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
def get_tail(k):
    return (k*(k-1))//2

def find_starter(n, k):
    f = get_tail(k)
    starter = (n-f)//k
    return starter

def answerYES(A):
    return "YES\n"+" ".join(map(str, A))

def get_array(n, k):
    starter = find_starter(n, k)
    if starter < 1:
        return "NO"
    A = [0]*k
    s = 0
    last = starter+k-1
    for i in range(starter, starter+k):
        A[i-starter] = i
        s+=i
    diff = n-s
    maxe = last-2
    if diff > maxe:
        while diff > 0 and A[-2]*2 - A[-1] >= 1:
            for i in range(k-1, -1, -1):
                if i-1 > -1 and A[i-1]*2 - A[i] >= 1:
                    A[i] += 1
                    diff -= 1
                    if diff == 0:
                        break
        if diff == 0:
            return answerYES(A)
        else:
            return "NO"
        
    else:
        A[-1] += diff
        return answerYES(A)
    return "NO"

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