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:
n,k = tuple(map(int,input().split(" ")))
ans = "YES"
bits = bin(n)[2:]
n_bits = bits.count("1")

if k>n or k<n_bits:
    ans = "NO"

power = []
[power.append(int(bits[i])*(2**(len(bits)-i-1))) for i in range (len(bits))]

power.reverse()

reqd = k-n_bits
ans_bits = []
if ans == "YES":
    while reqd > 0 or len(power) > 0:
        if power[len(power)-1] == 1 or reqd == 0:
            ans_bits.append(power.pop())
        else:
            val = power.pop()
            if val!=0:
                power.append(val // 2)
                power.append(val // 2)
               # print(power)

                reqd-=1
    print(ans)
    for i in ans_bits:
        if i!=0:
            print(i,end=" ")
else:
    print(ans)