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:
def split(power, terms):
    if terms == 0: return []
    if terms == 1: return [2 ** power]
    left = terms // 2
    right = terms - left
    return split(power - 1, left) + split(power - 1, right)

def main(n, k):
    # Se n for escrito na representação binária 2^0b0 + 2^1b1 + ..., 
    # onde bi = 0 ou 1, é possivel provar que ele pode ser escrito com, no minimo,
    # count(bi == 1) somas, e, no maximo, sum(2^bi | bi == 1) somas.
    bits_n = "{0:b}".format(n)
    count = sum(1 for bit in bits_n if bit == '1')
    if count > k:
        print("NO")
        return
    
    maximum_k = sum(2**power for power, bit in enumerate(bits_n[::-1]) if bit == '1')
    if k > maximum_k:
        print("NO")
        return
    
    print("YES")
    additional_terms_needed = k - count
    # print(bits_n)
    for i, bit in enumerate(bits_n):
        if bit == '0': continue

        power = len(bits_n) - i - 1
        # print("power", power)
        additional_to_do = min(additional_terms_needed, 2 ** power - 1)
        print(" ".join(str(x) for x in split(power, 1 + additional_to_do)), end=" ")
        additional_terms_needed -= additional_to_do
    
    print()

if __name__ == "__main__":
    n, k = [int(x) for x in input().split()]
    main(n, k)