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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;

public class Main {
    public static void main(String[] args) throws IOException {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        int[] s = Arrays.stream(reader.readLine().split(" "))
                .mapToInt(Integer::parseInt)
                .toArray();
        int n = s[0], k = s[1];
        char[] t = Integer.toBinaryString(n).toCharArray();
        int[] onesArray = new int[t.length];
        for (int i = 0; i < t.length; i++) {
            onesArray[i] = t[i] == '1' ? 1 : 0;
        }
        int ones = 0;
        for (int i = 0; i < t.length; i++) {
            ones += onesArray[i];
        }
        if (ones > k) {
            System.out.println("NO");
            return;
        }
        while (ones < k) {
            boolean upd = false;
            for (int i = 0; i < onesArray.length - 1; i++) {
                if (onesArray[i] > 0) {
                    onesArray[i]--;
                    onesArray[i+1] += 2;
                    ones++;
                    upd = true;
                    break;
                }
            }
            if (!upd) {
                System.out.println("NO");
                return;
            }
        }
        System.out.println("YES");
        int number = 1;
        for (int i = onesArray.length - 1; i >= 0; i--) {
            for (int j = 0; j < onesArray[i]; j++) {
                System.out.print(number + " ");
            }
            number *= 2;
        }
    }
}