How can I make rotate que by deque?

My Code (by. List)

n, m = map(int, input().split())
x = list(map(int,input().split()))

a = [z for z in range(1, n+1)]
print(a)
# x = [d, e, f]

f_idx = 0
b_idx = 0

for i in range(len(x)-1):
    if a.index(x[i]) == 0 :
            a.pop(0)
            print(a)
            
    
    elif a.index(x[i]) <= a.index(x[i+1]) :
            while True:
                a.append(a.pop(0))
                f_idx += 1
                if a.index(x[i]) == 0 :
                    a.pop(0)
                    print(a)
                    break    
                
    elif a.index(x[i]) > a.index(x[i+1]) :
           while True:
               a.insert(0,a.pop(-1))
               b_idx +=1
               if a.index(x[i]) == 0 :
                   a.pop(0)
                   print(a)
                   break
                   print(a)
                   break
    
    if i == len(x)-2 :
        if a.index(x[i+1]) == 0 :
            a.pop(0)

        elif a.index(x[i+1]) < len(a)/2:
            while True:
                a.append(a.pop(0))
                f_idx += 1
                if a.index(x[i+1]) == 0 :
                    a.pop(0)
                    print(a)
                    break    

        else:
            while True:
               a.insert(0,a.pop(-1))
               b_idx +=1
               if a.index(x[i+1]) == 0 :
                   a.pop(0)
                   print(a)
                   break

print("f_idx :", f_idx)
print("b_idx :", b_idx)
print(a)

Practice(To make rotate Que)

• input1 :

10, 3

1, 2, 3

• output1 : (f.idx + b.idx)

0

• input2 :

10, 3

2, 9, 5

• output2 : (f.idx + b.idx)

8

I already made rotate que by list.

But I want to make rotate que by deque.

So my question is 2.

1. What is the time complexity of my code?

2. How can I make rotate que by deque?