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.Arrays;
import java.util.Scanner;

public class C {
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		int k = in.nextInt();
		
		
		int vals[] = new int[32];
		for(int i = 0; i < 32; i++) {
			if(((1 << i) & n) != 0) {
				vals[i]++;
			}
		}
		
		if(Integer.bitCount(n) > k) {
			System.out.println("NO");
			return;
		}
		
		int count = Integer.bitCount(n);
		while(count < k) {
			boolean done = false;
			for(int i = 1; i < 32 && !done; i++) {
				if(vals[i] > 0) {
					done = true;
					vals[i]--;
					vals[i-1]+=2;
					count++;
				}
			}
			if(!done) break;
			
		}
		if(count != k) {
			System.out.println("NO");
		} else {
			System.out.println("YES");
			int v = 1;
			for(int i = 0; i < 32; i++) {
				for(int j = 0; j < vals[i]; j++) {
					System.out.print(v + " ");
				}
				v*=2;
			}
		}
		
	}
}