  static const int bs = 100000;
  char buf[bs];
  int p;
  inline InputReader() : p(bs) {}
  inline void Flush() {
    p = 0;
    fread(buf, 1, bs, stdin);
  }
  inline char C() {
    if (p >= bs) Flush();
    return buf[p++];
  }
  int Getnum() {
    char ch = C();
    while (ch < '0' || ch > '9') ch = C();
    return (int)(ch - '0');
  }
  inline int operator()() {
    int ans = 0;
    char ch = C();
    int fu = 1;
    while (ch < '0' || ch > '9') {
      if (ch == '-') fu = -1;
      ch = C();
    }
    while (ch >= '0' && ch <= '9') {
      ans *= 10;
      ans += ch - '0';
      ch = C();
    }
    return ans * fu;
  }
  long long Readll() {
    long long ans = 0LL;
    long long fu = 1;
    char ch = C();
    while (ch < '0' || ch > '9') {
      if (ch == '-') fu = -1;
      ch = C();
    }
    while (ch >= '0' && ch <= '9') {
      ans *= 10LL;
      ans += ch - '0';
      ch = C();
    }
    return ans * fu;
  }
  inline void Readstring(string &x) {
    x.clear();
    char ch = C();
    while (!isdigit(ch) && !isalpha(ch)) ch = C();
    while (isdigit(ch) || isalpha(ch)) {
      x += ch;
      ch = C();
    }
  }
  inline char Specialread() {
    char ch = C();
    while (ch != '1' && ch != '0' && ch != '*') ch = C();
    return ch;
  }
} In;
inline void Read(int &x) { x = In(); }
inline void Read(int &x, int &y) {
  x = In();
  y = In();
}
inline void Read(int &x1, int &x2, int &x3) {
  x1 = In();
  x2 = In();
  x3 = In();
}
inline void Read(int &x1, int &x2, int &x3, int &x4) {
  x1 = In();
  x2 = In();
  x3 = In();
  x4 = In();
}
inline void Read(long long &x) { x = In.Readll(); }
inline void Read(long long &x, long long &y) {
  x = In.Readll();
  y = In.Readll();
}
inline void Read(long long &x1, long long &x2, long long &x3) {
  x1 = In.Readll();
  x2 = In.Readll();
  x3 = In.Readll();
}
inline void Read(long long &x1, long long &x2, long long &x3, long long &x4) {
  x1 = In.Readll();
  x2 = In.Readll();
  x3 = In.Readll();
  x4 = In.Readll();
}
clock_t _starttime, _endtime;
inline void FILEIO() {}
inline void END() { exit(0); }
int n, k;
int tot = 0;
vector<int> e[300100];
void Count() {
  for (register int(i) = 1; (i) <= (n); (i)++)
    for (register int(j) = (i + i); (j) <= (n); (j) += (i)) {
      e[j].push_back(i);
      tot++;
    }
  if (tot < k) {
    printf("No\n");
    END();
  }
}
bool choose[300100];
bool Dfs(int pos, int sel) {
  if (sel == k) return 1;
  if (pos > n || sel > k) return 0;
  choose[pos] = 1;
  int cnt = 0;
  for (register int(i) = 0; (i) < (e[pos].size()); (i)++)
    cnt += (int)(choose[e[pos][i]]);
  if (Dfs(pos + 1, sel + cnt)) return 1;
  choose[pos] = 0;
  return Dfs(pos + 1, sel);
}
void Solve() {
  bool st = Dfs(1, 0);
  if (!st) {
    printf("No\n");
    END();
  }
  int ans = 0;
  for (register int(i) = 1; (i) <= (n); (i)++) ans += (int)(choose[i]);
  printf("Yes\n%d\n", ans);
  for (register int(i) = 1; (i) <= (n); (i)++)
    if (choose[i]) printf("%d ", i);
  printf("\n");
}
int main() {
  FILEIO();
  Read(n, k);
  Count();
  Solve();
  END();
}