DouKaku?

import java.math.BigInteger;
import java.util.HashMap;
import java.util.Map;

public class Sample106 {
    private final Map<Integer, BigInteger> fibMemo_ = new HashMap<Integer, BigInteger>();

    public BigInteger getFibValue(int index) {
        if (index == 1 || index == 2) return BigInteger.ONE;
        BigInteger fib = fibMemo_.get(index);
        if (fib == null) {
            fib = getFibValue(index - 2).add(getFibValue(index - 1));
            fibMemo_.put(index, fib);
        }
        return fib;
    }

    public static void main(String[] args) {
        Sample106 instance = new Sample106();
        BigInteger fib1999 = instance.getFibValue(1999);
        BigInteger fib2000 = instance.getFibValue(2000);
        System.out.println(fib2000.gcd(fib1999));
    }
}