Problem:
Problem H: Fibonacci Sets

Fibonacci number f(i) appear in a variety of puzzles in nature and math, including packing problems, family trees or Pythagorean triangles. They obey the rule f(i) = f(i - 1) + f(i - 2), where we set f(0) = 1 = f(-1).

Let V and d be two certain positive integers and be N ≡ 1001 a constant. Consider a set of V nodes, each node i having a Fibonacci label F[i] = (f(i) mod N) assigned for i = 1,..., V ≤ N. If |F(i) - F(j)| < d, then the nodes i and j are connected.

Given V and d, how many connected subsets of nodes will you obtain?

Figure 1: There are 4 connected subsets for V = 20 and d = 100.

Input

Each data set is defined as one line with two integers as follows:

Line 1: Number of nodes V and the distance d.

Input includes several data sets (i.e., several lines). The number of dat sets is less than or equal to 50.

Constraints

1 ≤ V ≤ 1000

1 ≤ d ≤ 150

Output

Output line contains one integer - the number of connected subsets - for each input line.

Sample Input

5 5
50 1
13 13

Output for the Sample Input

2
50
8

Solution in C# (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;


namespace Test1 {

    class ClassMain {

        public static int[] fibo = new int[1001];
        public static int mod = 1001;

        static void initFibo() {
            fibo[0] = 1; fibo[1] = 2;
            for (int i = 2; i <= 1000; i++) {
                fibo[i] = (fibo[i - 1] + fibo[i - 2]) % mod;
            }
        }


        public static void Main(String[] args) {
            initFibo();
            string line;
            while ((line = Console.ReadLine()) != null) {
                int[] ints = line.Split(' ').Select(int.Parse).ToArray();
                //int n = int.Parse(line);
                //if(n==0){break;}
                int v = ints[0];
                int d = ints[1];

                List<int> nodes = new List<int>();
                for (int i = 1; i <= v; i++) {
                    nodes.Add(fibo[i]);
                }
                nodes.Sort();

                int prev = nodes.ElementAt(0);
                int groupN = 1;
                for (int i = 1; i < v; i++) {
                    if (nodes.ElementAt(i) - prev < d) {
                        //nothing.
                    }
                    else {
                        groupN++;
                    }
                    prev = nodes.ElementAt(i);
                }


                Console.WriteLine(groupN);
            }   
        }   
    }
}