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:
# Question F. Powers of Two

def powersOfTwo(n, k):
    if k > n:
        return []
        
    # first, convert n into binary
    bin = [] # from least significant bit to highest
    while n > 0:
        bin.append(n % 2)
        n //= 2
    
    s = sum(bin)
    if s > k:
        return []

    idx = len(bin) - 1
    for i in range(k - s):
        # need to split (k - s) times
        bin[idx] -= 1
        bin[idx - 1] += 2
        if bin[idx] == 0:
            idx -= 1

    arr = []

    for i in range(idx + 1):
        if bin[i] > 0:
            power = 2 ** i
            for j in range(bin[i]):
                arr.append(power)

    return arr

if __name__ == "__main__":
    
    [n, k] = list(map(int, input().split(" ")))
    
    arr = powersOfTwo(n, k)
    if not arr:
        print("NO")
    else:
        print("YES")
        for n in arr:
            print(n, end = " ")