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 math
n,k = map(int,input().split())
ans = []
mem = []
left = 0
if n == k:
    print('YES')
    for i in range(n):
        print(1,end=' ')
elif k>n:
    print('NO')
else:
    if n %2 !=0:
        n-=1
        ans.append(1)
    num = 1
    while 1:
        while(num<n):
            num = num<<1
        if num > n:
            num = num>>1
        if num == n:
            ans.append(num)
            break
        else:
            n = n-num
            ans.append(num)
            num = 1
    length = len(ans)
    if length >k:
        print('NO')
    elif length <k:
        while length!=k:
            length -=1
            need = k - length
            next = ans.pop(-1)
            if next<=need:
                mem.append([1,next])
                length+=next
            else:
                ret = int(math.log(need,2))
                total = 1<<ret
                length+=total
                left = k -length
                keep =next >> ret
                mem.append([keep, total-left])
                mem.append([keep//2,2*left])
                break
        print('YES')
        sumA = len(ans)
        for v in ans:
            print(v,end=' ')
        for v in mem:
            for i in range(v[1]):
                print(v[0],end=' ')
    else:
        print('YES')
        print(*ans)