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.Scanner;
import java.util.Stack;

// http://codeforces.com/problemset/problem/1157/D
public class NProblemsDuringKDays {
    public static void main(String[] args) {
        // collect test data from input
        Scanner inputScanner = new Scanner(System.in);
        int sum = inputScanner.nextInt();
        int days = inputScanner.nextInt();
        inputScanner.nextLine();
        inputScanner.close();
        
        // process
        processAndDisplayResult(sum, days);
    }

    public static void processAndDisplayResult(int sum, int days) {
        // System.out.println(sum + ", " + days);
        Stack<Integer> numbers = new Stack<Integer>();
        if (isPossableWithCurrentStats(sum, days, numbers, 0)) {
            System.out.println("YES");
            for (int i = 0; i < days; i++) {
                System.out.print(numbers.pop() + " ");
            }
            System.out.println("");
        } else {
            System.out.println("NO");
        }
    }

    private static int getMaxStartValue(int sum, int days, int previous) {
        // a <= (sum - days * (days - 1) / 2) / days; 
        // => (sum + days) / (2 * days) - days/2
        int calculatedValue = (2 * sum + days) / (2 * days)- days/2;
        int maxLimit = 2 * previous;
        maxLimit = maxLimit == 0 ? 1 : maxLimit;
        if (previous != 0 && calculatedValue > maxLimit) {
            return maxLimit;
        } else {
            return calculatedValue;
        }
    }

    private static int getMinStartValue(int sum, int days, int previous) {
        // a >= sum / (2 pow days - 1)
        int powValue = 1;
        int maxDays = days >= 30 ? 30 : days;
        for (int i = 1; i <= maxDays; i++) {
            powValue *= 2;
        }
        int calculatedValue = sum / (powValue - 1);
        int minLimit = previous + 1;
        if (calculatedValue < minLimit) {
            return minLimit;
        } else {
            return calculatedValue;
        }
    }

    private static boolean isPossableWithCurrentStats(int currentSum, int currentDays, Stack<Integer> numbers, int prevousValue)  {
        // System.out.println(currentSum + ", " + currentDays + ", " + prevousValue);
        int startValue = getMinStartValue(currentSum, currentDays, prevousValue);
        int endValue = getMaxStartValue(currentSum, currentDays, prevousValue);
        // System.out.println(startValue + ", " + endValue);
        if (startValue > endValue) {
            return false;
        } else {
            for (int j = startValue; j <= endValue; j++) {
                currentSum -= j;
                currentDays -= 1;
                if (currentSum == 0 && currentDays == 0) {
                    numbers.push(j);
                    return true;
                } else if (currentSum == 0 || currentDays == 0) {
                    currentSum += j;
                    currentDays += 1;
                    return false;
                }
                if (isPossableWithCurrentStats(currentSum, currentDays, numbers, j)) {
                    numbers.push(j);
                    return true;
                } else {
                    currentSum += j;
                    currentDays += 1;
                }
            }
            return false;
        }
    }
        
}