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

/**
 * @author cplayer on 2018/6/23.
 * @version 1.0
 */

import java.util.*;
import java.util.stream.Collectors;
import java.io.*;
import java.lang.*;

public class Main {

	public static void main(String[] args) {
		try {
			InputReader in;
			PrintWriter out;
			boolean useOutput = false;
			if (System.getProperty("ONLINE_JUDGE") == null)
				useOutput = true;
			if (useOutput) {
				FileInputStream fin = new FileInputStream(new File("src/data.in"));
				in = new InputReader(fin);
				FileOutputStream fout = new FileOutputStream(new File("src/data.out"));
				out = new PrintWriter(fout);
			} else {
				InputStream inputStream = System.in;
				in = new InputReader(inputStream);
				OutputStream outputStream = System.out;
				out = new PrintWriter(outputStream);
			}
			Solver solver = new Solver(in, out);
			solver.solve();
			out.close();
		} catch (Exception e) {
			e.printStackTrace();
		}
	}

	static class Solver {

		private InputReader cin;
		private PrintWriter cout;

		Solver(InputReader cin, PrintWriter cout) {
			this.cin = cin;
			this.cout = cout;
		}

		boolean judge (int n, int k) {
			long tmp = k;
			tmp *= (k + 1);
			tmp /= 2;
			if (n < tmp) return false;
			return true;
		}

		public void solve() {
			try {
				int n = cin.nextInt(), k = cin.nextInt();
				int ans[] = new int[k];
				if (!judge(n, k)) {
					cout.println("NO");
				} else {
					int base = n - (k + 1) * k / 2;
					int mod = base % k;
					base = base / k;
					for (int i = 0; i < k; ++i) {
						ans[i] = base + (i + 1);
					}
					if (mod > 0) {
						ans[k - 1] += mod;
						if (k > 1) {
							if (ans[k - 1] > 2 * ans[k - 2]) {
								ans[k - 1]--;
								ans[k - 2]++;
							}
						}
					}
					for (int i = 0; i < k - 1; ++i) {
						if (!(ans[i] < ans[i + 1]) || !(2 * ans[i] >= ans[i + 1])) {
							cout.println("NO");
							return;
						}
					}
					cout.println("YES");
					for (int i = 0; i < k; ++i) {
						cout.print(ans[i]);
						if (i == k - 1) cout.println();
						else cout.print(" ");
					}
				}
			} catch (RuntimeException e) {
				e.printStackTrace();
				return;
			} catch (Exception e) {
				e.printStackTrace();
				return;
			}

		}
	}

	static class InputReader {
		public BufferedReader reader;
		public StringTokenizer tokenizer;

		public InputReader(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(stream), 1000);
			tokenizer = null;
		}

		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}

		public int nextInt() {
			return Integer.parseInt(next());
		}

		public long nextLong() {
			return Long.parseLong(next());
		}

		public double nextDouble() {
			return Double.parseDouble(next());
		}

	}

}