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 solve(n, k):
    if (k+1)*k // 2 > n: return ''
    if k == 1: return str(n)
    if k == 2:
        if n % 2: return '%d %d' % (n//2, n//2+1)
        else:
            if n <= 4: return ''
            return '%d %d' % (n//2-2, n//2+2)

    s = (k+1)*k // 2
    t, m = divmod(n, s)
    res = [v*t for v in range(1, k+1)]
    t, m = divmod(m, k)
    res = [v+t for v in res]
    res = helper(res, m)
    if not check(res): return ''
    return ' '.join(map(str, res))

def check(res):
    for i in range(1, len(res)):
        if res[i] > res[i-1] and res[i] <= 2*res[i-1]: continue
        return False
    return True

def helper(res, m):
    if res[0] == 1 and m >= 2*k - 4: return []
    index = len(res) - 1
    while m:
        res[index] += 1
        index -= 1
        if index == 1: index = len(res) - 1
        m -= 1
    return res


n, k = map(int, input().split())
res = solve(n, k)
if not res:
    print('NO')
else:
    print('YES')
    print(res)