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 sys
n, m = map(int, input().split())
if(m > n):
    print("NO")
    sys.exit(0)
l = 1
ct = 0
dic = {}
while(n > 0):
    if(n % 2):
        dic[l] = 1
        ct += 1
    else:
        dic[l] = 0
    n //= 2
    l *= 2
#print(ct)
if(m < ct):
    print("NO")
else:
    print("YES")
    q = l
    l //= 2
    #print(l)
    while(ct != m):
        if(ct+dic[l] < m):
            dic[l//2] += (2*(dic[l]))
            ct+=dic[l]
            dic[l] = 0
        else:
            dic[l//2] += (2*(m-ct))
            dic[l] -= (m-ct)
            ct = m
        l//=2
    l = 1
    while(l < q):
        print((str(l)+" ")*dic[l],end="")
        l *= 2
    print()