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 JAVA):

Solution:
import java.io.*;
import java.util.*;

public class Mainn {
	FastReader scn;
	PrintWriter out;
	String INPUT = "60 191";

	void solve() {
		int n = scn.nextInt(), k = scn.nextInt();
		int[] arr = new int[n + 1];
		for(int i = 1; i <= n; i++) {
			int j = 2 * i;
			while(j <= n) {
				arr[j]++;
				j += i;
			}
		}
		
		for(int i = 1; i <= n; i++) {
			arr[i] += arr[i - 1];
		}
		
		int[] primes = linearSieve(n);
		for(int i = 1; i <= n; i++) {
			if(arr[i] >= k) {
				int diff = arr[i] - k;
				HashSet<Integer> rem = new HashSet<>();
				for(int j = i / 2 + 1; j <= i && diff > 0; j++) {
					if(Arrays.binarySearch(primes, j) >= 0) {
						rem.add(j);
						diff--;
					}
				}
				if(diff == 1) {
					rem.remove(rem.iterator().next());
					diff++;
				}
				if(diff == 2) {
					for(int j = i / 3 + 1; j <= i / 2 && diff > 0; j++) {
						if(Arrays.binarySearch(primes, j) >= 0) {
							rem.add(j);
							diff -= 2;
						}
					}
				}
				if(diff == 2) {
					rem.remove(rem.iterator().next());
					diff++;
				}
				
				if(diff == 3) {
					for(int j = i / 4 + 1; j <= i / 3 && diff > 0; j++) {
						if(Arrays.binarySearch(primes, j) >= 0) {
							rem.add(j);
							diff -= 3;
						}
					}
				}
				out.println("Yes");
				out.println(i - rem.size());
				for(int j = 1; j <= i; j++) {
					if(!rem.contains(j)) {
						out.print(j + " ");
					}
				}
				out.println();
				
				return;
			}
		}
		out.println("No");
	}
	
	int[] linearSieve(int n) {
		boolean[] isComp = new boolean[n + 1];
		int[] prime = new int[n + 1];
		int k = 0;
		for (int i = 2; i <= n; i++) {
			if (!isComp[i]) {
				prime[k++] = i;
			}
			for (int j = 0; j < k && i * 1.0 * prime[j] <= n; j++) {
				isComp[i * prime[j]] = true;
				if (i % prime[j] == 0) {
					break;
				}
			}
		}
		return Arrays.copyOf(prime, k);
	}

	void run() throws Exception {
		long time = System.currentTimeMillis();
		boolean oj = System.getProperty("ONLINE_JUDGE") != null;
		out = new PrintWriter(System.out);
		scn = new FastReader(oj);
		solve();
		out.flush();
		if (!oj) {
			System.out.println(Arrays.deepToString(new Object[] { System.currentTimeMillis() - time + " ms" }));
		}
	}

	public static void main(String[] args) throws Exception {
		new Mainn().run();
	}

	class FastReader {
		InputStream is;

		public FastReader(boolean onlineJudge) {
			is = onlineJudge ? System.in : new ByteArrayInputStream(INPUT.getBytes());

		}

		byte[] inbuf = new byte[1024];
		public int lenbuf = 0, ptrbuf = 0;

		int readByte() {
			if (lenbuf == -1)
				throw new InputMismatchException();
			if (ptrbuf >= lenbuf) {
				ptrbuf = 0;
				try {
					lenbuf = is.read(inbuf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (lenbuf <= 0)
					return -1;
			}
			return inbuf[ptrbuf++];
		}

		boolean isSpaceChar(int c) {
			return !(c >= 33 && c <= 126);
		}

		int skip() {
			int b;
			while ((b = readByte()) != -1 && isSpaceChar(b))
				;
			return b;
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		char nextChar() {
			return (char) skip();
		}

		String next() {
			int b = skip();
			StringBuilder sb = new StringBuilder();
			while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}

		char[] next(int n) {
			char[] buf = new char[n];
			int b = skip(), p = 0;
			while (p < n && !(isSpaceChar(b))) {
				buf[p++] = (char) b;
				b = readByte();
			}
			return n == p ? buf : Arrays.copyOf(buf, p);
		}

		char[][] nextMatrix(int n, int m) {
			char[][] map = new char[n][];
			for (int i = 0; i < n; i++)
				map[i] = next(m);
			return map;
		}

		int[] nextArray(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}

		long[] nextLongArray(int n) {
			long[] a = new long[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}

		int nextInt() {
			int num = 0, b;
			boolean minus = false;
			while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
				;
			if (b == '-') {
				minus = true;
				b = readByte();
			}

			while (true) {
				if (b >= '0' && b <= '9') {
					num = num * 10 + (b - '0');
				} else {
					return minus ? -num : num;
				}
				b = readByte();
			}
		}

		long nextLong() {
			long num = 0;
			int b;
			boolean minus = false;
			while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
				;
			if (b == '-') {
				minus = true;
				b = readByte();
			}

			while (true) {
				if (b >= '0' && b <= '9') {
					num = num * 10 + (b - '0');
				} else {
					return minus ? -num : num;
				}
				b = readByte();
			}
		}

		int[] shuffle(int[] arr) {
			Random r = new Random();
			for (int i = 1, j; i < arr.length; i++) {
				j = r.nextInt(i);
				arr[i] = arr[i] ^ arr[j];
				arr[j] = arr[i] ^ arr[j];
				arr[i] = arr[i] ^ arr[j];
			}
			return arr;
		}
	}
}