问当计算n= ~11000 +带记忆的斐波那契递归方法时发生堆栈溢出

EN

public class BigInt {

static BigInteger[] fval;

public static void main(String[] args) {
    int index;
    Scanner input = new Scanner(System.in);
    index = input.nextInt();
    fval = new BigInteger[index + 1];

    System.out.println(fib_rec(index));
}

public static BigInteger fib_rec(int index) {
    BigInteger result = BigInteger.ONE;
    if (index <= 2) {
        return result;
    } else {
        if (fval[index] != null) {
            result = fval[index];
        } else {
            result = fib_rec(index - 1).add(fib_rec(index - 2));
            fval[index] = result;
        }
        return result;
    }
}