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 sys
input = sys.stdin.readline

'''

'''

from math import floor, ceil

s = lambda n: n*(n+1)/2

n, k = map(int, input().split())

if n < s(k):
    print("NO")
else:
    # s(k) + xk = n
    x = (n - s(k)) / k
    if x % 1 == 0:
        print("YES")
        print(*[int(i+x) for i in range(1, k+1)])
    else:
        x = int(floor(x))
        missing = int(n - (s(k) + x*k))
        res = [i+x for i in range(1, k+1)]

        for i in range(k-missing, k):
            res[i] += 1
        
        if k >= 2 and res[0] * 2 < res[1]:
            res[1] -= 1
            res[-1] += 1

        for j in range(k-1):
            if res[j] * 2 < res[j+1]:
                print("NO")
                sys.exit()
        
        print("YES")
        print(*res)
