Arithmetic with Large Integers using Chinese Remainder Theorem

Question

This is done by Python

Suppose we represent the sum of a collection of exponentiation operations as a list of tuples, where each tuple contains two integers: the base and the exponent. For example, the list [(2,4),(3,5),(-6,3)] represents the sum of powers 2⁴ + 3⁵ + (−6)³.

Implement a function sumOfPowers(nes, ps) that takes a list of one or more tuples nes (i.e., nes is of the form [(a1,n1),...,(ak,nk)]) as its first argument, and a list of one or more primes ps (i.e., of the form [p1,...,pm]) as its second argument. The function should return the correct result of the sum of powers as long as the following is true (e.g., on a computer with unlimited memory and time):

0 ≤ a1ⁿ¹ + ... + ak^nk < p1 ⋅ ... ⋅ pm

You may assume the second list contains distinct prime numbers. You may not assume that the numbers in the first input list have any particular patterns or relationships; they can be in any order, they can be of any size, and they may or may not share factors. Your implementation must work efficiently on very large inputs