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 C1095 {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int N = in.nextInt();
        int K = in.nextInt();
        int bitCount = Integer.bitCount(N);
        boolean possible = bitCount <= K && K <= N;
        System.out.println(possible ? "YES" : "NO");
        if (possible) {
            int[] bits = new int[30];
            for (int bit=0; bit<30; bit++) {
                if ((N&(1<<bit)) != 0) {
                    bits[bit]++;
                }
            }
            for (int bit=29; bit>=1; bit--) {
                int split = Math.min(K-bitCount, bits[bit]);
                bitCount += split;
                bits[bit] -= split;
                bits[bit-1] += 2*split;
            }
            StringBuilder answer = new StringBuilder();
            for (int bit=0; bit<30; bit++) {
                int power = 1 << bit;
                for (int i=0; i<bits[bit]; i++) {
                    answer.append(power).append(' ');
                }
            }
            System.out.println(answer);
        }
    }

}