1300. Sum of Mutated Array Closest to Target

from sortedcontainers import SortedList
class MKAverage:
    """tc O(MlgM)  M: size of q 
    """
    def __init__(self, m: int, k: int):
        self.left,self.mid,self.right = SortedList([]),SortedList([]),SortedList([])
        self.q = deque()
        self.m_sum = 0
        self.m = m
        self.k = k
    def addElement(self, x: int) -> None:
        # alwayse insert into mid before len(q) < m 
        if len(self.q) < self.m:
            self.mid.add(x)
        self.q.append(x)
        
        if len(self.q) == self.m:
            # when len(q) == m, move items off to left and right, calculate sum 
            for i in range(self.k):
                self.left.add(self.mid.pop(0))
            
            for j in range(self.k):
                self.right.add(self.mid.pop(-1))
            # add middle sum
            for val in self.mid:
                self.m_sum += val
        #   1. add new number nx : if we add nx to left/ right , make sure left right have exactly k numbers  
        # first left  then right, last try mid  
        elif len(self.q) > self.m : 
            if self.left.bisect_left(x) < len(self.left):
                self.left.add(x)
                v1 = self.left.pop(-1)
                self.mid.add(v1)
                self.m_sum += v1 
            elif self.right.bisect_left(x) > 0:
                self.right.add(x)
                v2 = self.right.pop(0)
                self.mid.add(v2)
                self.m_sum += v2 
            else: # x fall into mid 
                self.mid.add(x)
                self.m_sum += x 

            #2. remove oldest val in mid 
            rm = self.q.popleft() 
            # try to remove mid first, then right or left 
            # search
            if rm in self.mid:
                self.mid.remove(rm)
                # update sum 
                self.m_sum -= rm 
            elif rm in self.left:
            #elif self.left.bisect_left(rm) < len(self.left):
                self.left.remove(rm)
            else:
                #print(self.left,self.mid,self.right)
                self.right.remove(rm) #lg(N)
            # 3. balance left and right if needed
            if len(self.left) < self.k and len(self.mid)>0:
                v = self.mid.pop(0)
                self.left.add(v)
                self.m_sum -= v
            elif len(self.right) < self.k and len(self.mid)>0:
                v = self.mid.pop()
                self.right.add(v)
                self.m_sum -= v 
            
        

    def calculateMKAverage(self) -> int:
        if len(self.q) == self.m:
            return self.m_sum//(self.m-2*self.k) 
        return -1


# Your MKAverage object will be instantiated and called as such:
# obj = MKAverage(m, k)
# obj.addElement(num)
# param_2 = obj.calculateMKAverage()