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 solve(n, k):
    u = k * (k - 1) / 2
    b = (n - u) / k
    #print n, u, b, n - b * k - u
    if b <= 0:
        return False, []
    res = [b for i in xrange(k)]
    n -= b * k
    for i in xrange(1, k):
        res[i] += i
        n -= i
    res[-1] += n
    if n and n == k - 1 and res[-2] * 2 < res[-1]:
        res[-1] -= 1
        res[-2] += 1
    for i in xrange(k - 1):
        if res[i] * 2 < res[i + 1] or res[i] == res[i + 1]:
            return False, []
    return True, res

assert solve(26, 6)[0]
assert solve(9, 3)[0]
assert solve(8, 3)[0] == False
assert solve(1, 1)[0]
assert solve(9, 4)[0] == False

(n, k) = map(int, raw_input().split())
flag, ns = solve(n, k)

if flag:
    print 'YES'
    print ' '.join(map(str, ns))
else:
    print 'NO'
