Jamie is preparing a Codeforces round. He has got an idea for a problem, but does not know how to solve it. Help him write a solution to the following problem:

Find k integers such that the sum of two to the power of each number equals to the number n and the largest integer in the answer is as small as possible. As there may be multiple answers, you are asked to output the lexicographically largest one. 

To be more clear, consider all integer sequence with length k (a1, a2, ..., ak) with <image>. Give a value <image> to each sequence. Among all sequence(s) that have the minimum y value, output the one that is the lexicographically largest.

For definitions of powers and lexicographical order see notes.

Input

The first line consists of two integers n and k (1 ≤ n ≤ 1018, 1 ≤ k ≤ 105) — the required sum and the length of the sequence.

Output

Output "No" (without quotes) in a single line if there does not exist such sequence. Otherwise, output "Yes" (without quotes) in the first line, and k numbers separated by space in the second line — the required sequence.

It is guaranteed that the integers in the answer sequence fit the range [ - 1018, 1018].

Examples

Input

23 5


Output

Yes
3 3 2 1 0 


Input

13 2


Output

No


Input

1 2


Output

Yes
-1 -1 

Note

Sample 1:

23 + 23 + 22 + 21 + 20 = 8 + 8 + 4 + 2 + 1 = 23

Answers like (3, 3, 2, 0, 1) or (0, 1, 2, 3, 3) are not lexicographically largest.

Answers like (4, 1, 1, 1, 0) do not have the minimum y value.

Sample 2:

It can be shown there does not exist a sequence with length 2.

Sample 3:

<image>

Powers of 2:

If x > 0, then 2x = 2·2·2·...·2 (x times).

If x = 0, then 2x = 1.

If x < 0, then <image>.

Lexicographical order:

Given two different sequences of the same length, (a1, a2, ... , ak) and (b1, b2, ... , bk), the first one is smaller than the second one for the lexicographical order, if and only if ai < bi, for the first i where ai and bi differ.
import java.util.*;
import java.io.*;

/**
 * 19-Jan-2018
 * 8:11:58 PM
 * @author HulkBuster
 *
 */
public class CF916 {
	public static int mod = (int) (1e9 + 7);
	public static InputReader in;
	public static PrintWriter out;

	public static void solve() throws FileNotFoundException {

		in = new InputReader(System.in);
		out = new PrintWriter(System.out);

		long n = in.nl();
		int k = in.ni();


		PriorityQueue<Integer>qq = new PriorityQueue<>(Collections.reverseOrder());
		HashMap<Integer,Integer>hmp = new HashMap<>();
		int c = 0;
		while(n>0) {
			if(n%2==1) {
				qq.add(c);
                hmp.put(c,1);
			}
			c++;
			n  = n/2;
		}
		if(qq.size()>k) {
			out.println("No");
		}
		else {
			while(qq.size()<k) {
			    int r = k-qq.size();
				int p = qq.peek();
				if(hmp.get(p)>r){
				    break;
                }
                else{
				    qq.poll();
                    qq.add(p-1);
                    qq.add(p-1);
                    int z = hmp.get(p);
                    hmp.put(p,z-1);
                    int y = 0;
                    if(hmp.containsKey(p-1))
                        y = hmp.get(p-1);
                    y+=2;
                    hmp.put(p-1,y);

                }

			}
			int sz = qq.size();
			out.println("Yes");
			int ar[] = new int[k];
			for(int i=0;i<sz-1;i++) {
				ar[i]= qq.poll();
				out.print(ar[i]+" ");
			}
			if(sz==k)
			    out.print(qq.poll());
			else{
			    int ll =qq.poll();
			    for(int i=sz-1;i<(k-1);i++){
			        ll =ll-1;
			        out.print(ll+" ");
                }
                out.println(ll);
            }
		}

		out.close();
	}

	public static void main(String[] args) {
		new Thread(null, new Runnable() {
			public void run() {
				try {
					solve();
				} catch (Exception e) {
					e.printStackTrace();
				}
			}
		}, "1", 1 << 26).start();
	}

	static class Pair implements Comparable<Pair> {

		int x, y, i;

		Pair(int x, int y, int i) {
			this.x = x;
			this.y = y;
			this.i = i;
		}

		Pair(int x, int y) {
			this.x = x;
			this.y = y;
		}

		public int compareTo(Pair o) {
			if (this.x != o.x)
				return Integer.compare(this.x, o.x);
			else
				return Integer.compare(this.y, o.y);
			//return 0;
		}

		public boolean equals(Object o) {
			if (o instanceof Pair) {
				Pair p = (Pair) o;
				return p.x == x && p.y == y && p.i == i;
			}
			return false;
		}

		public int hashCode() {
			return new Integer(x).hashCode() * 31 + new Integer(y).hashCode() + new Integer(i).hashCode() * 37;
		}

	}

	public static long add(long a, long b) {
		long x = (a + b);
		while (x >= mod)
			x -= mod;
		return x;
	}

	public static long sub(long a, long b) {
		long x = (a - b);
		while (x < 0)
			x += mod;
		return x;
	}

	public static long mul(long a, long b) {
		long x = (a * b);
		while (x >= mod)
			x -= mod;
		return x;
	}

	public static boolean isPal(String s) {
		for (int i = 0, j = s.length() - 1; i <= j; i++, j--) {
			if (s.charAt(i) != s.charAt(j))
				return false;
		}
		return true;
	}

	public static String rev(String s) {
		StringBuilder sb = new StringBuilder(s);
		sb.reverse();
		return sb.toString();
	}

	public static long gcd(long x, long y) {
		if (x % y == 0)
			return y;
		else
			return gcd(y, x % y);
	}

	public static int gcd(int x, int y) {
		if (x % y == 0)
			return y;
		else
			return gcd(y, x % y);
	}

	static int modInverse(int a, int m) {
		int m0 = m, t, q;
		int x0 = 0, x1 = 1;
		if (m == 1)
			return 0;
		while (a > 1) {
			// q is quotient
			q = a / m;
			t = m;
			// m is remainder now, process same as
			// Euclid's algo
			m = a % m;
			a = t;
			t = x0;
			x0 = x1 - q * x0;
			x1 = t;
		}
		// Make x1 positive
		if (x1 < 0)
			x1 += m0;
		return x1;
	}

	public static long gcdExtended(long a, long b, long[] x) {

		if (a == 0) {
			x[0] = 0;
			x[1] = 1;
			return b;
		}
		long[] y = new long[2];
		long gcd = gcdExtended(b % a, a, y);

		x[0] = y[1] - (b / a) * y[0];
		x[1] = y[0];

		return gcd;
	}

	public static long mulmod(long a, long b, long m) {
		if (m <= 1000000009)
			return a * b % m;

		long res = 0;
		while (a > 0) {
			if ((a & 1) != 0) {
				res += b;
				if (res >= m)
					res -= m;
			}
			a >>= 1;
			b <<= 1;
			if (b >= m)
				b -= m;
		}
		return res;
	}

	public static int abs(int a, int b) {
		return (int) Math.abs(a - b);
	}

	public static long abs(long a, long b) {
		return (long) Math.abs(a - b);
	}

	public static int max(int a, int b) {
		if (a > b)
			return a;
		else
			return b;
	}

	public static int min(int a, int b) {
		if (a > b)
			return b;
		else
			return a;
	}

	public static long max(long a, long b) {
		if (a > b)
			return a;
		else
			return b;
	}

	public static long min(long a, long b) {
		if (a > b)
			return b;
		else
			return a;
	}

	public static long pow(long n, long p, long m) {
		long result = 1;
		if (p == 0)
			return 1;
		if (p == 1)
			return n;
		while (p != 0) {
			if (p % 2 == 1)
				result *= n;
			if (result >= m)
				result %= m;
			p >>= 1;
			n *= n;
			if (n >= m)
				n %= m;
		}
		return result;
	}

	public static long pow(long n, long p) {
		long result = 1;
		if (p == 0)
			return 1;
		if (p == 1)
			return n;
		while (p != 0) {
			if (p % 2 == 1)
				result *= n;
			p >>= 1;
			n *= n;
		}
		return result;
	}

	public static void debug(Object... o) {
		System.out.println(Arrays.deepToString(o));
	}

	static class InputReader {
		private final InputStream stream;
		private final byte[] buf = new byte[8192];
		private int curChar, snumChars;
		private SpaceCharFilter filter;

		public InputReader(InputStream stream) {
			this.stream = stream;
		}

		public int snext() {
			if (snumChars == -1)
				throw new InputMismatchException();
			if (curChar >= snumChars) {
				curChar = 0;
				try {
					snumChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (snumChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		public int ni() {
			int c = snext();
			while (isSpaceChar(c)) {
				c = snext();
			}
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = snext();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = snext();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public long nl() {
			int c = snext();
			while (isSpaceChar(c)) {
				c = snext();
			}
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = snext();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = snext();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public int[] nIArr(int n) {
			int a[] = new int[n];
			for (int i = 0; i < n; i++) {
				a[i] = ni();
			}
			return a;
		}

		public long[] nLArr(int n) {
			long a[] = new long[n];
			for (int i = 0; i < n; i++) {
				a[i] = nl();
			}
			return a;
		}

		public String readString() {
			int c = snext();
			while (isSpaceChar(c)) {
				c = snext();
			}
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = snext();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		public String nextLine() {
			int c = snext();
			while (isSpaceChar(c))
				c = snext();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = snext();
			} while (!isEndOfLine(c));
			return res.toString();
		}

		public boolean isSpaceChar(int c) {
			if (filter != null)
				return filter.isSpaceChar(c);
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		private boolean isEndOfLine(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}

		public interface SpaceCharFilter {
			public boolean isSpaceChar(int ch);
		}

	}
}