Explain how you derived its complexity of the given algorithm. $($Normally$,$ this explanation involves identifying its characteristic operation, expressing as a summation the number of times the characteristic operation is executed, and simplifying the summation.$)$

#check pre$-$conditions

if isEmpty$($list$)$ OR m $<=0$ OR m $>$ length$($list$)$:

# if invalid input

return "Invalid input"

#initialize an empty list to store the m smallest numbers

result $=[]$

#iterate through the list

for i from $1$ to m:

#find the minimum element in the remaining unprocessed list

minElement $=$ min$($list$)$

#add the minimum element to the list

result.append$($minElement$)$

#remove the minimum element from the list

list.remove$($minElement$)$

#returns the final list

return result