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
n, k = map(int, raw_input().strip().split())

p = float('inf')
if k <= 32:
    p = 2 ** k - 1

lo = 1
if n >= p:
    lo = (n + p - 1) // p

if 2 * n <= k * (k - 1):
    print "NO"
    exit()

hi = (n - (k * (k - 1)) // 2) // k

if hi < lo:
    print "NO"
    exit()

lista = []
flag = 0

while k:
    a = (n - (k * (k - 1)) // 2) // k
    if len(lista) == 0: lista.append(a)
    else:
        a = min(a, 2 * lista[-1])
        if a < lista[-1] + 1:
            flag = 1
            break
        lista.append(a)

    k -= 1
    n -= lista[-1]

if flag == 1:
    print "NO"
    exit()
    
for i in xrange(k - 1):
    if a[i] > 0 and a[i + 1] <= 2 * a[i] and a[i + 1] > a[i]: continue
    else:
        flag = 1
        break

if flag == 1:
    print "NO"
    exit()

print "YES"
print ' '.join(map(str, lista))