Detect currency arbitrage with costs

You are given a K×K matrix R of currency exchange rates where R[i][j] is the amount of currency j obtainable for one unit of currency i, and R[i][i] = 1 for all i. A closed cycle of exchanges incurs a transaction cost of 0.01% of the initial amount (applied once per completed cycle). Determine whether there exists any cycle of exchanges that yields a strictly higher final amount than the initial after accounting for this cost. Return true if such an arbitrage opportunity exists, otherwise return false.