448_E. Divisors
Bizon the Champion isn't just friendly, he also is a rigorous coder.

Let's define function f(a), where a is a sequence of integers. Function f(a) returns the following sequence: first all divisors of a1 go in the increasing order, then all divisors of a2 go in the increasing order, and so on till the last element of sequence a. For example, f([2, 9, 1]) = [1, 2, 1, 3, 9, 1].

Let's determine the sequence Xi, for integer i (i ≥ 0): X0 = [X] ([X] is a sequence consisting of a single number X), Xi = f(Xi - 1) (i > 0). For example, at X = 6 we get X0 = [6], X1 = [1, 2, 3, 6], X2 = [1, 1, 2, 1, 3, 1, 2, 3, 6].

Given the numbers X and k, find the sequence Xk. As the answer can be rather large, find only the first 105 elements of this sequence.

Input

A single line contains two space-separated integers — X (1 ≤ X ≤ 1012) and k (0 ≤ k ≤ 1018).

Output

Print the elements of the sequence Xk in a single line, separated by a space. If the number of elements exceeds 105, then print only the first 105 elements.

Examples

Input

6 1


Output

1 2 3 6 


Input

4 2


Output

1 1 2 1 2 4 


Input

10 3


Output

1 1 1 2 1 1 5 1 1 2 1 5 1 2 5 10 
```python
import sys 
solSaved = {}
solSavedPropios = {}

def DivisorsN(n): 
    key = solSaved.get(str(n))
    if key == None : 
        divisors = []
        divisors2 = []
        for i in range(1,int(n ** (1/2)) + 1): 
            if n % i == 0 : 
                if abs(i - (n/i)) < 10 ** (-7) : divisors.append(int(i))
                else : 
                    divisors.append(int(i))
                    temp = []
                    temp.append(int(n/i))
                    divisors2 = temp + divisors2
        divisors = divisors + divisors2
        solSaved[str(n)] = divisors.copy()
        return divisors
    return key

def TodosLosDivisores(arrayN) : 
    sol = []
    if len(arrayN) > 10 ** 5 : 
        newArrayN = []
        for k in range(len(arrayN)): 
            newArrayN.append(arrayN[k])
        arrayN = newArrayN
    for i in range(len(arrayN) - 1):
        temp = DivisorsN(arrayN[i])
        for t in range(len(temp)) : sol.append(temp[t])
    #sol = sol + solSaved.get(str(arrayN[len(arrayN) - 1]))
    temp = sol.copy()
    temp2 = solSaved.get(str(arrayN[len(arrayN) - 1]))
    sol.append(temp2)
    for t in range(len(temp2)) : temp.append(temp2[t])
    solSaved[str(temp2)] = temp
    return sol

def DivisorsXk():
    a, b = input().split()
    x = int(a)
    k = int(b)
    if x == 1 : return 1
    if k == 0 : return x
    if k == 1 : return DivisorsN(x)
    sol = []
    sol.append(x)
    solSaved[str(x)] = DivisorsN(x)
    # index = 0
    # for i in range(k):
    #     prev_index = len(sol)
    #     for j in range(index, len(sol)):
    #         divs = DivisorsN(sol[j])
    #         sol = sol + divs
    #     index = prev_index
    i = 1
    while i <= k : 
        # j = 0
        # while j < len(sol): 
        #     if type(sol[j]) == int : newSol.append(DivisorsN(sol[j])) 
        #     else : newSol = newSol + DivisorAll(sol[j])
        #     j+=1
        # sol = newSol
        if type(sol[i - 1]) == int : sol.append(DivisorsN(sol[i - 1])) 
        else : sol.append(TodosLosDivisores(sol[i - 1]))
        i += 1
    temp = []
    temp2 = sol[len(sol) - 1]
    for t in range(len(temp2) - 1) : temp.append(temp2[t])
    temp = temp + temp2[len(temp2) - 1]
    return temp 

def LosFuckingDivisoresDeUnArrayConLista(a) : 
    sol = []
    if type(a) == int : return DivisorsN(a)
    for i in range(len(a)) : 
        temp = []
        key = solSaved.get(str(a[i]))
        if key == None : temp = LosFuckingDivisoresDeUnArrayConLista(a[i])
        else : temp = key
        sol.append(temp) 
    solSaved[str(a)] = sol
    return sol

def Divisors(x, k) : 
    if k == 0 : return x 
    if k > 10 ** 5 : 
        Ones = []
        for i in range(10 ** 5) : Ones.append(1)
        return Ones
    key = solSaved.get(str((x,k)))
    if key == None : 
        sol = []
        if type(x) == int : return Divisors(DivisorsN(x), k - 1)
        else : 
            sol = []
            for i in range(len(x)) : 
                temp = []
                temp.append(Divisors(x[i], k - 1))
                sol = sol + temp
            return sol
    else : return key

def DivisorsPropios(n) : 
    key = solSavedPropios.get(str(n))
    if key == None : 
        divisors = []
        divisors2 = []
        for i in range(2,int(n ** (1/2)) + 1): 
            if n % i == 0 : 
                if abs(i - (n/i)) < 10 ** (-7) : divisors.append(int(i))
                else : 
                    divisors.append(int(i))
                    temp = []
                    temp.append(int(n/i))
                    divisors2 = temp + divisors2 #divisors2.append(int(n / i))
        divisors = divisors + divisors2
        solSavedPropios[str(n)] = divisors.copy()
        return divisors
    return key

def UltimateDivisors(x, k) :
    if x == 1 : return 1
    if k == 0 : return x
    if k == 1 : return DivisorsN(x)
    if k >= 10 ** 5 : 
        a = []
        for i in range(10 ** 5) : a.append(1)
        return a
    Unos = []
    sol = []
    sol.append(1)
    temp = DivisorsPropios(x).copy()
    for i in range(k - 1) : Unos.append(1)
    if len(temp) == 0 : return [1] + Unos + [x]
    temp.append(x)
    for t in range(len(temp)) : 
        if len(sol) >= 10 ** 5 : return sol
        temp3 = DivisorsPropios(temp[t]).copy()
        if len(temp3) == 0 : 
            temp4 = UltimateDivisors(temp[t], k - 1)
            if type(temp4) == int : sol = sol  + [temp4]
            else : sol = sol + temp4
        else : sol = sol + NewUltimateDivisores(temp[t], k - 1)
    return sol

def NewUltimateDivisores(x, k) : 
    temp = DivisorsPropios(x)
    i = k - 1
    sol = []
    while i >= 1 : 
        if len(sol) >= 10**5 : return sol
        sol = sol + [1]
        for t in range(len(temp)) : 
            temp2 = UltimateDivisors(temp[t], i)
            if type(temp2) == int : sol = sol + [temp2]
            else : sol = sol + temp2
        i -= 1
    return sol + DivisorsN(x)

#print(UltimateDivisors(963761198400,65535))
#print(UltimateDivisors(549755813888,269))

a, b = input().split()
x = int(a)
k = int(b)
sol = UltimateDivisors(x,k)
if type(sol) == int : print(sol)
else :     
    if(len(sol) >= 10 ** 5):
        for i in range(10 ** 5 - 1) : 
            sys.stdout.write(str(sol[i]) + ' ')
        sys.stdout.write(str(sol[10**5 - 1]))
    else :  
        for i in range(len(sol) - 1) : 
            sys.stdout.write(str(sol[i]) + ' ')
        sys.stdout.write(str(sol[len(sol) - 1]))

```