Hidden Sequence

It's not always easy to make up stories around problems ― like this one. We know that there is a hidden sequence $A_1, A_2, \ldots, A_N$ which contains only integers between $1$ and $K$ inclusive. We have acquired $M$ triplets $(X_1, Y_1, Z_1), (X_2, Y_2, Z_2), \ldots, (X_M, Y_M, Z_M)$. A very reliable source has given us intel that for each valid $i$, the $Y_i$-th occurrence of the integer $X_