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 fun(x1, x2, i, s):
    # print (x,i,s)
    j = 31
    if i < 32:j = i
    
    z1 = i*(2*x1 + i - 1)/2
    z2 = x2*(2**j-1)
    
    if s < z1 or s > z2 or x2 < x1: return 0
    
    y1 = (2*s + i - i*i)/(2*i)
    y2 = s*x2/z2
    if (s*x2)%z2 > 0:y2 += 1
    
    if y1<x1 or y2>x2 or y1<y2:return 0
    
    return max(x1, y2)
    
n , k =map(int, raw_input().split())
s = n

a = []
x1 = 1
x2 = n

for i in range(k):
    z = fun(x1, x2, k-i, n)
    # print (k-i, x1, x2, z, n)
    a.append(z)
    n -= z
    x1 = z+1
    x2 = 2*z
    
# print (a)
if sum(a)==s:
    print ("YES")
    for i in a:
        print i,
        
else:
    print ("NO")
    