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:
//package Codef;

import java.util.ArrayList;
import java.util.Scanner;

public class C_1095 {
	static String ans = "";

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner s = new Scanner(System.in);

		int n = s.nextInt();
		int k = s.nextInt();
		if (k > n || totalPower(n) > k) {
			System.out.println("NO");
			return;
		}

		System.out.println("YES");
		while (k > 0) {
			int tmp = lp2(n);
			//System.out.println(tmp);
			while (n - tmp < k - 1) {
				tmp /= 2;
			}
			n -= tmp;
			k--;
			System.out.print(tmp + " ");
		}
	}

	static int totalPower(int n) {
		int res = 0;
		while (n > 0) {
			n -= lp2(n);
			res++;
		}

		return res;
	}

	static int lp2(int n) {
		int res = 1;
		while (res <= n) {
			res <<= 1;
		}

		return res /2;

	}

}