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,math
from fractions import gcd
from bisect import bisect_left, bisect
from collections import defaultdict
from io import BytesIO
sys.stdin = BytesIO(sys.stdin.read())
input = lambda: sys.stdin.readline().rstrip('\r\n')
#n = int(input())
n,k = [int(_) for _ in input().split()]
#b = [int(_) for _ in input().split()]

if k == 1:
    print('YES')
    print(n)
    exit()
elif n < 3:
    print('NO')
    exit()
x = 1
while x * k + k * (k-1) / 2 <= n:
    x += 1
res = [x-1]
if x <= 1:
    print('NO')
    exit()
num = x-1
for i in range(1,k):
    x = res[-1] * 2
    if num + x * (k - i) + (k-i) * (k-i-1) / 2 <= n:
        res.append(x)
        num += x
    elif i < k-1:
        num += res[-1] + 1
        res.append(res[-1] + 1)
    elif n - num <= res[-1] * 2 and n-num > res[-1]:
        res.append(n-num)
        num = n
    else:
        print('NO')
        exit()
if num == n:
    print('YES')
    print(' '.join([str(x) for x in res]))
else:
    print('NO')
        
        