K-th smallest quick sort python

Question

I have to get K-th smallest element in unsorted array. Not to sort the whole array I am trying only sort the subarrays that include K-th element. Then I am printing all K-th from 0 to len(array)

array = [6,5,4,3,2,1]
def quick_sort(lst, k):
    if len(lst) <= 1:
        return lst
    else:
        p = (lst[0] + lst[len(lst)-1])/2
        left = [x for x in lst if x <= p]
        right = [x for x in lst if x > p]
        
        if  k > len(left) -1 :
            k = k - len(left)+1
            return quick_sort(right,k)
        else:
            return quick_sort(left, k)
  
for i in range(len(array)):    
    print(*quick_sort(array,i+1))

I want to get 1,2,3,4,5,6 but my code does 2,3,5,6,6,6. What I need to change?

PS THe main idea is not sorting all arrays and not using python sort functions

Answer 1

array = [6, 5, 4, 3, 2, 1]

def quick_sort(lst, k):
    if len(lst) <= 1:
        return lst
    else:
        p = (lst[0] + lst[-1]) / 2
        left = [x for x in lst if x <= p]
        right = [x for x in lst if x > p]

        if k > len(left):
            k = k - len(left)
            return quick_sort(right, k)
        else:
            return quick_sort(left, k)

for i in range(len(array)):
    print(*quick_sort(array, i + 1))