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.io.*;
import java.util.*;

public class D {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader inp = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Solver solver = new Solver();
        /*for (int n = 1; n <= 10; n++) {
            int i = (n + 1) * n / 2;
            for (int m = i; m < i + 100; m++) {
                out.println("\n-- " + n + " " + m);
                solver.solve(inp, out, n, m);
            }
        }*/
        solver.solve(inp, out);//, 6, 22);

        out.close();
    }

    private static class Solver {
        private void solve(InputReader inp, PrintWriter out) {//, int n, int k) {
            long k = inp.nextInt();
            int n = inp.nextInt();
            long startK = k;
            int[] a = new int[n];
            a[0] = 1;
            for (int i = 1; i < n; i++) a[i] = a[i-1] + 1;
            for (int i: a) k -= i;
            if (k < 0) {
                out.println("NO");
                return;
            }
            for (int i = 0; i < n; i++) a[i] += k / n;
            k %= n;
            //for (int i: a) out.print(i + " ");
            //out.print("\n" + k + "\n");
            for (int i = n - 1; i >= 0; i--) {
                while (k > 0 && (i == 0 || 2*a[i-1] >= a[i] + 1)) {
                    a[i]++;
                    k--;
                }
            }
            // 21
            // 1,2,3,4,6,10
            for (int i = 0; i < n - 1; i++) {
                if (2*a[i] < a[i+1]) {
                    out.println("NO");
                    return;
                }
                if (a[i] >= a[i+1]) {
                    out.println("NO");
                    return;
                }
            }
            int sum = 0;
            for (int i: a) sum += i;
            if (sum != startK) {
                out.println("NO");
                return;
            }
            out.println("YES");
            for (int i: a) out.print(i + " ");
        }
    }

    static class InputReader {
        BufferedReader reader;
        StringTokenizer tokenizer;

        InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        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());
        }
    }
}