the official solution is here (from the Japanese version editorial)

I loved this problem. The problem can be seen as the coin change problem with negative weights: given the value $$$X$$$ and the coins array $$$A = (a_1, a_2 \ldots a_n)$$$, write $$$X = x_1a_1 + x_2a_2 + ... x_na_n$$$ with the $$$x_i$$$ allowed to be negative, and find the minimum possible value of $$$|x_1| + |x_2| + ... |x_n|$$$. The claim from the editorial is that for the sample testcase where $$$X=87, A=(1,10,100)$$$, in any valid solution, $$$x_1 = 7$$$ or $$$x_1 = -3$$$.

Ok well, my submission passes so this is how I did it.

First of all just form X using coins greedily i.e without any change.

You can store the count of each coin you ended up using.

Let's index them as 0 to n — 1. let's indicate their quantity as value[index]. Let's also denote the coin count procured through greedy as count[index].

An observation :- It's optimal to use either the count[index] of each coin which you procured through greedy or complement of it. (Here complement means value[i + 1] / value[i] — count[index] and if you do use complement for an index you will have to add 1 to count[index + 1]).

Any other value of count[index] aside from the two mentioned will not improve our answer.

Now since we have at most two values u can apply a dp kinda solution to solve it but do be careful since if u do use the complement of coin count u have to pass + 1 to the next index.. and my dp states were index, carry where carry means how much is being passed to the next index. (Without proof here but it will not exceed 2 at most)

I couldn't understand the editorial solution but I think it meant this only.

https://atcoder.jp/contests/abc231/submissions/28047816