Problem: A positive integer x is called a power of two if it can be represented as x = 2^y, where y is a non-negative integer. So, the powers of two are 1, 2, 4, 8, 16, ....

You are given two positive integers n and k. Your task is to represent n as the sum of exactly k powers of two.

Input

The only line of the input contains two integers n and k (1 ≤ n ≤ 10^9, 1 ≤ k ≤ 2 ⋅ 10^5).

Output

If it is impossible to represent n as the sum of k powers of two, print NO.

Otherwise, print YES, and then print k positive integers b_1, b_2, ..., b_k such that each of b_i is a power of two, and ∑ _{i = 1}^{k} b_i = n. If there are multiple answers, you may print any of them.

Examples

Input


9 4


Output


YES
1 2 2 4 


Input


8 1


Output


YES
8 


Input


5 1


Output


NO


Input


3 7


Output


NO

Solution (in JAVA):

Solution:
import java.io.*;
import java.math.*;
import java.text.*;
import java.util.*;
import java.util.regex.*;

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

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

        public int read() {
            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 nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long nextLong() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

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

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

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

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

        private boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }
    }
    public static void main(String[] args) throws IOException 
    {
        InputReader in=new InputReader(System.in);
        PrintWriter w=new PrintWriter(System.out);
        int n=in.nextInt();
        int k=in.nextInt();
        String s=Integer.toBinaryString(n);
        boolean odd=false;
        int oc=Integer.bitCount(n);
        if(oc>k || k>n)
        {
            w.println("NO");
        }
        else if(oc==k)
        {
            w.println("YES");
            long power=1;
            for(int i=s.length()-1;i>=0;i--)
            {
                if(s.charAt(i)=='1')
                {
                    w.print(power+" ");
                }
                power=power*2L;
            }
        }
        else
        {
            w.println("YES");
            if(n%2==1)
            {
                w.print("1 ");
                n--;
                odd=true;
                k--;
            }
            int num=n/2;
            if(k>num)
            {
                int dif=k-num;
                for(int i=0;i<dif;i++)
                {
                    w.print("1 1 ");
                    k--;
                }
                for(int i=0;i<num-dif;i++)
                {
                    w.print("2 ");
                }
            }
            else if(k==num)
            {
                for(int i=0;i<k;i++)
                {
                    w.print("2 ");
                }
            }
            else
            {
                if(odd)
                {
                    s=Integer.toBinaryString(n);
                }
                int[] ar=new int[32];
                for(int i=0;i<s.length();i++)
                {
                    ar[i]=(int)s.charAt(s.length()-i-1)-48;
                    k-=(int)s.charAt(s.length()-i-1)-48;
                }
                int i=31;
                while(i>0 && k>0)
                {
                    if(k-ar[i]<0)
                    {
                        break;
                    }
                    ar[i-1]+=2*ar[i];
                    k-=ar[i];
                    ar[i]=0;
                    i--;
                }
                if(k!=0)
                {
                    ar[i-1]+=2*k;
                    ar[i]-=k;
                    k=0;
                }
                long power=1L;
                for(i=0;i<32;i++)
                {
                    if(ar[i]!=0)
                    {
                        for(int j=0;j<ar[i];j++)
                        {
                            w.print(power+" ");
                        }
                    }
                    power=power*2L;
                }
            }
        }
        w.close();
    }
}