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>
int deg[300005];
int after[300005];
int np[300005];
int bye[300005];
struct node {
  int val;
  int i;
} arr[300005];
int comparator(const void *p, const void *q) {
  int l = ((struct node *)p)->val;
  int r = ((struct node *)q)->val;
  return (l - r);
}
int binaryupper(int m, int l, int u) {
  int mid, c = 0;
  if (l <= u) {
    mid = (l + u) / 2;
    if (m == arr[mid].val) {
      c = m;
      return binaryupper(m, mid + 1, u);
    } else if (m < arr[mid].val) {
      return binaryupper(m, l, mid - 1);
    } else {
      return binaryupper(m, mid + 1, u);
    }
  } else
    return u;
}
int main() {
  int n, k;
  scanf("%d %d", &n, &k);
  for (int i = 1; i <= n; i++) {
    for (int j = i * 2; j <= n; j = j + i) {
      deg[j]++;
    }
  }
  np[0] = np[1] = 1;
  for (int i = 2; i <= n; i++) {
    for (int j = i * 2; j <= n; j = j + i) {
      np[j] = 1;
    }
  }
  int now = 0;
  int m;
  for (m = 1; m <= n && now < k; ++m) {
    now += deg[m];
  }
  --m;
  for (int i = 1; i <= m; i++) {
    for (int j = i * 2; j <= m; j = j + i) {
      after[i]++;
    }
  }
  if (now < k) {
    printf("No\n");
    return 0;
  }
  int cnt = 0;
  for (int i = 2; i <= m; i++) {
    arr[cnt].val = deg[i] + after[i];
    arr[cnt].i = i;
    cnt++;
  }
  qsort((void *)arr, cnt, sizeof(arr[0]), comparator);
  int i;
  int byecnt = 0;
  while (now > k) {
    int it = binaryupper(now - k, 2, cnt);
    it--;
    bye[arr[it].i] = 1;
    byecnt++;
    now = now - arr[it].val;
    for (it; it <= cnt - 1; it++) {
      arr[it].i = arr[it + 1].i;
      arr[it].val = arr[it + 1].val;
    }
    cnt--;
  }
  printf("Yes\n");
  printf("%d\n", m - byecnt);
  for (int i = 1; i <= m; i++)
    if (!bye[i]) printf("%d ", i);
}