In this task, you will be given a list of numbers. The goal is to divide all the numbers in the list by a constant such that the sum of the resulting list is 1. The output should be rounded to 3 decimals.
Example: [1, 2, 3]
Example solution: [0.167, 0.333, 0.500]
Example explanation: The output list sums to 1.0 and has the same weight as the input 0.333 is twice as large as 0.167, .5 is 3 times as large as 0.167, and 0.5 is 1.5 times as large as 0.333. This is a good example.

Problem: [31.697, -83.277, 4.13, -50.027, -84.58, -31.329, -95.988, -35.997, 111.188]

Solution: [-0.135  0.356 -0.018  0.214  0.361  0.134  0.41   0.154 -0.475]