Not getting correct output using recursion in python sort because of arguments

I am trying merge with a different type, and I am unable to get the correct output. I just want to pass the list in the final function and get the sorted output. Can anyone please guide me where I am wrong??

def merge(arr, start, mer1, mer2, end):

    left_array = arr[start - 1 : mer1]
    mid_array = arr[mer1: mer2 + 1]
    right_array = arr[mer2 + 1 : end]

    left_array.append(float('inf'))
    mid_array.append(float('inf'))
    right_array.append(float('inf'))
    
    ind_left = 0
    ind_mid = 0
    ind_right = 0

    for i in range(start - 1, end):
        minimum = min([left_array[ind_left], mid_array[ind_mid], right_array[ind_right]])
        if minimum == left_array[ind_left]:
            arr[i] = left_array[ind_left]
            ind_left += 1
        elif minimum == mid_array[ind_mid]:
            arr[i] = mid_array[ind_mid]
            ind_mid += 1
        else:
            arr[i] = right_array[ind_right]
            ind_right += 1
            
def merge_sort(L, start = None, end = None):
    
    start = start or 1
    end = end or (len(L) - 1)

    if len(L[start - 1: end]) < 2:
        return L
    else: 
        meg1 = start + ((end - start) // 3)
        meg2 = start + 2 * ((end - start) // 3)

        merge_sort(L, start, meg1)
        merge_sort(L, meg1 + 1, meg2 + 1)
        merge_sort(L, meg2 + 2, end)
        merge(L, start, meg1, meg2, end)
        return L
    
arr = [312,413,3,423,5,3,342,1,2, 69, 69, 76]
print (merge_sort(arr))

The output I am getting is

[1, 2, 3, 3, 5, 69, 69, 312, 342, 413, 423, 76]

>Solution :

I think you’re just computing the wrong initial end position in the second line of your merge_sort function. When I change the line:

end = end or (len(L) - 1)

to:

end = end or len(L)

I get the right result:

[1, 2, 3, 3, 5, 69, 69, 76, 312, 342, 413, 423]