How to generate two random integers such that their running sums have a given ratio

I am trying to generate two random integers each with their own potential range of values. I keep a running sum of each value, and need to ensure that the ratio between these sums stays within range of a given value.

For each trial, I want both numbers to be random. Ie. I don't want to generate a single value and then calculate the other value to make the ratio I want.

The best solution I have found is for each trial, to just generate pairs of random numbers until The pair matches my constraints. However its not guaranteed to find a solution, and may loop for a long time.

import random

XMIN, XMAX = 64, 2500
YMIN, YMAX = 16, 2000
GOAL, THRESH =0.90, 0.03

def trial(sumX, sumY):
  x,y=0,0
  while True:
    x = random.randint(XMIN,XMAX)
    y = random.randint(YMIN,YMAX)
    if abs( (sumX+x)/(sumX+x+sumY+y)-GOAL) <= THRESH:
      return x,y


sumX,sumY=0,0
for I in range(10000):
  x,y=trial(sumX,sumY)
  trial_ratio = x/(x+y)

  sumX, sumY = sumX+x, sumY+y
  sum_ratio = sumX/(sumX+sumY)
  print(f"+({x:5d}, {y:5d}) = {trial_ratio:0.2%}      :     ({sumX:8d}, {sumY:8d})  = {sum_ratio:0.2%}")

The snippet is in python, but the language doesn't matter

The above works as expected, however if possible I would like to be able to terminate faster than just making a random guess and throwing out invalid results.