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:
a,b = map(int,raw_input().split(" "))

def do(v):
    ret = []
    while v:
        if v%2:
            ret.append(1)
        else:
            ret.append(0)
        v/=2
    return ret[::-1]

bins = [1]*40
for i in range(1,40):
    bins[i] = 2*bins[i-1]


if b>a:
    print "NO"
else:
    bits = do(a)
    s = sum(bits)
    if sum(bits)>b:
        print "NO"
        exit()
    else:
        l1 = len(bits)
        for i in range(l1-1):
            if bits[i] > 0:
                tmp = min(bits[i],b-s)
                bits[i] -= tmp
                bits[i+1]+= tmp*2
                s += tmp

            if s == b:
                break
    ans = []
    for i in range(l1):
        ans+= [bins[l1-i-1]]*bits[i]

    print "YES"
    print " ".join(map(str,ans))