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 fun(a,n):
    p=[]
    if(n==1):
        return [a]
    if(a==n):
        p.extend([1 for i in range(a)])
        return p
    manager=n-1
    p=[a]
    while(manager>0):
        q=p.pop()
        p.extend([int(q/2),int(q/2)])
        manager=manager-1
        if(manager>=int(q/2)):
            r=p.pop()
            p=[1 for i in range(r)]+p
            manager=manager-r+1
        elif(manager<int(q/2)):
            if(manager==0):
                break
            s=p.pop()
            p=fun(s,manager+1)+p
            manager=0
            
    return p
x=str(input())
x=x.split(' ')
x=[i for i in x if x!='']
x[0]=int(x[0])
x[1]=int(x[1])
def bin1(a):
    y=bin(a)
    a=(str(y)).lstrip('0b')
    b=a.strip('0')
    z=b.split('0')
    z=[i for i in z if z!='']
    z="".join(z)
    return [a,z]
l=bin1(x[0])
cl=len(l[1])
lenny=len(l[0])
a=[]
manager=x[1]-cl
activate=1
if((cl<=x[1])and(x[1]<=x[0])):
    print("YES")
    for i in range(lenny):
        if(l[0][i]!='0'):
            if(activate==1):
                manager=manager-2**(lenny-i-1)+1
            if(activate!=1):
                a.append(2**(lenny-i-1))
            if(activate==1):
                if(manager>0):
                    a.extend(fun(2**(lenny-i-1),2**(lenny-i-1)))
                if(manager==0):
                    a.extend(fun(2**(lenny-i-1),2**(lenny-i-1)))
                    activate=-1
                if(manager<0):
                    manager=2**(lenny-i-1)+manager
                    a.extend(fun(2**(lenny-i-1),manager))
                    activate=-1
    a.sort()
    for i in range(x[1]):
        print(a[i],end=" ")
        
else:
    print("NO")