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.*;
import java.util.Collections;
import java.util.Scanner;

public class Main {

  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    int k = sc.nextInt();
    int num = check(n);
    if(num > k){
      System.out.println("NO");
      return;
    } else if(num == k){
      System.out.println("YES");
      int c = 0;
      while(n > 0){
        if(n%2 == 1)
          System.out.print((int)(1<<c)+" ");
        n >>= 1;
        c++;
      }
      System.out.println();
      return;
    }
    PriorityQueue<Integer> arr = new PriorityQueue<>(Collections.reverseOrder());
    int c = 0;
    int n2 = n;
    while(n2 > 0){
      if(n2%2 == 1) arr.add(c);
      c++;
      n2 /= 2;
    }
    while(arr.size() != k){
      int temp = arr.poll();
      if(temp == 0) {
        System.out.println("NO");
        return;
      }
      arr.add(temp-1);
      arr.add(temp-1);
    }
    System.out.println("YES");
    while(! arr.isEmpty()){
      System.out.print((1<<arr.poll())+" ");
    }
    System.out.println();
  }

  public static int check(int n){
    int out = 0;
    while(n > 0){
      if(n % 2 == 1) out ++;
      n /= 2;
    }
    return out;
  }


}