human
Write me a code to hensel 's Lemma and the other steps required given the following:
Hensel 's Lemma | Function to find the modular inverse of a modulo m.
Apply the Euclidean algorithm , to find the modular inverse.
Function to find the derivative of f ( x ) and f '(x) = 3 * (x ^ 2).
Function to find the image of x in f ( x ) = x ^ 3 - k ..
Function to find the next power of the number.
Next power of prime for which solution is to be found.
Using Hensel 's recursion to  find the solution(next_a) for  next power of prime.
If next_a < 0 return equivalent positive remainder modulo p.
Return the next power of a.
Function to find the solution of the required exponent of prime.
The lemma does not work for derivative of f ( x ) at a1.
Looping from 1 to power of prime whose solution is to be found.
Final answer after evaluating all the exponents up till the required exponent.
Driver Code.
Function Call"
Solution in Python:
assistant
#Here is code to hensel 's Lemma and the other steps required.
 def inv ( a , m ) :
	m0 = m
	x0 = 0
	x1 = 1
	if ( m == 1 ) :
		return 0
	while ( a > 1 ) :
		q = a // m
		t = m
		m = a % m
		a = t
		t = x0
		x0 = x1 - q * x0
		x1 = t
	if ( x1 < 0 ) :
		x1 += m0
	return x1
def derivative ( x ) :
	return 3 * x * x
def Image ( x , k ) :
	return x * x * x - k
def next_power ( a_t , t , a1 , prime , k ) :
	power_p = int ( pow ( prime , t + 1 ) )
	next_a = ( a_t - Image ( a_t , k ) * inv ( derivative ( a1 ) , prime ) ) % power_p
	if ( next_a < 0 ) :
		next_a += power_p
		return next_a
	return next_a
def powerOfPrime ( prime , power , k , a1 ) :
	if ( derivative ( a1 ) != 0 ) :
		a_t = a1
		for p in range ( 1 , power ) :
			a_t = next_power ( a_t , p , a1 , prime , k )
		return a_t
	return - 1
prime = 7
a1 = 3
power = 2
k = 3
print ( powerOfPrime ( prime , power , k , a1 ) )