Polycarp has to solve exactly n problems to improve his programming skill before an important programming competition. But this competition will be held very soon, most precisely, it will start in k days. It means that Polycarp has exactly k days for training!

Polycarp doesn't want to procrastinate, so he wants to solve at least one problem during each of k days. He also doesn't want to overwork, so if he solves x problems during some day, he should solve no more than 2x problems during the next day. And, at last, he wants to improve his skill, so if he solves x problems during some day, he should solve at least x+1 problem during the next day.

More formally: let [a_1, a_2, ..., a_k] be the array of numbers of problems solved by Polycarp. The i-th element of this array is the number of problems Polycarp solves during the i-th day of his training. Then the following conditions must be satisfied: 

  * sum of all a_i for i from 1 to k should be n; 
  * a_i should be greater than zero for each i from 1 to k; 
  * the condition a_i < a_{i + 1} ≤ 2 a_i should be satisfied for each i from 1 to k-1. 



Your problem is to find any array a of length k satisfying the conditions above or say that it is impossible to do it.

Input

The first line of the input contains two integers n and k (1 ≤ n ≤ 10^9, 1 ≤ k ≤ 10^5) — the number of problems Polycarp wants to solve and the number of days Polycarp wants to train.

Output

If it is impossible to find any array a of length k satisfying Polycarp's rules of training, print "NO" in the first line.

Otherwise print "YES" in the first line, then print k integers a_1, a_2, ..., a_k in the second line, where a_i should be the number of problems Polycarp should solve during the i-th day. If there are multiple answers, you can print any.

Examples

Input


26 6


Output


YES
1 2 4 5 6 8 


Input


8 3


Output


NO


Input


1 1


Output


YES
1 


Input


9 4


Output


NO
import java.util.*;
import java.io.*;
import java.math.BigInteger;
import static java.lang.Math.*;
 
public class Main
{
	static final int mod = (int)1e9+7;
	static ArrayList<Integer>[] adj;
	public static void main(String[] args) throws Exception
	{
		FastReader in = new FastReader();
		PrintWriter out = new PrintWriter(System.out);
		int test = 1;
		while(test-- > 0)
		{
			int n = in.nextInt();
			int k = in.nextInt();
			long minSum = (long)k * (k + 1) / 2;
			if(minSum > n) {
				out.println("NO");
				continue;
			}
			n -= minSum;
			long[] ans = new long[k];
			for(int i = 0; i < k; i++) {
				ans[i] = i + 1;
				ans[i] += n / k;
			}
			n %= k;
			int j = k - 1;
			while(n > 0 && j > 0) {
				long t = ans[j];
				ans[j] = min(2 * ans[j - 1], ans[j] + n);
				n -= ans[j] - t;
				j--;
			}
			if(n > 0) {
				out.println("NO");
				continue;
			}
			out.println("YES");
			for(int i = 0; i < k; i++) {
				out.print(ans[i] + " ");
			}
		}
		out.flush();
	}
}
 
class FastReader
{
	BufferedReader br;
	StringTokenizer st;
 
	public FastReader()
	{
	    br = new BufferedReader(new InputStreamReader(System.in));
	}
 
	public String next() throws IOException
	{
	    if(st == null || !st.hasMoreElements())
	    {
	        st = new StringTokenizer(br.readLine());
	    }

	    return st.nextToken();
	}
 
	public int nextInt() throws IOException
	{
	    return Integer.parseInt(next());
	}
 
	public long nextLong() throws IOException
	{
	    return Long.parseLong(next());
	}
 
	public String nextLine() throws IOException
	{
		return br.readLine();
	}
}