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.util.*;

public class CCC {
	
    //static FastInput k = new FastInput("C:/Users/rajkin.h/Desktop/input.txt");
    static FastInput k = new FastInput(System.in);
    static FastOutput z = new FastOutput();
    static int n, K;
    static Treap powers;
    
    static int log(int n) {
    	return 31 - Integer.numberOfLeadingZeros(n);
    }
    
    public static void main(String[] args) throws Exception {
    	while(k.hasNext()){
    		n = k.nextInt();
    		K = k.nextInt();
    		powers = new Treap();
    		
    		while(n > 0) {
    			int log = log(n);
    			powers.insert(log);
    			n -= (1<<log);
    		}
    		
    		if(powers.length > K) {
    			z.println("NO");
    			continue;
    		}
    		
    		boolean isFound = false;
    		
    		while(true) {
    			long maxPower = powers.getMax();
    			//if(maxPower == (long)0) break;
    			if(powers.length == K) {
    				isFound = true;
    				break;
    			}
    			
    			if(maxPower == (long)0) break;
    			
    			powers.delete(maxPower);
    			
    			powers.insert(maxPower-1);
    			powers.insert(maxPower-1);
    		}
    		
    		if(isFound) {
    			z.println("YES");
        		while(powers.length != 0) {
        			long maxValue = powers.getMax();
        			z.print((1<<(int)maxValue)+" ");
        			powers.delete(maxValue);
        		}
        		
        		z.println();
    		}
    		else {
    			z.println("NO");
    		}
    	}
    	
    	z.flush();
    	System.exit(0);
    }
    
    public static class FastInput {
        BufferedReader reader;
        StringTokenizer tokenizer;
 
        public FastInput(InputStream stream){
        	reader = new BufferedReader(new InputStreamReader(stream));
        }
        
	    public FastInput(String path){
	        try {
	        	reader = new BufferedReader(new FileReader(path));
			} catch (FileNotFoundException e) {
				// TODO Auto-generated catch block
				e.printStackTrace();
			}
	        tokenizer = null;
	    }
 
        public String next() {
            return nextToken();
        }
        
        public String nextLine() {
            try {
				return reader.readLine();
			} catch (IOException e) {
				// TODO Auto-generated catch block
				e.printStackTrace();
			}
            
            return null;
        }
 
        public boolean hasNext(){
            try {
                return reader.ready();
            } catch (IOException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
            }
            return false;
        }
 
        public String nextToken() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                String line = null;
                try {
                    line = reader.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
                if (line == null) {
                    return null;
                }
                tokenizer = new StringTokenizer(line);
            }
            return tokenizer.nextToken();
        }
 
        public Integer nextInt() {
            return Integer.parseInt(nextToken());
        }
       
        public Long nextLong() {
            return Long.valueOf(nextToken());
        }
    }
    
    public static class FastOutput extends PrintWriter {
    	public FastOutput() { 
            super(new BufferedOutputStream(System.out)); 
    	}
    }
    
    static class Treap {
        Node root;
       
        int length;
        int g_seed;
        int ans;
 
        long lowerValue, higherValue;
        long ceilValue, floorValue;
       
        public Treap(){
            g_seed = 1;
            length = 0;
           
            lowerValue = higherValue = -1;
            ceilValue = floorValue = -1;
        }
       
        int fastrand() {
            g_seed = (214013 * g_seed + 2531011);
           
            return (g_seed>>16) & 0x7FFF;
        }
       
        int getSize(Node cursor){
            if(cursor == null) return 0;
            int leftSubTreeSize = cursor.left != null ? cursor.left.size : 0;
            int rightSubTreeSize = cursor.right != null ? cursor.right.size : 0;
           
            return 1 + leftSubTreeSize + rightSubTreeSize;
        }
       
        Node rotateRight(Node cursor){
            Node returedNode = cursor.left;
           
            Node z = cursor.left.right;
            cursor.left.right = cursor;
            cursor.left = z;
           
            return returedNode;
        }
       
        Node rotateLeft(Node cursor){
            Node returedNode = cursor.right;
           
            Node z = cursor.right.left;
            cursor.right.left = cursor;
            cursor.right = z;
           
            return returedNode;
        }
       
        Node insert(Node cursor, long value){
            if(cursor == null) {
                return new Node(value);
            }
           
            if(value < cursor.value){
                cursor.left = insert(cursor.left, value);
               
                if(cursor.left.priority > cursor.priority){
                    cursor = rotateRight(cursor);
                }
            }
            else{
                cursor.right = insert(cursor.right, value);
               
                if(cursor.right.priority > cursor.priority){
                    cursor = rotateLeft(cursor);
                }
            }
           
            if(cursor.left != null) cursor.left.size = getSize(cursor.left);
            if(cursor.right != null) cursor.right.size = getSize(cursor.right);
           
            cursor.size = getSize(cursor);
           
            return cursor;
        }
        
        void insert(long value){
            root = insert(root, value);
            length++;
        }
       
        long getMax(Node cursor){
            if(cursor == null){
            	return -1;
            }
            
            if(cursor.right == null) return cursor.value;
            
            return getMax(cursor.right);
        }
       
        long getMax(){
            return getMax(root);
        }
       
        Node delete(Node cursor, long key) {
            if (cursor == null) return cursor;
           
            if (key < cursor.value) {
                cursor.left = delete(cursor.left, key);
            }
            else if (key > cursor.value) {
                cursor.right = delete(cursor.right, key);
            }
            else if (cursor.left == null) {
                cursor = cursor.right;
            }
            else if (cursor.right == null) {
                cursor = cursor.left;
            }
            else if (cursor.left.priority < cursor.right.priority){
                cursor = rotateLeft(cursor);
                cursor.left = delete(cursor.left, key);
            }
            else {
                cursor = rotateRight(cursor);
                cursor.right = delete(cursor.right, key);
            }
           
            if(cursor != null) {
                if(cursor.left != null) cursor.left.size = getSize(cursor.left);
                if(cursor.right != null) cursor.right.size = getSize(cursor.right);
               
                cursor.size = getSize(cursor);
            }
         
            return cursor;
        }
       
        void delete(long key){
            root = delete(root, key);
            length--;
        }

        class Node {
            double priority;
            long value;
            int size;
           
            Node left, right;
            public Node(long value){
                this.value = value;
                //this.priority = Math.random();
                this.priority = fastrand();
            }
        }
	}
}