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.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;
import java.util.Vector;



public class Main {
	public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Task solver = new Task();
        solver.solve(1, in, out);
        out.close();
    }

	static class P implements Comparable<P> {

		int a;
		int b;
		
		@Override
		public int compareTo(P arg0) {
			if(arg0.a < this.a) return 1;
			else return -1;
		}
	}
	
	static class Task {
		final static int maxl = 200020;
		public static long pow2(int n) {
			long ans = 1;
			for(int i=0;i<n;i++) {
				ans*=2;
			}
			return ans;
		}
		public void solve(int testNumber, InputReader in, PrintWriter out) {
        	long n = in.nextLong();
        	int k = in.nextInt();
        	int a[] = new int[maxl];
        	int res = 0;
        	long m = n;
        	while(n>0) {
        		int i ;
        		for(i=0;i<=33;i++) {
        			if(pow2(i)>n) {
        				n-=pow2(i-1);
        				a[res++] = i-1;
        				break;
        			}
        		}
        	}
        	int b[] = new int[maxl];
        	int len = 0;
        	if(res>k) out.println("NO");
        	else {
        		int sum = 0;
            	for(int i=0;i<res;i++) {
            		sum+=pow2(a[i]);
            	}
            	if(sum<k) out.println("NO");
            	else {
            		out.println("YES");
            		while(m>0&&k>=0) {
                		int i ;
                		for(i=33;i>=0;i--) {
                			if((m - pow2(i))>=(k-1)) {
                				m-=pow2(i);
                				k--;
                				b[len++] = i;
                				break;
                			}
                		}
                	}
            		for(int i=len-1;i>=1;i--) {
            			out.print(pow2(b[i]));
            			out.print(' ');
            		}
            		out.println(pow2(b[0]));
            	}
        	}
        }
    }
	static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }
        public long nextLong() {
            return Long.parseLong(next());
        }
        
        public int nextInt() {
            return Integer.parseInt(next());
        }

    }
}