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
//package com.example.hackerranksolutions;

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.*;

public class Temp {



    public static void main(String[] args) throws Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        String[] ins = br.readLine().split(" ");
        int n = Integer.parseInt(ins[0]);
        int k = Integer.parseInt(ins[1]);
        int x = (k * (k+1))/2;
        if(n<x) {
            System.out.println("NO"); return;
        }
        int avg = n/k;
        avg -= k/2;
        if(avg == 0) avg = 1;
        int sum = 0;
        StringBuilder sb = new StringBuilder("YES\n");
        int[] arr = new int[k];
        for(int i = 0; i<k-1; i++) {
            sum += avg;
            arr[i] = avg;
            avg++;
        }

        arr[k-1] = n - sum;
        x = k-1;
        while(x>0 && arr[x] > 2 * arr[x-1]) {
            int y = arr[x] - 2 * arr[x-1];
            y/=2;
            if(y == 0) y = 1;
            arr[x] -= y;
            arr[x-1] += y;
        }

        for(int i = 0; i<k-1; i++) {
            if(arr[i] == arr[i+1] || arr[i]*2<arr[i+1]) {
                System.out.println("NO"); return;
            }
        }
        for(int i = 0; i<k-1; i++) sb.append(arr[i]).append(' ');
        sb.append(arr[k-1]);
        System.out.println(sb);
    }


}

