OSN 2019 Problem 2

Given $19$ red boxes and $200$ blue boxes filled with balls. None of which is empty. Suppose that every red boxes have a maximum of $200$ balls and every blue boxes have a maximum of $19$ balls. Suppose that the sum of all balls in the red boxes is less than the sum of all the balls in the blue boxes. Prove that there exists a subset of the red boxes and a subset of the blue boxes such that their sum is the same.