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=map(int,input().split())
if k*(k+1)>n*2:
    print('NO')
elif k*(k+1)==n*2:
    print('YES')
    for i in range(1,k+1):
        print(i,end=' ')
elif k == 1:
    print('YES')
    print(n)
else:
    list1 = [n//k]*k
    list1[k-1] += n%k
    if k==2 and n%2 != 0:
        print('YES')
        for i in list1:
            print(i,end=' ')
        sys.exit()
    for i in range(k//2):
        list1[i] -=k//2-i
        if i>0 and list1[i]>2*list1[i-1]:
            print('NO')
            sys.exit()
    if k%2!=0:
        for i in range(k//2,k):
            list1[i] +=i-k//2
            if list1[i]>2*list1[i-1]:
                print('NO')
                sys.exit()
    else:
        for i in range(k//2,k):
            list1[i] +=i-k//2+1
            if list1[i]>2*list1[i-1]:
                print('NO')
                sys.exit()
    print('YES')
    for i in list1:
        print(i,end=' ')
