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
import math

tasks, days = [int(x) for x in sys.stdin.readline().split()]

if days == 1:
    print("YES")
    print(tasks)
    sys.exit(0)

min_sum = int((days + 1) * days / 2)
if min_sum > tasks:
    print("NO")
    sys.exit(0)

uncheduled = tasks - min_sum
uniform_daily_part = uncheduled // days
uncheduled = uncheduled % days


ans = []
for d in range(days):
    ans.append(1 + d + uniform_daily_part)

a = ans[-2]
b = ans[-1]

x = min(max(0, math.ceil((b + uncheduled - 2*a) / 3)), uncheduled)
y = uncheduled - x

ans[-2] += x
ans[-1] += y

if days > 1 and ans[-2] >= ans[-1]:
    print("NO")
    sys.exit(0)

if days > 2 and ans[-3]*2 < ans[-2]:
    print("NO")
    sys.exit(0)

# # going to print answer
# for i in range(1, days):
#     if ans[i] > ans[i-1]*2:
#         raise ValueError
#     # вот этот инвариант нарушен
#     if ans[i] <= ans[i-1]:
#         raise ValueError

sys.stdout.write("YES\n")
sys.stdout.write(" ".join([str(x) for x in ans]))
