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:
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import java.util.*;
import java.lang.*;
import java.io.*;
public class Main
{
	//Fast IO class
    static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
        public FastReader() 
        { 
        	boolean env=System.getProperty("ONLINE_JUDGE") != null;
        	if(!env) {
        		try {
					br=new BufferedReader(new FileReader("src\\input.txt"));
				} catch (FileNotFoundException e) {
					e.printStackTrace();
				}
        	}
        	else {
        		br = new BufferedReader(new
                        InputStreamReader(System.in)); 
        	}
        } 
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    }     
    static long MOD=1000000000+7;
    //Euclidean Algorithm
    static long gcd(long A,long B){
        if(B==0) return A;
        return gcd(B,A%B);
    }
    //Modular Exponentiation
    static long fastExpo(long x,long n){
        if(n==0) return 1;
        if((n&1)==0) return fastExpo((x*x)%MOD,n/2)%MOD;
        return ((x%MOD)*fastExpo((x*x)%MOD,(n-1)/2))%MOD;
    }
    //Prime Number Algorithm
    static boolean isPrime(long n){
        if(n<=1) return false;
        if(n<=3) return true;
        if(n%2==0 || n%3==0) return false;
        for(int i=5;i*i<=n;i+=6)
            if(n%i==0 || n%(i+2)==0) return false;
        return true;
    }
    //Sieve of eratosthenes
    static int[] findPrimes(int n){
        boolean isPrime[]=new boolean[n+1];
        ArrayList<Integer> a=new ArrayList<>();
        int result[];
        Arrays.fill(isPrime,true);
        isPrime[0]=false;
        isPrime[1]=false;
        for(int i=2;i*i<=n;++i)
            if(isPrime[i]==true)
                for(int j=i*i;j<=n;j+=i) isPrime[j]=false;
        for(int i=0;i<=n;i++) if(isPrime[i]==true) a.add(i);
        result=new int[a.size()];
        for(int i=0;i<a.size();i++) result[i]=a.get(i);
        return result;
    } 
    // Pair
    static class pair{
    	int x,y;
    	pair(int a,int b){
    		this.x=a;
    		this.y=b;
    	}
    	public boolean equals(Object obj) {
    		if(obj == null || obj.getClass()!= this.getClass()) 
                return false;
            pair p = (pair) obj;
            return (this.x==p.x && this.y==p.y);
        }
    	public int hashCode() {
            return Objects.hash(x,y);
        }
    }
    //Main function(The main code starts from here)
    public static void main (String[] args) throws java.lang.Exception
    {
        FastReader sc=new FastReader();
        PrintWriter out=new PrintWriter(System.out);
    	int test=1;
        while(test-->0) {
        	long n=sc.nextLong(),k=sc.nextLong();
        	long x=n;
        	int ones=0,idx=0;
        	ArrayList<Integer> pow=new ArrayList<>();
        	while(x>0) {
        		long f=(x&1);
        		if(f==1) {
        			pow.add(idx);
        			ones++;
        		}
        		x=x>>1;
                idx++;
        	}
        	if(k<ones || k>n) {
        		System.out.println("NO");
        		return;
        	}
        	out.println("YES");
        	k-=pow.size();
        	int i=0;
        	while(k>0) {
        		if(pow.get(i)==0) {
        			i++;
        			continue;
        		}
        		pow.set(i, pow.get(i)-1);
        		pow.add(pow.get(i));
        		k--;
        	}
        	for(Integer num: pow) out.print((long)Math.pow(2, num)+" "); 
        }
        out.close();
    }
}