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.*;
import java.util.*;
     
public class Solution {
    	 private static String a;
    	 private static String b;
    	 
    public static void main(String[] args) throws Exception{ 
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);
        StringTokenizer st = new StringTokenizer(br.readLine());
        
        int n = Integer.parseInt(st.nextToken());
        int k= Integer.parseInt(st.nextToken());
        
        int low = 1;
        if(k<31){
           low = binarySearch(n,k);  
        } 
        int high = binarySearch(low,n,k);
        if(high < low){
             out.println("NO");
        }
        else{
             out.println("YES");
             long N = n;
             long rem = (k-1)*((long)k)/2;
             long value= high*k+rem;
             if(value == n){
                  for(int i=0;i<k;i++){
                   out.print((high+i)+" ");
                  }
             }
             else{
                  long value2 = (high+1)*k+rem;
                  if(high == 1 && n == value2 -1){
                      for(int i=0;i<k-2;i++){
                         out.print((high+i)+" ");
                      } 
                      long left = n-value-1;
                      out.print((high+k-1)+" "+(high+k-1+left));
                  }
                  else{
                     for(int i=0;i<k-1;i++){
                         out.print((high+i)+" ");
                      }  
                      long left = n-value;
                      out.print((high+k-1+left));
                  }
             }
        }
        out.close();
     }
     
     private static int binarySearch(long n,int k){
          long low= 1,high = 30;
          long value = (long)(Math.pow(2,k))-1;
          
          while(low < high){
             long mid = (low+high)/2;
             if(value*mid >= n)high = mid;
             else low = mid+1;
          }
          return (int)low;
     }
     
     private static int binarySearch(long low,long n,long k){
          long high = 1000000001;
          long rem = (k-1)*k/2;
          
          while(low <high){
               long mid = (low+high)/2;
               if(k*mid+rem >= n)high= mid;
               else low = mid+1;
          }
          if(low*k+rem > n) return (int)(low-1);
          return (int)low;
     }
}