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.util.*;import java.io.*;import java.math.*;

public class Main
{
	static void print_res(int arr[]){
		StringBuilder res = new StringBuilder();
		for(int i=0;i<=50;i++){
			if(arr[i]==0)
				continue;

			long ele=(long)Math.pow(2,i);
			for(int j=1;j<=arr[i];j++)
				res.append(ele+" ");
		}
		pn("YES\n"+res);
	}

    public static void process()throws IOException
    {
    	int n=ni(),k=ni(),cnt=0;

    	int bin[]=new int[60];

    	int temp=n,place=0;
    	while(temp!=0){
    		int rem=temp%2;
    		cnt+=(rem==1?1:0);
    		bin[place]=rem;
    		temp/=2;
    		place++;
    	}

    	if(cnt<k){
    		for(int i=35;i>0;i--){
    			temp=bin[i];
    			for(int j=1;j<=temp;j++){
    				if(cnt==k)
    					break;

    				cnt++;
    				bin[i]--;
    				bin[i-1]+=2;
    			}
    		}
    	}
    	// else if(cnt>k){
    	// 	for(int i=0;i<=40;i++){
    	// 		temp=bin[i];

    	// 		for(int j=1;j<=temp;j+=2){
    	// 			if(cnt==k || bin[i]<2)
    	// 				break;

    	// 			cnt--;
    	// 			bin[i]-=2;
    	// 			bin[i+1]++;
    	// 		}
    	// 	}
    	// }

    	if(cnt==k){
    		print_res(bin);
    	}
    	else{
    		pn("NO");
    	}
    }


    static AnotherReader sc;
    static PrintWriter out;
    public static void main(String[]args)throws IOException
    {
        out = new PrintWriter(System.out);
        sc=new AnotherReader();
        boolean oj = true;

    	oj = System.getProperty("ONLINE_JUDGE") != null;
    	if(!oj) sc=new AnotherReader(100);

        long s = System.currentTimeMillis();
        int t=1;
		//t=ni();
        while(t-->0)
            process();
        out.flush();
        if(!oj)
            System.out.println(System.currentTimeMillis()-s+"ms");
        System.out.close();  
    }
	
    
    static void pn(Object o){out.println(o);}
    static void p(Object o){out.print(o);}
    static void pni(Object o){out.println(o);System.out.flush();}
    static int ni()throws IOException{return sc.nextInt();}
    static long nl()throws IOException{return sc.nextLong();}
    static double nd()throws IOException{return sc.nextDouble();}
    static String nln()throws IOException{return sc.nextLine();}
    static long gcd(long a, long b)throws IOException{return (b==0)?a:gcd(b,a%b);}
    static int gcd(int a, int b)throws IOException{return (b==0)?a:gcd(b,a%b);}
    static int bit(long n)throws IOException{return (n==0)?0:(1+bit(n&(n-1)));}
    static boolean multipleTC=false;
    static long mod=(long)1e9+7l;

    static void r_sort(int arr[],int n){
        Random r = new Random(); 
        for (int i = n-1; i > 0; i--){ 
            int j = r.nextInt(i+1); 
                  
            int temp = arr[i]; 
            arr[i] = arr[j]; 
            arr[j] = temp; 
        } 
        Arrays.sort(arr); 
    }

    static long mpow(long x, long n) {
        if(n == 0)
            return 1;
        if(n % 2 == 0) {
            long root = mpow(x, n / 2);
            return root * root % mod;
        }else {
            return x * mpow(x, n - 1) % mod;
        }
    }
    
    static long mcomb(long a, long b) {
        if(b > a - b)
            return mcomb(a, a - b);
        long m = 1;
        long d = 1;
        long i;
        for(i = 0; i < b; i++) {
            m *= (a - i);
            m %= mod;
            d *= (i + 1);
            d %= mod;
        }
        long ans = m * mpow(d, mod - 2) % mod;
        return ans;
    }
/////////////////////////////////////////////////////////////////////////////////////////////////////////

    static class AnotherReader{BufferedReader br; StringTokenizer st;
    AnotherReader()throws FileNotFoundException{
    br=new BufferedReader(new InputStreamReader(System.in));}
    AnotherReader(int a)throws FileNotFoundException{
    br = new BufferedReader(new FileReader("input.txt"));}
    String next()throws IOException{
    while (st == null || !st.hasMoreElements()) {try{
    st = new StringTokenizer(br.readLine());}
    catch (IOException  e){ e.printStackTrace(); }}
    return st.nextToken(); } int nextInt() throws IOException{
    return Integer.parseInt(next());}
    long nextLong() throws IOException
    {return Long.parseLong(next());}
    double nextDouble()throws IOException { return Double.parseDouble(next()); }
    String nextLine() throws IOException{ String str = ""; try{
    str = br.readLine();} catch (IOException e){
    e.printStackTrace();} return str;}}
/////////////////////////////////////////////////////////////////////////////////////////////////////////////
}