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 check(n, k, fl, fr):
    if n < k * (2 * fl + k - 1) // 2:
        return 1
    if k <= 32 and n > fr * (2**k - 1):
        return -1
    return 0

def main():
    n, k = map(int, input().split(' '))
    
    l, r = 1, n
    ans = []

    while k > 0:
        ll, rr = l, r
        cnt = -1
        while rr >= ll:
            mid = (ll + rr) // 2
            ck = check(n - mid, k - 1, mid + 1, mid * 2)
            
            if ck == 0:
                cnt = mid
                break
            elif ck < 0:
                ll = mid + 1
            else:
                rr = mid - 1

        if cnt == -1:
            print('NO')
            return

        ans.append(cnt)

        k -= 1
        n -= cnt
        l = cnt + 1
        r = min(n, cnt * 2)

    print('YES')
    print(*ans)

if __name__ == '__main__':
    main()
