Problem: You are given two integers n and k. Find k-th smallest divisor of n, or report that it doesn't exist.

Divisor of n is any such natural number, that n can be divided by it without remainder.

Input

The first line contains two integers n and k (1 ≤ n ≤ 1015, 1 ≤ k ≤ 109).

Output

If n has less than k divisors, output -1.

Otherwise, output the k-th smallest divisor of n.

Examples

Input

4 2


Output

2


Input

5 3


Output

-1


Input

12 5


Output

6

Note

In the first example, number 4 has three divisors: 1, 2 and 4. The second one is 2.

In the second example, number 5 has only two divisors: 1 and 5. The third divisor doesn't exist, so the answer is -1.

Solution (in PYTHON3):

Solution:
inputList = input().split()

if len(inputList) != 2:
  print('Invalid input!')

num1 = int(inputList[0])
num2 = int(inputList[1])
outList = []

for i in range(int(num1 ** 0.5)):
  if num1 % (i+1) == 0:
    outList.append(i+1)

outSize = len(outList)
for j in range(outSize):
  if num1/(outList[outSize - j - 1]) != outList[outSize - j - 1]:
    outList.append(int(num1/(outList[outSize - j - 1])))

if num2 > len(outList) or num2 < 1:
  print(-1)
else:
  print(outList[num2-1])