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:
k, n = map(int, input().split())

if n > k:
    print("NO")
elif n == k:
    print("YES")
    print("1 " * n)
else:
    bits = []
    count = 1
    x = 1
    
    while x < k.bit_length()+1:
        if k & count:
            bits.append(x-1)
        count = 1 << x
        x += 1
    
    if len(bits) > n:
        print("NO")
    
    else:
        print("YES")
    
        if len(bits) == n:
            for el in bits:
                print(1<<el, end=" ")
            print()
    
        elif len(bits) << 1 > n:
            diff = abs(len(bits)-n)
            ans, count = "", 0
            
            for x in range(len(bits)-1, -1, -1):
                if count < diff:
                    ans += str(1<<(bits[x]-1)) + " " + str(1<<(bits[x]-1)) + " "
                    count += 1
                else:
                    ans += str(1<<bits[x]) + " "
            
            print(ans)
    
        else:
            ans = ""
            hmm = n - len(bits)
            
            while hmm > 0:
                ans = ""
                current = []
                
                for el in bits[::-1]:
                    cnt = 0
                        
                    while True:
                        a = (1<<(el-cnt)) - 1
                        if a <= hmm:
                            hmm -= a
                            ans += (str(1<<cnt)+" ") * (a+1)
                            current.extend([cnt] * (a+1))
                            break
                        cnt += 1
                
                bits = current
            
            print(ans)