Problem:
Score : 500 points

Problem Statement

There are N towns numbered 1 to N and M roads. The i-th road connects Town A_i and Town B_i bidirectionally and has a length of C_i.

Takahashi will travel between these towns by car, passing through these roads. The fuel tank of his car can contain at most L liters of fuel, and one liter of fuel is consumed for each unit distance traveled. When visiting a town while traveling, he can full the tank (or choose not to do so). Travel that results in the tank becoming empty halfway on the road cannot be done.

Process the following Q queries:

The tank is now full. Find the minimum number of times he needs to full his tank while traveling from Town s_i to Town t_i. If Town t_i is unreachable, print -1.

Constraints

All values in input are integers.

2 \leq N \leq 300

0 \leq M \leq \frac{N(N-1)}{2}

1 \leq L \leq 10^9

1 \leq A_i, B_i \leq N

A_i \neq B_i

\left(A_i, B_i\right) \neq \left(A_j, B_j\right) (if i \neq j)

\left(A_i, B_i\right) \neq \left(B_j, A_j\right) (if i \neq j)

1 \leq C_i \leq 10^9

1 \leq Q \leq N\left(N-1\right)

1 \leq s_i, t_i \leq N

s_i \neq t_i

\left(s_i, t_i\right) \neq \left(s_j, t_j\right) (if i \neq j)

Input

Input is given from Standard Input in the following format:

N M L
A_1 B_1 C_1
:
A_M B_M C_M
Q
s_1 t_1
:
s_Q t_Q

Output

Print Q lines.

The i-th line should contain the minimum number of times the tank needs to be fulled while traveling from Town s_i to Town t_i. If Town t_i is unreachable, the line should contain -1 instead.

Sample Input 1

3 2 5
1 2 3
2 3 3
2
3 2
1 3

Sample Output 1

0
1

To travel from Town 3 to Town 2, we can use the second road to reach Town 2 without fueling the tank on the way.

To travel from Town 1 to Town 3, we can first use the first road to get to Town 2, full the tank, and use the second road to reach Town 3.

Sample Input 2

4 0 1
1
2 1

Sample Output 2

-1

There may be no road at all.

Sample Input 3

5 4 4
1 2 2
2 3 2
3 4 3
4 5 2
20
2 1
3 1
4 1
5 1
1 2
3 2
4 2
5 2
1 3
2 3
4 3
5 3
1 4
2 4
3 4
5 4
1 5
2 5
3 5
4 5

Sample Output 3

0
0
1
2
0
0
1
2
0
0
0
1
1
1
0
0
2
2
1
0

Solution in C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Runtime.CompilerServices;
using System.Text;
using static Template;
using static System.Console;
using static System.Convert;
using static System.Math;
using Pi = Pair<int, int>;
using Graph;
//using DataStructure;

class Solver
{
    public void Solve()
    {
        int num, m, l;
        Input.Make(out num, out m, out l);

        var g = new Dijkstra_Dence<Pair<int, int>, Ed>(num);
        Ed.L = l;Ed.Zero = new Pi(0, -l);
        Ed.Inf = new Pi(int.MaxValue, 0);
        for (var i = 0; i < m; i++)
        {
            int a, b, c;
            Input.Make(out a, out b, out c);
            a--; b--;
            if (c > l) continue;
            g.AddEdge(new Ed(a, b, c));
            g.AddEdge(new Ed(b, a, c));
        }
        var dist = new Pi[num][];
        for (var i = 0; i < num; i++)
            dist[i] = g.Execute(i);
        var q = Input.num;
        while (q-- > 0)
        {
            int s, t;
            Input.Make(out s, out t);
            s--; t--;
            WriteLine(dist[s][t].v1 == int.MaxValue ? -1 : dist[s][t].v1);
        }
    }
    
}

public class Ed : DijEdge<Pi>
{
    public static int L;
    int d;
    public override Pi Add(Pi p)
    {
        Pi n;
        if (p.v2 + d > 0)
            n = new Pi(p.v1 + 1, -L + d);
        else n = new Pi(p.v1, p.v2 + d);
        return n;
    }
    public Ed(int from, int to, int d) : base(from, to, null)
    { this.d = d; }
}

namespace Graph
{
    #region テンプレート
    public class Graph<E> where E : IEdge
    {
        public List<E>[] Edges { get; set; }
        public int Count { get; }
        public Graph(int count)
        {
            Count = count;
            Edges = Create(count, () => new List<E>());
        }
    }
    public class Directed<E> : Graph<E> where E : Edge
    { public Directed(int count) : base(count) { } }
    public class Undirected<E> : Graph<E> where E : Edge
    { public Undirected(int count) : base(count) { } }

    public interface IWeight<T> where T : IComparable<T> { T Weight { get; set; } T Add(T t); }
    public interface INNegWeight<T> : IWeight<T> where T : IComparable<T> { }
    public interface IVertex
    {
        int Id { get; }
    }
    public interface IEdge
    {
        int From { get; set; }
        int To { get; set; }
    }
    public class Edge : IEdge
    {
        public int From { get; set; }
        public int To { get; set; }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public Edge(int from, int to)
        { From = from; To = to; }
    }
    #endregion
}
namespace Graph
{
    using Number = System.Int64;
    #region 密なグラフでのダイクストラ
    public abstract class DijEdge<W> : Edge, INNegWeight<W> where W : IComparable<W>
    {
        public static W Zero, Inf;
        public W Weight { get; set; }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public abstract W Add(W w);
        public DijEdge(int from, int to, W weight) : base(from, to)
        { Weight = weight; }
    }

    public class Dijkstra_Dence<W, DEdge> where W : IComparable<W> where DEdge : DijEdge<W>
    {
        private Graph<DEdge> g;
        public Dijkstra_Dence(int c) { g = new Graph<DEdge>(c); }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public void AddEdge(DEdge e)
         => g.Edges[e.From].Add(e);
        public W[] Execute(int st = 0)
        {
            var dist = Create(g.Count, () => DijEdge<W>.Inf);
            dist[st] = DijEdge<W>.Zero;
            var use = new bool[g.Count];
            while (true)
            {
                var min = DijEdge<W>.Inf;int minj = -1;
                for (var i = 0; i < g.Count; i++)
                    if (!use[i] && chmin(ref min, dist[i]))
                        minj = i;
                if (minj == -1) break;
                use[minj] = true;
                foreach (var e in g.Edges[minj])
                    chmin(ref dist[e.To], e.Add(min));
            }
            return dist;
        }
    }
    public class Dijkstra_Dence
    {
        private Dijkstra_Dence<Number, DijEdge> dij;
        public Dijkstra_Dence(int count)
        { dij = new Dijkstra_Dence<Number, DijEdge>(count); }
        public void AddEdge(int from, int to, Number weight)
            => dij.AddEdge(new DijEdge(from, to, weight));
        public Number[] Execute(int st = 0)
            => dij.Execute(st);
        public class DijEdge : DijEdge<Number>
        {
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            public override long Add(Number w)
                => Weight + w;
            public DijEdge(int from, int to, Number weight) : base(from, to, weight)
            { Zero = 0; Inf = Number.MaxValue; }
        }
    }
    #endregion
}

#region Template
public class Template
{
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static bool chmin<T>(ref T num, T val) where T : IComparable<T>
    { if (num.CompareTo(val) == 1) { num = val; return true; } return false; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static bool chmax<T>(ref T num, T val) where T : IComparable<T>
    { if (num.CompareTo(val) == -1) { num = val; return true; } return false; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static void swap<T>(ref T v1, ref T v2)
    { var t = v2; v2 = v1; v1 = t; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static T[] Create<T>(int n, Func<T> f)
        => Enumerable.Repeat(0, n).Select(_ => f()).ToArray();
    public static void Fail() => Fail("No");
    public static void Fail<T>(T s) { WriteLine(s); Console.Out.Close(); Environment.Exit(0); }
    static void Main(string[] args)
    {
        var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
        Console.SetOut(sw);
        var p = new Solver();
        for (var i = 1; i > 0; --i)
            p.Solve();
        Console.Out.Flush();
    }
}

public class Input
{
    public static string read => ReadLine().Trim();
    public static int[] ar => read.Split(' ').Select(int.Parse).ToArray();
    public static int num => ToInt32(read);
    public static long[] arL => read.Split(' ').Select(long.Parse).ToArray();
    public static long numL => ToInt64(read);
    public static char[][] grid(int h)
        => Create(h, () => read.ToCharArray());
    public static int[] ar1D(int n)
        => Create(n, () => num);
    public static long[] arL1D(int n)
        => Create(n, () => numL);
    public static string[] strs(int n)
        => Create(n, () => read);
    public static int[][] ar2D(int n)
        => Create(n, () => ar);
    public static long[][] arL2D(int n)
        => Create(n, () => arL);
    public static List<T>[] edge<T>(int n)
        => Create(n, () => new List<T>());
    public static void Make<T1, T2>(out T1 v1, out T2 v2)
    {
        v1 = Next<T1>();
        v2 = Next<T2>();
    }
    public static void Make<T1, T2, T3>(out T1 v1, out T2 v2, out T3 v3)
    {
        Make(out v1, out v2);
        v3 = Next<T3>();
    }
    public static void Make<T1, T2, T3, T4>(out T1 v1, out T2 v2, out T3 v3, out T4 v4)
    {
        Make(out v1, out v2, out v3);
        v4 = Next<T4>();
    }
    public static void Make<T1, T2, T3, T4, T5>(out T1 v1, out T2 v2, out T3 v3, out T4 v4, out T5 v5)
    {
        Make(out v1, out v2, out v3, out v4);
        v5 = Next<T5>();
    }
    public static void Make<T1, T2, T3, T4, T5, T6>(out T1 v1, out T2 v2, out T3 v3, out T4 v4, out T5 v5, out T6 v6)
    {
        Make(out v1, out v2, out v3, out v4, out v5);
        v6 = Next<T6>();
    }
    static Input()
    {
        sc = new Queue<string>();
        dic = new Dictionary<Type, Func<string, object>>();
        dic[typeof(int)] = s => int.Parse(s);
        dic[typeof(long)] = s => long.Parse(s);
        dic[typeof(char)] = s => char.Parse(s);
        dic[typeof(double)] = s => double.Parse(s);
        dic[typeof(uint)] = s => uint.Parse(s);
        dic[typeof(ulong)] = s => ulong.Parse(s);
        dic[typeof(string)] = s => s;
    }
    private static Dictionary<Type, Func<string, object>> dic;
    private static Queue<string> sc;
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static T Next<T>() { if (sc.Count == 0) foreach (var item in read.Split(' ')) sc.Enqueue(item); return (T)dic[typeof(T)](sc.Dequeue()); }
    public const int MOD = 1000000007;
}

public class Pair<T1, T2> : IComparable<Pair<T1, T2>>
{
    public T1 v1;
    public T2 v2;
    public Pair() { v1 = Input.Next<T1>(); v2 = Input.Next<T2>(); }
    public Pair(T1 v1, T2 v2)
    { this.v1 = v1; this.v2 = v2; }

    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public int CompareTo(Pair<T1, T2> p)
    {
        var c = Comparer<T1>.Default.Compare(v1, p.v1);
        if (c == 0)
            c = Comparer<T2>.Default.Compare(v2, p.v2);
        return c;
    }
    public override string ToString()
        => $"{v1.ToString()} {v2.ToString()}";
}

public class Pair<T1, T2, T3> : Pair<T1, T2>, IComparable<Pair<T1, T2, T3>>
{
    public T3 v3;
    public Pair() : base() { v3 = Input.Next<T3>(); }
    public Pair(T1 v1, T2 v2, T3 v3) : base(v1, v2)
    { this.v3 = v3; }

    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public int CompareTo(Pair<T1, T2, T3> p)
    {
        var c = base.CompareTo(p);
        if (c == 0)
            c = Comparer<T3>.Default.Compare(v3, p.v3);
        return c;
    }
    public override string ToString()
        => $"{base.ToString()} {v3.ToString()}";
}
#endregion