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 E {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int k = sc.nextInt();
		StringBuilder sb = new StringBuilder();
		
		if((long)(k+1) * k / 2 > n) {
			sb.append("NO\n");
		}
		else {
			int a[] = new int[k+1];
			
			n -= (k+1) * k / 2;
			int q = n / k;
			int r = n % k;
			
			for(int i=1;i<=k;i++) {
				a[i] = i + q;
			}
			
			for(int i=k;r>0;i--) {
				a[i]++;
				r--;
			}
			
			if(k >= 2 && a[1] * 2 < a[2]) {
				a[2]--;
				a[k]++;
			}
			
			boolean ok = true;
			for(int i=1;i<k;i++) {
				if(a[i] * 2 < a[i+1]) {
					ok = false;
				}
			}
			
			if(!ok) {
				sb.append("NO\n");
			}
			else {
				sb.append("YES\n");

				for(int i=1;i<=k;i++) {
					sb.append(a[i] + " ");
				}
			
			}
					
		}
		System.out.println(sb);
	}

}
