Given a Number N Sum 1 to N-1

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Problem

During QA validation of large totals in the Coupa Supplier Portal, you need to compute the sum of every integer from 1 through N - 1. Because N may contain hundreds of thousands of digits, you must not iterate through the range or convert the entire value to a native integer.

Return the result modulo mod.

Formal Specification

Implement sum_before_mod(n, mod), where:

n is a decimal string representing an integer N >= 1.
mod is a positive integer.
The output is an integer equal to (1 + 2 + ... + (N - 1)) % mod.

Use the identity N * (N - 1) / 2, but divide one factor by 2 before applying the modulo so the method works even when mod is even.

Constraints

1 <= len(n) <= 100000
n represents an integer N >= 1
1 <= mod <= 10^18
n contains only decimal digits
The algorithm must not enumerate the range from 1 through N - 1
The algorithm must not use floating-point arithmetic

Function Signature

def sum_before_mod(n, mod):

Your solutionPython 3

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