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.*;
import java.lang.*;
import java.io.*;

public class Main
{
	PrintWriter out = new PrintWriter(System.out);
	BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
    StringTokenizer tok = new StringTokenizer("");
    String next() throws IOException {
        if (!tok.hasMoreTokens()) { tok = new StringTokenizer(in.readLine()); }
        return tok.nextToken();
    }
    int ni() throws IOException { return Integer.parseInt(next()); }
    long nl() throws IOException { return Long.parseLong(next()); }
    
    void solve() throws IOException {
        int n=ni();
        int k=ni();
        long min=0;
        if (k%2==1) min = ((long)k+1)*((long)k/2) + ((long)k+1)/2;
        else min = ((long)k+1)*((long)k/2);
        if (min>n) { System.out.println("NO"); System.exit(0); }
        
        int[] A = new int[k+1];
        int left=n-(int)min;
        A[1]=1;
        if (k<=left) { A[1]+=left/k; left=left%k; }
        for (int x=2;x<=k;x++) {
            A[x]=A[x-1]+1;
            if (left==0) continue;
            while (A[x]<2*A[x-1]) {
                if (k+1-x>left) break;
                A[x]++;
                left -= (k+1-x);
            }
        }
        if (left>0) { System.out.println("NO"); System.exit(0); }
        out.println("YES");
        for (int x=1;x<=k;x++) out.printf("%d ",A[x]);
        out.println();
        out.flush();
    }
    
    public static void main(String[] args) throws IOException {
        new Main().solve();
    }
}