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

_ = input().split()
n = int(_[0])
k = int(_[1])
def lower(k,i):
    return k*i + int(k*(k-1)/2)
def _max(k,i):
    return i*(pow(2,k)-1)
if n < lower(k,1):
    print("NO")
else:
    i = int((n - int(k*(k-1)/2)) / k) - 1
    # i = 1
    while lower(k,i) <= n:
        i = i + 1
    i = i - 1
    if _max(k,i) < n:
        print("NO")
    else:
        answer = [_ + i for _ in range(k)]
        adder = n - lower(k,i)
        for _ in range(adder):
            answer[-_-1] = answer[-_-1] + 1
        if k > 2 and answer[0] == 1 and answer[1] == 3:
            answer[1] = answer[1] - 1
            answer[-1] = answer[-1] + 1

        answer = [str(_) for _ in answer]
        print("YES")
        print(" ".join(answer))