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 = [int(s) for s in input().split()]
if n < k * (k + 1) / 2:
    print("NO")
    exit()
if ((k == 3 and n == 8) or (k == 2 and (n < 3 or n == 4))):
    print("NO")
    exit()
print("YES")
if k == 1:
    print(n)
elif (k == 2):
    print((n + 2) // 3, n - (n + 2) // 3)
else:
    i = 1
    while i * k + k * (k - 1) // 2 <= n:
        i += 1
    i -= 1
    last = i + k - 1
    last_ = last - 1
    sum = i * (k - 1) + (k - 2) * (k - 1) // 2
    last = n - sum
    if last_ * 2 >= last:
        for q in range(i, last_ + 1):
            print(q, end = " ")
        print(last)
        exit()
    last_ += 1
    last -= 1
    for q in range(i, i + k - 2):
        print(q, end=" ")
    print(last_, end=' ')
    print(last)