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 NProblemsKDays {
    public static void main(String[] args) {
        FastScanner scanner = new FastScanner();
        PrintWriter out = new PrintWriter(System.out);
        int N = scanner.nextInt();
        int K = scanner.nextInt();
        long k = (long) K;
        long min = (k * (k+1))/2;
        if (k == 1) {
            out.println("YES");
            out.println(N);
            out.flush();
            return;
        }
        if (min > N) {
            out.println("NO");
            out.flush();
            return;
        }
        long dist = N-min;
        long off = dist/K;
        if ((k + off) < 32 && (( 1 << (k+off))-1) < N) {
            out.println("NO");
            out.flush();
            return;
        }
        out.println("YES");
        long prev = 1 + off;
        for(int i = 1; i <= K; i++) {
            if (i > 1) out.print(" " );
            out.print(prev);
            N-= prev;
            long pprev = prev;
            prev++;
            //This is making sure you are above the lower bound
            //This needs to make sure we are below the upper bound
            long hi = 2 * pprev;
            long lo = prev;
//            while(midPt(prev+1, prev + K-i) <= N && prev < 2 * pprev) {
//                prev++;
//            }
            while(lo < hi) {
                long mid = (hi + lo) /2;
                if (midPt(mid + 1, mid + K-i) > N) hi = mid;
                else lo = mid + 1;
            }
            prev = hi;
//            out.flush();
        }
        out.println();
        out.flush();
    }
    
    public static long midPt(long a, long b) {
        long B = (b * (b + 1)) /2;
        long A = (a * (a - 1)) /2;
//        long temp = B-A;
        return B-A;
    }
    
    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;
        
        public FastScanner(Reader in) {
            br = new BufferedReader(in);
        }
        
        public FastScanner() {
            this(new InputStreamReader(System.in));
        }
        
        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
        
        int nextInt() {
            return Integer.parseInt(next());
        }
        
        long nextLong() {
            return Long.parseLong(next());
        }
        
        double nextDouble() {
            return Double.parseDouble(next());
        }
        
        String readNextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
        
        int[] readIntArray(int n) {
            int[] a = new int[n];
            for (int idx = 0; idx < n; idx++) {
                a[idx] = nextInt();
            }
            return a;
        }
    }
}
