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:
# alpha = "abcdefghijklmnopqrstuvwxyz"
t = 1
from heapq import heappop, heappush
for test in range(t):
    n,k = (map(int, input().split()))
    # n = int(input())
    # a = list(map(int, input().split()))
    binary = bin(n)[2:]
    dig = []
    counter = 0
    for i in range(len(binary)):
        if binary[-(i+1)]=="1":
            heappush(dig, -pow(2,counter))
        counter+=1
    left = k-len(dig)
    ans="YES"
    if left<0:
        print("NO")
        continue
    # print(dig)
    while left>0:
        el = heappop(dig)
        if el==-1:
            ans="NO"
            break
        else:
            heappush(dig, el//2)
            heappush(dig, el//2)
            left-=1

    print(ans)
    if ans=="YES":
        for i in dig:
            print(-i, end=" ")