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 PYTHON3):

Solution:
inp = input().split()
n = int(inp[0])
k = int(inp[1])
a = []
cc = 0
ck =k
while(n!=0):
    a.append(n%2)
    cc += n%2
    n //= 2
a = a[::-1]
if(k<cc):
    print("NO")
else:
    k-=cc
    for i in range(len(a)-1):
        if(a[i]>0):
            temp2 = min(k,a[i])
            a[i]-=temp2
            a[i+1]+=temp2*2
            k-=temp2
        if(k<=0):
            break
    if(k<0 or k>0):
        print("NO")
    else:
        print("YES")
        s= []
        for i in range(len(a)):
            for j in range(a[i]):
                s.append(str(2**(len(a)-i-1)))
        s = s[::-1]
        print(" ".join(s))