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.*;

public class Main {

	public static void main(String[] args) throws IOException {
		// TODO Auto-generated method stub
		BufferedReader s= new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st= new StringTokenizer(s.readLine());
		StringBuilder salida= new StringBuilder();
		int num= Integer.parseInt(st.nextToken());
		int can= Integer.parseInt(st.nextToken());
		int []pt= new int[31];
		pt[0]=1;
		for(int i=1;i<31;i++){
			pt[i]=pt[i-1]*2;
		}
		if( (can>num&&(can>(num/2)+(num%2))) || (num%2==can && num>1 )){
			System.out.println("NO");
		}
		else{
			int contador=0;
			int []res=new int[can];
			int total=can;
			if(num%2==1){
				contador++;
				res[0]=0;
			}
			while(total!=num){
				res[contador]++;
				total=0;
				for(int i=0;i<can;i++){
					total+=pt[res[i]];
				}
				if(total>num){
					if(contador+1==can){
						System.out.println("NO");
						break;
					}
					else{
						res[contador]--;
						contador++;
					}
				}
			}
			if(total==num){
				salida.append("YES");
				salida.append(System.lineSeparator());
				for(int i=0;i<can;i++){
					salida.append(pt[res[i]] + " ");
				}
				System.out.println(salida);
			}
		}
	}
}