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.*;

public class App {

    public static <T> void print(T element){
        System.out.println(element);
    }

    public static void main(String[] args){
        int n, k;
        Scanner in = new Scanner(System.in);
        n = in.nextInt();
        k = in.nextInt();
        Long minSum = 1L*k*(k+1)/2;
        if(minSum > n){
            System.out.println("NO");
            Runtime.getRuntime().exit(0);
        }
        Long j = 0L;
        j = ((n-minSum)*1L) / k;
        minSum += j*k;
        //print(minSum);
        //print(minSum);
        Long arr[] = new Long[k];
        for(int i=0; i<k; i++){
            arr[i] = j+i+1;
            //print(arr[i]);
        }
        Long diff = n - minSum;
        int r = k-1;
        //print(diff);
        while(diff > 0){
            Long pdiff = diff;
            if(arr[r-1]*2 - arr[r] > pdiff){
                arr[r] += pdiff;
                pdiff = 0L;
            }
            else {
                pdiff -= arr[r - 1] * 2 - arr[r];
                arr[r] = arr[r - 1] * 2;
            }
            //print(diff);
            if(pdiff == diff) break;
            diff = pdiff;
            if (r == 1){
                r = k-1;
                continue;
            }
            r--;
        }
        int actualSum = 0;
        for(int i=0;i<k;i++) actualSum += arr[i];
        if (actualSum == n){
            System.out.println("YES");
            for(int i=0; i<k;i++){
                System.out.print(arr[i]+" ");
            }
        }
        else {
            System.out.println("NO");
        }
    }
}