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().split())
t=(k*(k+1))/2
if n<(k*(k+1))/2:
    print "NO"
    exit()
n=n-t
a=[i+1 for i in xrange(k)]
t=n/k
for i in xrange(k): a[i]+=t
n%=k
i=k-1
while n>0:
    a[i]+=1
    n=n-1
for i in xrange(k-1,0,-1):
    d=a[i]-2*a[i-1]
    if d>0:
        if d/2==0:
            a[i]-=1
            a[i-1]+=1
        else:
            a[i]-=d/2
            a[i-1]+=d-d/2
test=0
for i in xrange(1,k):
    if a[i]>2*a[i-1] or a[i]==a[i-1]:
        test=1

if test==1:
    print "NO"
else:
    print "YES"
    print " ".join(map(str,a))
