1157_D. N Problems During K Days
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
```python

"""

b[i] = a[i] - i - 1

b[i] <= b[i+1] < 2b[i] + i - 1

sum(b) == r
"""

def solve(n, k):

    r = n - k*(k+1)//2
    if r < 0:
        return None

    b0 = r//k

    r -= b0*k

    seq = [None]*k
    seq[0] = b0
    b = b0

    for i in range(1,k):
        bn = b*2 + i - 1

        h = r//(k-i)
        if h > 0:
            if h+b > bn:
                h = bn - b
            r -= h*(k-i)
            b = h+b
        seq[i] = b
    if r != 0:
        return None
    A = [b+i+1 for i,b in enumerate(seq)]
    return A


def main():
    n,k = map(int,input().split())
    res = solve(n,k)
    if res is None:
        print('NO')
    else:
        print('YES')
        print(*res)
main()
```