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:
import io,os,sys
input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
from heapq import *
from math import log2
heap=[]
n,kk=map(int,input().split())
t=n
if kk>n:
    print("NO")
else:
    while t > 0:
        k=int(log2(t))

        h=2**k
        heappush(heap,-k)

        t-=h
    if len(heap) == kk:
        sys.stdout.write("YES" + "\n")
        for i in heap:
            sys.stdout.write(str(2**(-i)) + " ")
    elif len(heap) > kk:
        sys.stdout.write("NO" + "\n")
    else:
        while len(heap) < kk:
            k=-heappop(heap)
            heappush(heap,-(k-1))
            heappush(heap,-(k-1))
        sys.stdout.write("YES" + "\n")
        for i in heap:
            sys.stdout.write(str(2**(-i)) + " ")