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 statistics import median
#import collections
#aa = collections.Counter(a) # list to list || .most_common(2)で最大の2個とりだせるお a[0][0]
from fractions import gcd
from itertools import combinations,permutations,accumulate, product # (string,3) 3回
#from collections import deque
from collections import deque,defaultdict,Counter
import decimal
import re
import math
import bisect
import heapq
#
#
#
# pythonで無理なときは、pypyでやると正解するかも！！
#
#
# my_round_int = lambda x:np.round((x*2 + 1)//2)
# 四捨五入g
#
# インデックス系
# int min_y = max(0, i - 2), max_y = min(h - 1, i + 2);
# int min_x = max(0, j - 2), max_x = min(w - 1, j + 2);
#
#
import sys
sys.setrecursionlimit(10000000)
mod = 10**9 + 7
#mod = 9982443453
#mod = 998244353
from sys import stdin
readline = stdin.readline
def readInts():
  return list(map(int,readline().split()))
def readTuples():
    return tuple(map(int,readline().split()))
def I():
  return int(readline())
LIST = list()
LIST.append(1)
a = 2
for i in range(32):
    LIST.append(a**i)
n,k = readInts()
if n < k:
    print('NO')
    exit()
ans = []
if n == 1 and k == 1:
    print('YES')
    print(1)
    exit()
if n%2:
    ans.append(1)
    n -= 1
    k -= 1
least = n
while least != 0 and k >= 0:
    l = bisect.bisect_right(LIST,least)
    v = LIST[l-1]
    ans.append(v)
    k -= 1
    least = least - v
if k < 0:
    print('NO')
    exit()
ans = list(map(lambda x:x*(-1), ans))
heapq.heapify(ans)
for _ in range(k):
    a = heapq.heappop(ans) * (-1)
    a //= 2
    for i in range(2):
        heapq.heappush(ans,-a)
ans = sorted(list(map(lambda x:x*(-1),ans)))
if 0 in ans:
    print('NO')
else:
    print('YES')
    print(*ans)