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
/*
If you want to aim high, aim high
Don't let that studying and grades consume you
Just live life young
******************************
If I'm the sun, you're the moon
Because when I go up, you go down
*******************************
I'm working for the day I will surpass you
https://www.a2oj.com/Ladder16.html
*/
import java.util.*;
import java.io.*;
import java.math.*;

   public class x1157D
   {
      public static void main(String omkar[]) throws Exception
      {
         BufferedReader infile = new BufferedReader(new InputStreamReader(System.in));  
         StringTokenizer st = new StringTokenizer(infile.readLine());
         int N = Integer.parseInt(st.nextToken());
         int K = Integer.parseInt(st.nextToken());
         StringBuilder sb = new StringBuilder();
         int first = search(N, K);
         if((long)K*(K+1)/2 > N)
            System.out.println("NO");
         else
         {
            int[] res = new int[K];
            for(int i=0; i < K; i++)
               res[i] = i+first;
            long over = -1*N;
            for(int x: res)   
               over += x;
            over *= -1;
            int[] inc = new int[K];
            for(int i=1; i < K && over > 0; i++)
            {
               if(first == 1 && i == 1)
                  continue;
               if(over < K-i)
               {
                  inc[K-(int)over] = 1;
                  over = 0;
               }
               else
               {
                  //I love binary search
                  long low = 1L;
                  long high = N;
                  while(low != high)
                  {
                     long mid = (low+high+1)/2;
                     if(mid*(K-i) > over)
                        high = mid-1;
                     else
                        low = mid;
                  }
                  inc[i] = (int)low;
                  over -= low*(K-i);
               }
            }
            int check = 0;
            for(int i=0; i < K; i++)
            {
               check += inc[i];
               res[i] += check;
               if(i > 0 && res[i] > 2*res[i-1])
               {
                  System.out.println("NO");
                  return;
               }
            }
            long sum = 0L;
            for(int x: res)
               sum += x;
            if(sum != N)
               System.out.println("NO");
            else
            {
               System.out.println("YES");
               for(int x: res)
                  sb.append(x+" ");
               System.out.println(sb);
            }
         }
      }
      public static int search(int N, int K)
      {
         int low = 1;
         int high = N;
         while(low != high)
         {
            int mid = (low+high+1)/2;
            long sum = 0L;
            for(int i=0; i < K; i++)
               sum += mid+i;
            if(sum > N)
               high = mid-1;
            else
               low = mid;
         }
         return low;
      }
   }