Flattening a Nested Dictionary

You are given a nested dictionary. Your task is to flatten the dictionary by concatenating the keys of the nested dictionaries into a single key, with levels separated by a given delimiter.

For example, if the input dictionary is {"a": 1, "b": {"c": 2, "d": {"e": 3}}} and the delimiter is ., the flattened dictionary should be {"a": 1, "b.c": 2, "b.d.e": 3}. In mathematical form, if you have keys \(k_1, k_2, \dots, k_n\) then the new key is given by

$$ concatenated\_key = k_1 \; delimiter \; k_2 \; delimiter \; \dots \; delimiter \; k_n$$

Write a program that reads a JSON string representing the dictionary from standard input and a delimiter on the next line, and outputs the flattened dictionary as a JSON string. If the delimiter line is empty, use . as the default delimiter.

inputFormat

The input is given via stdin as follows:

1. The first line is a JSON string representing a nested dictionary. Keys are strings and values will be either integers or another dictionary.
2. The second line is a string representing the delimiter. If this line is empty, use . as the default delimiter.

outputFormat

Output the flattened dictionary as a JSON string to stdout.

{"a":1,"b":2}
.

{"a":1,"b":2}