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
def top(d,f,tot):
    zero = f*(k-d) + (k-d)*(k-d-1)//2
    return tot-zero

n,k = map(int,input().split())
a = []
if n < k*(k+1)//2:
    print("NO")
else:
    if k == 1:
        print("YES")
        print(n)
    else:
        const = 0
        if n > 2**k-1:
            const = (n-(k*(k+1)//2))//k
            n -= const*k
            if const == 0:
                print('NO')
        if const > 0 or n <= 2**k-1:
            print("YES")
            a = [const]*k
            summ = n
            #print(a,const,summ)
            for i in range(0,k):
                a[i] += i + 1
                summ -= (i + 1)
            #print(a,const,summ)
            for i in range(1,k):
                if summ//(k-i) < 2**i-i-1 and (a[i] + summ//(k-i)) <= a[i-1]*2:
                    add = summ//(k-i)
                    for j in range(i,k):
                        a[j] += add
                        summ -= add
                    break
            #print(a,const,summ)
            while summ > 0:
                for i in range(k-1,0,-1):
                    if a[i-1]*2 >= (a[i]+1):
                        add = min(a[i-1]*2-a[i],summ)
                        a[i] += add
                        summ -= add
                    if summ == 0:
                        break
            #print(a,const,summ)
            for x in a:
                print(x)
