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 Main {

    public static void main(String[] args) throws IOException {
//        br = new BufferedReader(new FileReader(new File("input.txt")));
//        out = new PrintWriter(new File("output.txt"));
        int nasral = 1;
        for (int JOPA = 0; JOPA < nasral; JOPA++) {
            long n = nextInt();
            long k = nextInt();
            if (k == 1) {
                out.println("YES");
                out.println(n);
                continue;
            }
            long[] ans = new long[(int) k];
            long ll = 0;
            long rr = (int) 1e10;
            while (ll + 1 != rr) {
                long mid = (ll + rr) / 2;
                long cnt = (k / 2) * (k + 1);
                cnt += (mid - 1) * k;
                if (k % 2 == 1) cnt += (mid / 2) + 1;
                if (cnt <= n) ll = mid;
                else rr = mid;
            }
            if (ll == 0) {
                out.println("NO");
                continue;
            }
            long sum = ll;
            ans[0] = ll;
            long[] pr = new long[(int) k];
            pr[0] = ll;
            for (int i = 1; i < k; i++) {
                ans[i] = ans[i - 1] * 2;
                if (ans[i] > 1e9 + 10) ans[i] = ans[i - 1] + 1;
                sum += ans[i];
                pr[i] = sum;
            }
            if (sum < n) {
                out.println("NO");
                continue;
            }
            int l = 0;
            int r = (int) k;
            while (l + 1 != r) {
                int mid = (l + r) / 2;
                long popka = (k - mid);
                long cnt = ans[mid - 1] * (popka);
                cnt += (popka / 2) * (popka + 1);
                if (popka % 2 == 1) cnt += popka / 2 + 1;
                if (cnt + pr[mid - 1] <= n) l = mid;
                else r = mid;
            }
            for (int i = Math.max(l, 1); i < k; i++) {
                ans[i] = ans[i - 1] + 1;
            }
            sum = 0;
            for (int i = 0; i < k; i++) {
                sum += ans[i];
            }
            int ind = (int) (k - 1);
            while (sum < n) {
                if (sum + ans[ind - 1] * 2 - ans[ind] <= n) {
                    sum += ans[ind - 1] * 2 - ans[ind];
                    ans[ind] = ans[ind - 1] * 2;
                } else {
                    ans[ind] += n - sum;
                    sum = n;
                }
                ind--;
            }
            if (sum > n) {
                out.println("NO");
            } else {
                out.println("YES");
                for (int i = 0; i < k; i++) {
                    out.print(ans[i] + " ");
                }
            }

        }
        out.close();

    }


    public static StringTokenizer in = new StringTokenizer("");
    public static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    public static PrintWriter out = new PrintWriter(System.out);

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

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

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