Select out images from an ImageCollection using a list and make a new collection

Question

I have an image collection that spans multiple years. I have looked at each image in the collection and created a list of the image's indices that I'd like to keep for my future analyses. However, I still haven't figure out how to use that index list to filter the entire original image collection and make a new one with my desired images. So far, I have the following:

Let's say that originalCollection is the first collection I obtained.

var imageList = originalCollection.toList(originalCollection.size());
var good_indices = ee.List([0,2,3,5,6,7,10,11,12,14,15,16,17,19,21,28,29,30,31,32,33,34,35,36,37,38,39,40]); 
print(good_indices);

Then I have tried this:

var i=0; //Index
var good_i = good_indices.get(i);
var img= ee.Image(imageList.get(good_i));
print(img);

This definitely gives me the first image in the ee.List but I need to iterate over all of the list. I've tried using a loop -although I know it is not recommend:

var i=0;
for (i; i == good_indices.length;i++){
var good_i = good_indices.get(i);
var img= ee.Image(imageList.get(good_i));
var col = ee.ImageCollection(img);
}
print(col);

But the result is undefined.

Answer 1

I found a way to do it and I am posting the answer in case anyone is interested.

I made a function to get an image for each number in the good_indices list, then mapped this function into function to create an image collection from those images.

function getImages(list){
var img = ee.Image(imageList.get(list));
return img;
} 

var final = ee.ImageCollection.fromImages(good_indices.map(getImages));
print(final);