Problem B: How many Fibs?

Recall the definition of the Fibonacci numbers:

f₁ := 1
f₂ := 2
f_n := f_n-1 + f_n-2     (n>=3)

Given two numbers a and b, calculate how many Fibonacci numbers are in the range [a,b].

Input Specification

The input contains several test cases. Each test case consists of two non-negative integer numbers a and b. Input is terminated by a=b=0. Otherwise, a<=b<=10¹⁰⁰. The numbers a and b are given with no superfluous leading zeros.

Output Specification

For each test case output on a single line the number of Fibonacci numbers f_i with a<=f_i<=b.

Sample Input

10 100
1234567890 9876543210
0 0

Sample Output

5
4

---

import java.util.Scanner;
import java.math.BigInteger;

public class Main {
	public static void main(String[] args) {
		Scanner keyboard = new Scanner(System.in);
		String x, y;
		BigInteger[] F = new BigInteger[500];
		F[1] = BigInteger.valueOf(1);
		F[2] = BigInteger.valueOf(2);
		for(int i = 3; i < 500; i++)
			F[i] = F[i-1].add(F[i-2]);
		while(keyboard.hasNext()) {
			x = keyboard.next();
			y = keyboard.next();
			if(x.equals("0") && y.equals("0"))
				break;
			BigInteger a, b;
			a = new BigInteger(x);
			b = new BigInteger(y);
			int ans = 0;
			for(int i = 1; i < 500; i++) {
				if(F[i].compareTo(a) >= 0 && F[i].compareTo(b) <= 0)
					ans++;
			}
			System.out.println(ans);
		}
	}
}