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 Solution{
    static int[] getPowerArray(int n){
        int[] powers = new int[32];
        for(int i = 0; i < powers.length; i++){
            powers[i] = ((n >> i) & 1);
        }

        return powers;
    }

    static int getCount(int[] powers){
        int res = 0;
        for(int i = 0; i < powers.length; i++) res += powers[i];
        return res;
    }

    static void process(int[] powers, int k){
        for(int i = 31; i > 0; i--){
            int curCount = getCount(powers);
            int lagging = k - curCount;

            if(lagging <= 0) return;

            int toSwap = Math.min(lagging, powers[i]);
            powers[i] -= toSwap;
            powers[i - 1] += 2*toSwap;
        }

    }

    static void printPowerOfTwo(int[] powers){
        StringBuilder stringBuilder = new StringBuilder();
        for(int i = 0; i < powers.length; i++){
            while (powers[i]-- > 0){
                stringBuilder.append((Math.round(Math.pow(2, i))) + " ");
            }
        }

        System.out.println(stringBuilder.toString());
    }

    public static void main(String[] args)  {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        int k = scanner.nextInt();

        int[] powers = getPowerArray(n);
        process(powers, k);

        if(getCount(powers) != k){
            System.out.println("NO");
        }else{
            System.out.println("YES");
            printPowerOfTwo(powers);
        }

    }
}