Winning Ways

Welcome to the finals of Chef's Combinatorial Games Competition 2019! The finalists Irshad and Mehedi are ready to play against each other no matter what game is given. As it is the final round, Chef prepared a completely new game with the following rules: - There are $K$ stacks of stones (numbered $1$ through $K$). For each valid $i$, the $i$-th stack has a *threshold* $H_i$. - Initially, each