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(x) for x in input().split()]
a = [i for i in range(1, k+1)]
s = (k*(k+1))//2
p = 0
if n == s:
    p = 0
elif n > s:
    if n - s == k:
        p = 0
        for i in range(k):
            a[i] += 1
    elif n - s > k:
        d = (n - s) // k
        for i in range(k):
            a[i] += d
        p = (n-s) - (d*k)
        for i in range(k-2, -1, -1):
            c = (2 * a[i]) - a[i+1]
            if p <= 0:
                break
            elif p >= c:
                a[i+1] += c
                p -= c
            elif p < c:
                a[i+1] += p
                p = 0
    elif n - s < k:
        p = n - s
        for i in range(k-2, -1, -1):
            c = (2 * a[i]) - a[i + 1]
            if p <= 0:
                break
            elif p >= c:
                a[i+1] += c
                p -= c
            elif p < c:
                a[i+1] += p
                p = 0
else:
    p = 1

if p <= 0:
    print('YES')
    for i in range(k):
        print(a[i], end=' ')
else:
    print('NO')
