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.Closeable;
import java.io.IOException;
import java.io.PrintWriter;
import java.util.Scanner;

/**
 * @author Lu Kongwen
 * @version Create time：2019-1-4 上午10:30:20
 * @Description
 */
public class Test implements Closeable {

	private PrintWriter out = new PrintWriter(System.out);

	public static void main(String args[]) throws IOException {

		try (Test instance = new Test()) {
			instance.init();
		}
	}

	public void init() {

		Scanner scan = new Scanner(System.in);

		int n = scan.nextInt();

		int k = scan.nextInt();

		if (k > n) {
			out.println("NO");
			return;
		}

		int[] arr = new int[31];
		int sum = 0;
		for (int i = 0; i <= 30; i++) {
			int bit = 1 << i;
			if ((n & bit) != 0) {
				sum++;
				arr[i]++;
			}
		}

		if (sum > k) {
			out.println("NO");
			return;
		}

		out.println("YES");

		int pos = 30;
		while (pos >= 0) {

			if (sum == k) {
				break;
			}

			if (arr[pos] == 0) {
				pos--;
				continue;
			}

			arr[pos]--;
			arr[pos - 1] = arr[pos - 1] + 2;
			sum++;
		}

		for (int i = 0; i < 30; i++) {
			for (int j = 0; j < arr[i]; j++) {
				out.print((1 << (i)) + " ");
			}

		}
	}

	@Override
	public void close() throws IOException {
		out.close();
	}

}