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:
import sys
import bisect
import heapq

INF = 10**9+7
sys.setrecursionlimit(INF)


n, k = map(int, sys.stdin.readline().split())

ss = bin(n)[2:][::-1]

sol = []
class maxheap:
    def __init__(self):
        self.h = []

    def add(self, x):
        heapq.heappush(self.h, -x)

    def pop(self):
        x = heapq.heappop(self.h)
        return -x


sol = maxheap()

for i in range(len(ss)):
    p = int(ss[i])*2**i
    if p:
        sol.add(p)


        
if len(sol.h) > k:
    print 'NO'
    exit(0)

while len(sol.h) != k:
    x = sol.pop()
    if x == 1:
        print 'NO'
        exit(0)
    else:
        sol.add(x/2)
        sol.add(x/2)


print 'YES'
sol = sol.h


ans = []
for i in sol:
    ans.append(str(-i))

ans = ' '.join(ans)
print ans