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.Scanner;

public class Main {

	static Scanner scan = new Scanner(System.in);
	static int n, k;
	static int[] table = new int[30];

	public static void main(String[] args) {
		n = scan.nextInt();
		k = scan.nextInt();
		table[0] = 1;
		for (int i = 1; i < table.length; i++) {
			table[i] = table[i - 1] * 2;
		}
		char[] data = Integer.toBinaryString(n).toCharArray();
		int count = 0;
		for (int i = 0; i < data.length; i++) {
			if (data[i] == '1') {
				count++;
			}
		}
		if (count > k || n < k) {
			System.out.println("NO");
			return;
		} else {
			System.out.println("YES");
			if(k==1){
				System.out.println(n);
				return;
			}
			int[] num = new int[data.length];
			for (int i = 0; i < num.length; i++) {
				if (data[i] == '1')
					num[num.length-i-1] = 1;
				else
					num[num.length-i-1] = 0;
			}
			for (int i = num.length - 2; i >= 0; i--) {
				num[i] = num[i] + num[i + 1] * 2;
				num[i + 1] = 0;
				int sum = count(num);
				if (sum >= 0) {
					fun(sum, num,i);
					break;
				}
			}

		}

	}

	static void fun(int sum, int[] num,int lie) {
		if (sum == 0) {
			print(num);
		}else{
			num[lie]=num[lie]-2*sum;
			num[lie+1]=sum;
			print(num);
		}

	}

	static void print(int[] num) {
		StringBuffer sb = new StringBuffer();
		for (int i = 0; i < num.length; i++) {
			for (int j = 0; j < num[i]; j++) {
				sb.append(table[i] + " ");
			}
		}
		System.out.println(sb);
	}

	static int count(int[] num) {
		int sum = 0;
		for (int i = 0; i < num.length; i++) {
			sum = sum + num[i];
		}
		return sum - k;
	}
}