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.io.*;

public class A101177 {


    public static void main(String[] args) throws IOException {
        Scanner sc = new Scanner(System.in);
        PrintWriter pw = new PrintWriter(System.out);

        int n = sc.nextInt();
        int k = sc.nextInt();
        if (n < 1l * k * (k + 1) / 2) {
            pw.println("NO");
        } else {

            int[] ans = new int[k];
            int diff = n - (k * (k + 1) / 2);
            int add = diff / k;
            int rem = diff - k * add;
            for (int i = 0; i < k; i++)
                ans[i] = i + 1 + add;
            int count = 0;
            for (int i = k - 1; count < 100 && rem > 0; i--) {
                while (rem > 0 && (i == 0 || ans[i] < 2 * ans[i - 1]) && (i == k - 1 || ans[i] + 1 < ans[i + 1])) {
                    ans[i]++;
                    rem--;
                }
                if (i == 0) {
                    i = k;
                    count++;
                }
            }
            if (count<100) {
                pw.println("YES");
                for (int x : ans)
                    pw.print(x + " ");
            }else pw.println("NO");
            pw.println();
        }
        pw.flush();
    }

    static class Scanner {
        BufferedReader br;
        StringTokenizer st;

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public Scanner(FileReader f) {
            br = new BufferedReader(f);
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

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

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

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

        public int[] nextIntArr(int n) throws IOException {
            int[] arr = new int[n];
            for (int i = 0; i < n; i++) {
                arr[i] = Integer.parseInt(next());
            }
            return arr;
        }

    }
}
