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

public class cft7
{ 

	static int[] arr;
	public static void main(String[] args) 
	{ 
		FastReader fr=new FastReader();
		int n=fr.nextInt();
		int k=fr.nextInt();
		if(k==1){
			System.out.println("YES\n"+n);
		}
		else if(calc(n,k)==1){
			System.out.println("YES");
			for(int a:arr)System.out.print(a+" ");
			System.out.println();
		}
		else System.out.println("NO");

	}
	public static int calc(int n,int k){
		 arr=new int[k];
		 int curr=0;
		for(int i=0;i<k;i++){
			
			int l=(i>0)?arr[i-1]:1;
			int u=(n-curr)/(k-i);
			int val=bins(l,u,curr,k,i,n);
			
			/*while(clim(val,k-i-1)>(n-curr-val)||(i>0&&val>2*arr[i-1])){
				val--;
			}*/
			
			if(val==0)return -1;
			if(i>0&&val==arr[i-1])return -1;
			arr[i]=val;
			curr+=val;

		}
		if(curr==n)return 1;
		return -1;
		
	}

	public static int bins(int l,int u,int curr,int k,int i,int n){
		while(l<=u){
			int m=l+(u-l)/2;
			int lim=clim(m,k-i-1);
			
			 if(lim>(n-curr-m)||(i>0&&m>arr[i-1]*2))u=m-1;
			else l=m+1;
		}
		return u;
	}
	public static int clim(int val,int p){
		return p*(val+1)+((p*(p-1))/2);
	} 

	public static int crem(int n,int curr,int val){
		return n-curr-val;
	} 





	static class FastReader 
	{ 
		BufferedReader br; 
		StringTokenizer st; 

		public FastReader() 
		{ 
			br = new BufferedReader(new
					InputStreamReader(System.in)); 
		} 



		String next() 
		{ 
			while (st == null || !st.hasMoreElements()) 
			{ 
				try
				{ 
					st = new StringTokenizer(br.readLine()); 
				} 
				catch (IOException e) 
				{ 
					e.printStackTrace(); 
				} 
			} 
			return st.nextToken(); 
		} 

		int nextInt() 
		{ 
			return Integer.parseInt(next()); 
		} 

		long nextLong() 
		{ 
			return Long.parseLong(next()); 
		} 

		double nextDouble() 
		{ 
			return Double.parseDouble(next()); 
		} 

		String nextLine() 
		{ 
			String str = ""; 
			try
			{ 
				str = br.readLine(); 
			} 
			catch (IOException e) 
			{ 
				e.printStackTrace(); 
			} 
			return str; 
		} 
	} 

} 


















