BigInteger memory leak causes stack overflow in Java

I am trying to write an optimized fibonacci as an assignment to be able to compute fib (300) and fib (8000). Here is what I have so far (map is a HashMap).

public static BigInteger fibMemo(int n) {

    if (n <= 1){
        return BigInteger.valueOf(n);
    }

    if (!map.containsKey(n)){
        map.put(n, fibMemo(n-1).add(fibMemo(n-2)));
    }
    return map.get(n);        
}

      

        
        
        
      

    

When i call

System.out.println("300: " + FibonacciMemo.fibMemo(300));

      

        
        
        
      

    

by itself, it works fine. Besides,

System.out.println("8000: " + FibonacciMemo.fibMemo(8000));

      

        
        
        
      

    

works great if I comment out the previous call to fib (300). But if I keep both calls, I get a stack overflow on the recursive fibMemo. This is very strange to me. Can anyone please clarify the situation? Thanks in advance.

Here is the code:

import java.util.HashMap; // Import Java HashMap so we can use it
import java.math.BigInteger;

public class FibonacciMemo {
    private static HashMap<Integer, BigInteger> map = new HashMap<Integer, BigInteger>();
    /**
     * The classic recursive implementation with no memoization. Don't care
     * about graceful error catching, we're only interested in performance.
     * 
     * @param n
     * @return The nth fibonacci number
     */
    public static int fibNoMemo(int n) {
        if (n <= 1) {
            return n;
        }
        return fibNoMemo(n - 2) + fibNoMemo(n - 1);
    }
    /**
     * Your optimized recursive implementation with memoization. 
     * You may assume that n is non-negative.
     * 
     * @param n
     * @return The nth fibonacci number
     */
    public static BigInteger fibMemo(int n) {
        // YOUR CODE HERE
        if (n <= 1){
            return BigInteger.valueOf(n);
        }

        if (!map.containsKey(n)){
            map.put(n, fibMemo(n-1).add(fibMemo(n-2)));
        }
        return map.get(n);        
    }
public static void main(String[] args) {
        // Optional testing here        
        String m = "Fibonacci real name was Leonardo Pisano Bigollo.";
        m += "\n" + "He was the son of a wealthy merchant.\n";
        System.out.println(m);
         System.out.println("300: " + FibonacciMemo.fibMemo(300));
        System.out.println("8000: " + FibonacciMemo.fibMemo(8000));
        // 46th Fibonacci = 1,836,311,903
        // 47th Fibonacci = 2,971,215,073
    }
}