-----Description-----  
his task requires writing a Lean 4 method decomposes a natural number `n` into its prime factorization components based on a user-provided list of primes. Specifically, it calculates the exponents for each prime in the factorization such that:
\[ n = \prod p^e \]
In other words, it determines the exponent e for each prime p.

-----Input-----  
The input consists of a natural number n, and a list of prime numbers. The input n is obtained by multiplying together any powers of the prime numbers from the provided list.
n: The natural number to be factorized.  
primes: A list of primes to decompose n into.  

-----Output-----  
The output is `List (Nat × Nat)`:
Return a list of pair/Cartesian product of two natural numbers (p, e), where p is the prime and e is the exponent of p in the factorization. Each prime in the output must be from the input list, and every prime in the input list must appear in the output.

