Problem: A positive integer x is called a power of two if it can be represented as x = 2^y, where y is a non-negative integer. So, the powers of two are 1, 2, 4, 8, 16, ....

You are given two positive integers n and k. Your task is to represent n as the sum of exactly k powers of two.

Input

The only line of the input contains two integers n and k (1 ≤ n ≤ 10^9, 1 ≤ k ≤ 2 ⋅ 10^5).

Output

If it is impossible to represent n as the sum of k powers of two, print NO.

Otherwise, print YES, and then print k positive integers b_1, b_2, ..., b_k such that each of b_i is a power of two, and ∑ _{i = 1}^{k} b_i = n. If there are multiple answers, you may print any of them.

Examples

Input


9 4


Output


YES
1 2 2 4 


Input


8 1


Output


YES
8 


Input


5 1


Output


NO


Input


3 7


Output


NO

Solution (in PYTHON):

Solution:
N,K = map(int,raw_input().split())
ans = []
cur = []
while N:
    cur.append(N%2)
    if (N%2):
        K -= 1
    N /= 2
if K < 0:
    print "NO"
    exit()
tmp = 1
temp = []
for i in range(len(cur)):
    if cur[i]:
        temp.append(tmp)
    tmp *= 2
for i in range(len(cur)-1,-1,-1):
    if i==0 and K:
        print "NO"
        exit()
    if cur[i]>=K:
        cur[i-1] += K*2
        cur[i] -= K
        K = 0
    else:
        cur[i-1] += cur[i]*2
        K -= cur[i]
        cur[i] = 0
tmp = 1
for i in range(len(cur)):
    for j in range(cur[i]):
        ans.append(tmp)
    tmp *= 2
print "YES"
print " ".join(map(str,ans))