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:
from collections import Counter
import os
import sys
from io import BytesIO, IOBase

BUFSIZE = 8192
import math

class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)


class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")


sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
def divs(n, start=2):
    divisors = []
    for i in range(start, int(math.sqrt(n) + 1)):
        if n % i == 0:
            if n / i == i:
                divisors.append(i)
            else:
                divisors.extend([i, n // i])
    return divisors
##########################################################
#it=iter(t)
#if all(c in it for c in s):
#ls.sort(key=lambda x: (x[0], x[1]))
# ls.sort(key=lambda x: (x[0], x[1]))
import sys

inf = float("inf")
mod = 1000000007


def get_array(): return list(map(int, sys.stdin.readline().split()))


def get_i(): return map(int, sys.stdin.readline().split())

from bisect import bisect_left

import sys



def fxn(st,en,ind,step):

    mid=st+(en-st)//2

    if ind<mid:

        return fxn(st,mid-1, ind, step-1)

    elif ind>mid:

        return fxn(mid+1, en, ind, step-1)

    else:

        return step

#n, k = map(int, sys.stdin.readline().split())
#arr = list(map(int, sys.stdin.readline().split()))
#arr=[(int(x),i) for i,x in enumerate(input().split())]
# ls=list(map(int,input().split()))
# for i in range(m):
#print(s[i],end="")
#n=int(sys.stdin.readline())
#arr=list(map(int,input().split()))
import sys
#n=int(sys.stdin.readline())
n,k=get_i()
r=bin(n)[2:]
if k>n or k<r.count("1"):
    print("NO")
else:
    ans=[1]*k
    s=k
    for i in range(k):
        while s+ans[i]<=n:
            s+=ans[i]
            ans[i]<<=1
    if sum(ans)==n:
        print("YES")
        print(*sorted(ans))
    else:
        print("NO")