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
import sys

n, k = tuple(map(int, input().split()))

if n == 1 == k:
    print('YES')
    print(1)
    sys.exit(0)

sum_s = sum(i+1 for i in range(k))
if sum_s > n:
    print('NO')
    sys.exit(0)

r = (n - sum_s) // k
ost = (n - sum_s) % k

if r == 0 and ost == k - 1:
    if n == 4 or n == 8:
        print('NO')
        sys.exit(0)
    else:
        print('YES')
        print(1, 2, end='')
        for i in range(2, k-1):
            print(' {}'.format(i+2),  end='')
        print(' {}'.format(k+2),  end='')

else:
    print('YES')
    print(r+1, end='')
    for i in range(1, k-ost):
        print(' {}'.format(r+i+1),  end='')
    for i in range(k-ost, k):
        print(' {}'.format(r+i+2),  end='')

print()
    
