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


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

d = [0]*k

if k == 1:
    print ('YES')
    print (n)
else:
    for i in range(k):
        d[i] = i + 1

    if sum(d) > n:
        print ('NO')
    else:
        t = n - sum(d)

        if t >= k:

            a = t // k
            t = t % k
            for i in range(k):
                d[i] += a

        if t > 0:
            if d[0] > 1:

                for i in range(k-1, k-1-t, -1):
                    d[i] += 1

            elif d[0] == 1:

                for i in range(k-1, 1, -1):
                    d[i] += 1
                    t -= 1
                    if t == 0: 
                        break


                if t > 0:
                    for i in range(k-1, 2, -1):
                        d[i] += 1
                        t -= 1
                        if t == 0: 
                            break


        # print (d)
        chk = True
        for i in range(k - 1):
            if d[i + 1] > 2 * d[i]:
                chk = False
                break

        if sum(d) != n:
            chk = False
            
        if chk:    
            print ('YES')
            s = ""
            for i in d:
                s += str(i) + " "
            print (s[:-1])
        else:
            print ('NO')

