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.*;
import static java.lang.Math.*;
public class Main {
    static final long MOD = 1_000_000_007 , INF = 1_000_000_000_000_000L;
    static final int INf = 1_000_000_000;
    static FastReader reader;
    static PrintWriter writer;
    public static void main(String[] args) {
        Thread t = new Thread(null, new O(), "Integer.MAX_VALUE", 100000000);
        t.start();
    }
    static class O implements Runnable {
        public void run() {
            try {
                magic();
            }
            catch (Exception e) {
                e.printStackTrace();
                System.exit(1);
            }
        }
    }
    static class FastReader {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

        public FastReader() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public FastReader(String file_name) throws IOException {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public String readLine() throws IOException {
            byte[] buf = new byte[1000000];
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n') break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public int nextInt() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ') c = read();
            boolean neg = (c == '-');
            if (neg) c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg) return -ret;
            return ret;
        }

        public long nextLong() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ') c = read();
            boolean neg = (c == '-');
            if (neg) c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg) return -ret;
            return ret;
        }

        public double nextDouble() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ') c = read();
            boolean neg = (c == '-');
            if (neg) c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (c == '.') while ((c = read()) >= '0' && c <= '9') ret += (c - '0') / (div *= 10);
            if (neg) return -ret;
            return ret;
        }

        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1) buffer[0] = -1;
        }

        private byte read() throws IOException {
            if (bufferPointer == bytesRead) fillBuffer();
            return buffer[bufferPointer++];
        }

        public void close() throws IOException {
            if (din == null) return;
            din.close();
        }
    }

    static void magic() throws IOException {
        reader = new FastReader();
        writer = new PrintWriter(System.out, true);
        int n = reader.nextInt(), k = reader.nextInt();
        StringBuilder fast = new StringBuilder();
        int sum = 0, prev = 0;
        for(int i=0;i<k;++i) {
            int low = prev+1, high = min(n-sum, i==0 ? n : 2*prev), mid;
            //writer.println("i: "+i+" low: "+low+" high: "+high);
            if(low>high) {
                writer.println("NO");
                System.exit(0);
            }
            while(low<high) {
                mid = (low+high)>>1;
                int fm = f(k-i-1, n-sum-mid, mid);
               // writer.println("mid: "+mid+" fm: "+fm);
                if(fm==0) {
                    low = mid;
                    break;
                }
                else if(fm==-1) {
                    high =  mid-1;
                }
                else low = mid+1;
            }
            if(f(k-i-1, n-sum-low, low)!=0) {
                writer.println("NO");
                System.exit(0);
            }
            fast.append(low);
            sum+=low;
            prev = low;
            //writer.println("Selected: "+low);
            fast.append(" ");
        }
        writer.println("YES");
        writer.println(fast);
    }
    static int f(int moves_left, int req, int prev) {
//        writer.println("-----------------------------------------------------------------");
//        writer.println("Moves: "+moves_left+" req: "+req+" prev: "+prev);
        long min = 1L * moves_left * ((prev+1)+(prev+1)+moves_left-1);
        min/=2;
        //writer.println("Min: "+min);
        if(req<min) {
//            writer.println("Returning -1");
//            writer.println("-----------------------------------------------------------------");
            return -1;
        }
        if(moves_left>30) {
            return 0;
        }
        long max = (long)max(1, 2*prev) * (long)(pow(2, moves_left)-1);
        //writer.println("Max: "+(max));
        if(req>max) {
           // writer.println("Returning 1");
          //  writer.println("-----------------------------------------------------------------");
            return 1;
        }
      //  writer.println("Returning 0");
      //  writer.println("-----------------------------------------------------------------");
        return 0;
    }
}