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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.OutputStream;
import java.util.Arrays;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.FileNotFoundException;
import java.util.StringTokenizer;
import java.io.Writer;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Asgar Javadov
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        FastWriter out = new FastWriter(outputStream);
        TaskF solver = new TaskF();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskF {
        public void solve(int testNumber, InputReader in, FastWriter out) {
            int n = in.nextInt();
            int k = in.nextInt();

            int[] lower = new int[n + 1];
            for (int i = 1; i <= n; ++i) {
                for (int j = 2 * i; j <= n; j += i) {
                    ++lower[j];
                }
            }

            int total = 0;
            int m;
            for (m = 1; m <= n && total < k; ++m) {
                total += lower[m];
            }
            --m;

            int[] upper = new int[m + 1];
            for (int i = 1; i <= m; ++i) {
                for (int j = 2 * i; j <= m; j += i) {
                    ++upper[i];
                }
            }

            if (total < k) {
                out.println("No");
            } else if (total == k) {
                out.println("Yes");
                out.println(m);
                for (int i = 1; i <= m; ++i) {
                    if (i > 1)
                        out.print(' ');
                    out.print(i);
                }
                out.println();
            }
//        else if (k <= 6) {
//            for (int i = m; i > 0; --i) {
//                if (total - lower[i] == k) {
//                    out.println("Yes");
//                    out.println(m - 1);
//                    for (int j = 1; j <= m; ++j) {
//                        if (j != i) {
//                            out.print(j);
//                            out.print(' ');
//                        }
//                    }
//                    out.println();
//                    return;
//                }
//            }
//        }
            else {
//            int[] primes = NumberTheory.primes(m);
                boolean[] removed = new boolean[m + 1];

                int count = m;
//            int index = primes.length - 1;
//            int half = m / 2 + 1;
//            while (total > k && index >= 0 && primes[index] > half) {
//                removed[primes[index]] = true;
//                --count;
//                --total;
//                --index;
//            }
//            if (total > k) {
//                for (int i = m; i > half && total > k; --i) {
//                    if (lower[i] <= total - k) {
//                        total -= lower[i];
//                        --count;
//                    }
//                }
//            }

                MathUtils.Pair<Integer, Integer>[] pairs = new MathUtils.Pair[m];
                for (int i = 0; i < m; ++i) {
                    pairs[i] = new MathUtils.Pair<>(lower[i + 1] + upper[i + 1], i + 1);
                }

                Arrays.sort(pairs);
                MathUtils.Pair<Integer, Integer> temp = new MathUtils.Pair<>(0, 0);

                total -= k;
                while (total > 0) {
                    temp.first = total;
                    int pos = ArrayUtils.upperBound(pairs, temp);
                    removed[pairs[pos].second] = true;
                    total -= pairs[pos].first;
                    --count;
                }

                out.println("Yes");
                out.println(count);
                for (int i = 1; i <= m; ++i) {
                    if (!removed[i]) {
                        out.print(i);
                        out.print(' ');
                    }
                }
                out.println();
            }
        }

    }

    static class MathUtils {
        public static class Pair<K extends Comparable<K>, V> implements Comparable<MathUtils.Pair<K, V>> {
            public K first;
            public V second;

            public Pair(K first, V second) {
                this.first = first;
                this.second = second;
            }


            public int compareTo(MathUtils.Pair<K, V> o) {
                return first.compareTo(o.first);
            }

        }

    }

    static class FastWriter extends PrintWriter {
        public FastWriter(OutputStream outputStream) {
            super(outputStream);
        }

        public FastWriter(Writer writer) {
            super(writer);
        }

        public FastWriter(String filename) throws FileNotFoundException {
            super(filename);
        }

    }

    static class InputReader extends BufferedReader {
        StringTokenizer tokenizer;

        public InputReader(InputStream inputStream) {
            super(new InputStreamReader(inputStream), 32768);
        }

        public InputReader(String filename) {
            super(new InputStreamReader(Thread.currentThread().getContextClassLoader().getResourceAsStream(filename)));
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(readLine());
                } catch (IOException e) {
                    throw new RuntimeException();
                }
            }
            return tokenizer.nextToken();
        }

        public Integer nextInt() {
            return Integer.valueOf(next());
        }

    }

    static class ArrayUtils {
        public static <T extends Comparable<T>> int upperBound(T[] array, T val) {
            int low = 0, high = array.length - 1;
            while (low <= high) {
                int mid = low + high >> 1;
                if (val.compareTo(array[mid]) < 0)
                    high = mid - 1;
                else
                    low = mid + 1;
            }
            return high;
        }

    }
}