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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def pad_with_identity(circuit, k, n):
 """Pad a circuit by adding a `n`-channel identity circuit at index `k` That is, a circuit of channel dimension $N$ is extended to one of channel through the system unaffected. E.g. let ``A``, ``B`` be two single channel systems:: A + cid(2) + B This method can also be applied to irreducible systems, but in that case the result can not be decomposed as nicely. Args: circuit (Circuit):
 circuit to pad k (int):
 The index at which to insert the circuit n (int):
 The number of channels to pass through Returns: Circuit: An extended circuit that passes through the channels """

    circuit_n = circuit.cdim
    combined_circuit = circuit + circuit_identity(n)
    permutation = (list(range(k)) + list(range(circuit_n, circuit_n + n)) +
                   list(range(k, circuit_n)))
    return (CPermutation.create(invert_permutation(permutation)) <<
            combined_circuit << CPermutation.create(permutation))