Write a function extract$\_$order$($meas$,$ m$,$ a$,$ n$)$ given a measurement meas, number of qubits m$,$ a number a that is relatively prime to n$.$ The function return the order r if found using the successive approximation described above. If you cannot find the order, return None.

A modular$\_$exponentiation function is given to you.

def modular$\_$exponentiate$($a$,$ k$,$ n$)$: # a$^$k $\backslash$mod n

mu $=$ a

res $=1$

while k $>0$:

if k $\%2==1$:

res $=($res $*$ mu$)\%$ n

mu $=($mu $*$ mu$)\%$ n

k $=$ k $//2$

return res

def extract$\_$order$($meas$,$ m$,$ a$,$ n$)$:

# your code here

for r in range$(1,$ n$)$:

if modular$\_$exponentiate$($a$,$ r$,$ n$)==$ meas:

return r

$$

return None

r$1=$ extract$\_$order$(75,7,5,91)$

assert r$1==12$

$$

r$2=$ extract$\_$order$(53,7,5,91)$

assert r$2==12$

$$

r$3=$ extract$\_$order$(96,7,5,91)$

assert r$3==12$

$$

$$

r$4=$ extract$\_$order$(32,7,5,91)$

assert r$4==12$

$$

$$

r$5=$ extract$\_$order$(64,7,5,91)$

assert r$5==$ None

$$

$$

$$

r$6=$ extract$\_$order$(11,7,5,91)$

assert r$6==12$

$$