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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Main {
    public static void main(String[] args) throws IOException {

        BufferedReader br = new BufferedReader(new InputStreamReader(System.in), 1024 * 1024 * 2);

        int v[] = readArrayLine(br.readLine(), 2);
        long n = v[0];
        long k = v[1];
        long minSum = k * (k + 1) / 2;
        if (n < minSum) {
            System.out.println("NO");
            System.exit(0);
        }

//        long maxSum = 0;
//        long p = 1;
//        boolean canObtain = false;
//        for (int i = 0 ; i < k ; i ++) {
//            maxSum += p;
//            p <<= 1;
//            if (maxSum >= n) {
//                canObtain = true;
//                break;
//            }
//        }
//        if (!canObtain) {
//            System.out.println("NO");
//            System.exit(0);
//        }



        long x = k * (k - 1) / 2;
        long diff = n - x;
        long xx = diff / k;
        v = new int[(int) k];
        long sum = 0;
        for(int i = 0 ; i < k ; i ++) {
            v[i] = (int) (xx + i);
            sum += v[i];
        }

        diff = n - sum;

        while (diff > 0) {
//            System.out.println("diff = " + diff);

            if (diff < k) {
                long newSum = fillLower(v, (int) diff);
                long diff1  = n - newSum;
                if (newSum == -1) {
                    System.out.println("NO");
                    System.exit(0);
                }
                if (diff == diff1) {
                    break;
                }
                diff = diff1;
            } else {
                throw null;
            }

        }

        StringBuilder sb = new StringBuilder();
        for (int i = 0 ; i < k ; i ++) {
            sb.append(v[i]).append(' ');
        }
        System.out.println("YES");
        System.out.println(sb.toString());
    }

    private static long fillLower(int[] v, int diff) {
        int idx = -1;
        for (int i = 1 ; i < v.length; i ++) {
            if (v[i] < 2 * v[i-1]) {
                idx = i;
                break;
            }
        }

        if (idx == -1) {
            return -1;
        }
        int delta = Math.min(diff / (v.length - idx), v[idx] - v[idx - 1]);

        if (delta > 0) {
//            System.out.println("we add " + delta + " from " + idx);
            for (int i = idx; i < v.length; i++) {
                v[i] += delta;
            }
//            System.out.println(Arrays.toString(v));
        } else {
            int i = v.length - 1;
            while(diff > 0) {
                v[i--] ++;
                diff--;
            }
        }

        long sum = 0;
        for (int aV : v) {
            sum += aV;
        }
        return sum;
    }

    public static int[] readArrayLine(String line, int n) {
        return readArrayLine(line, n, null, 0);
    }

    private static int[] readArrayLine(String line, int n, int array[], int pos) {
        int[] ret = array == null ? new int[n] : array;
        int start = 0;
        int end = line.indexOf(' ', start);
        for (int i = pos; i < pos + n; i++) {
            if (end > 0)
                ret[i] = Integer.parseInt(line.substring(start, end));
            else
                ret[i] = Integer.parseInt(line.substring(start));
            start = end + 1;
            end = line.indexOf(' ', start);
        }
        return ret;
    }
}
