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 check(a):
    for x, y in zip(a[:-1], a[1:]):
        if x >= y or y > 2*x:  
            return False
    return True

def solve(n, k):
    if n < k*(k+1) // 2:
        return 'NO', None
    
    ans    = list(range(1, k+1))
    plus   = n - sum(ans)
    add    = plus // k
    r      = plus % k
    
    for i in range(k):
        ans[i] += add
        
    if r != 0: 
        last     = 2*ans[-2] - ans[-1] 
        ans[-1] += min(last, r)
        if r > last:
            ans[-2] += r-last 
            
    if check(ans) == True:
        return 'YES', ans
    
    return 'NO', None
    
n, k = map(int, input().split())
flg,ans=solve(n, k)
if flg=='NO':
    print(flg)
else:
    print(flg)
    print(' '.join([str(x) for x in ans]))