def inverse(L):
	fac = 1
	i = 1
	n = len(L)
 
	for x in range(n):
		L[n-x-1] *= fac
		fac *= i
		i += 1
 
	E = [L[0]*L[0]] + [0]*(n-1)
	I = []
 
	for x in range(n):
		I.append(E[x]//L[0])
		for y in range(x,n):
			E[y] -= I[x]*L[y-x]
 
		for y in range(0,n-x):
			L[y] //= n-x-y
 
	for x in range(n):
		I[x] //= fac
		i -= 1
		fac //= i
 
	return I
 
print(inverse([1,0,-1,0,1,0,-1,0]))
print(inverse([1,2,4,8,16,32,64]))
print(inverse([1,-1,0,0,0,0,0,0]))

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