Problem:
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Problem C:
TransferTrain

うなぎは電車に乗るのが好きである. いま，うなぎは駅 A から駅 B へ電車を使って行こうとしている. うなぎは急いでいるので, 最短時間の経路を選ぶことにした. ただし，うなぎは乗り換えが苦手なので, 最短時間の経路が複数ある場合は最も乗り換え回数の少ない経路を選ぶことにした.

$N$ 本の路線がある. $i$ 本目の路線は $a_i$ 個の駅を通っている. $i$ 本目の路線の通る駅名は通る順に $s_{i,0}, ... , s_{i,a_i -1}$ であり, 駅間の所要時間は $t_{i,0}, ..., t_{i,a_i - 2}$ である. 電車は路線上を上下方向に走っており, 入力で与えられた逆順に乗ることもできる. 複数の路線の同じ駅名は同じ駅を表しており，乗り換えをすることが出来る. 乗り換えには駅や路線によらず $T$ 分かかる.

一本の路線が同じ駅を複数回通ることもある．もし同じ路線，同じ駅の，路線内で異なる位置の駅に移動したい場合は乗り換えをする必要がある. たとえば, C - D - E - F - D - G という路線を使って C から G まで行く場合, 始点から終点まで一本の電車で行くことも，D 駅で乗り換えて C - D, D - G と乗ることもできる.

うなぎが駅 A から駅 B へ行くのにかかる時間と乗り換え回数を求めよ. 電車はとても頻繁に来るので待ち時間は無視してよい.

Constraints

$N$ will be between 1 and 50,000, inclusive.

$T$ will be an integer between 1 and 1,000, inclusive.

At least one train stops at A.

At least one train stops at B.

A and B will be distinct.

$a_i$ will be bigger than or equal to 2.

$a_1 + ... + a_N$ will be between 2 and 100,000, inclusive.

$s_{i,j}$ will contain between 1 and 10 characters, inclusive.

Each character in $s_{i,j}$ will be a letter ('A'-'Z', 'a'-'z').

$t_{i,j}$ will be an integer between 1 and 1,000, inclusive.

Input

入力は以下の形式で与えられる:

$N$ $T$

$A$ $B$

$a_1$

$s_{1,1}$ ... $s_{1,a_1}$

$t_{1,1}$ ... $t_{1,a_1 -1}$

...

$a_N$

$s_{N,1}$ ... $s_{N,a_N}$

$t_{N,1}$ ... $t_{N,a_N-1}$

Output

うなぎが駅 A から駅 B へ行くのにかかる時間と乗り換え回数を空白で区切って1 行に出力せよ.

Sample Input 1

2 10
Warsaw Petersburg
3
Kiev Moscow Petersburg
150 120
3
Moscow Minsk Warsaw
100 150

Sample Output 1

380 1

Sample Input 2

2 10
Warsaw Petersburg
3
Kiev Moscow Petersburg
150 120
2
Minsk Warsaw
150

Sample Output 2

-1

Solution in C# (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;
using Debug = System.Diagnostics.Debug;
using StringBuilder = System.Text.StringBuilder;
//using System.Numerics;
//using Point = System.Numerics.Complex;
using Number = System.Int64;
namespace Program
{
    public class Solver
    {
        public void Solve()
        {
            var n = sc.Integer();
            var dt = sc.Integer();
            var f = sc.Scan();
            var t = sc.Scan();
            var map = new HashMap<string, int>();
            map[f] = 0;
            map[t] = 1;
            var a = new int[n][];
            var b = new int[n][];
            for (int i = 0; i < n; i++)
            {
                var k = sc.Integer();
                var s = sc.Scan(k);
                a[i] = new int[k];
                b[i] = sc.Integer(k - 1);
                foreach (var x in s)
                {
                    if (!map.ContainsKey(x))
                    {
                        var cnt = map.Count;
                        map[x] = cnt;
                    }
                }
                for (int j = 0; j < k; j++)
                    a[i][j] = map[s[j]];
            }
            var ans = func(map.Count, map[f], map[t], dt, a, b);
            if (ans == (long)1e18)
            {
                IO.Printer.Out.WriteLine(-1);
                return;
            }
            var u = ans / 1000000000;
            u -= 2 * dt;
            u /= 2;
            var v = ans % 1000000000;
            v -= 2;
            v /= 2;
            IO.Printer.Out.WriteLine("{0} {1}", u, v);
        }
        long func(int n, int f, int t, int dt, int[][] a, int[][] b)
        {
            var G = Enumerate(n + a.Sum(x => x.Length), x => new List<KeyValuePair<int, int>>());
            var ptr = n;
            for (int i = 0; i < a.Length; i++)
            {
                var x = a[i];
                var y = b[i];
                for (int j = 0; j < x.Length; j++)
                {
                    G[ptr].Add(new KeyValuePair<int, int>(x[j], -dt));
                    G[x[j]].Add(new KeyValuePair<int, int>(ptr, -dt));
                    if (j + 1 < x.Length)
                    {
                        G[ptr].Add(new KeyValuePair<int, int>(ptr + 1, 2 * y[j]));
                        G[ptr + 1].Add(new KeyValuePair<int, int>(ptr, 2 * y[j]));
                    }
                    ptr++;
                }
            }
            var dist = Enumerate(G.Length, x => (long)(1e18));
            dist[f] = 0;
            var pq = new BinaryHeapPriorityQueue<KeyValuePair<int, long>>((l, r) => l.Value.CompareTo(r.Value));
            pq.Enqueue(new KeyValuePair<int, long>(f, 0));
            while (pq.Any())
            {
                var p = pq.Dequeue();
                Debug.WriteLine(p);
                if (dist[p.Key] < p.Value) continue;
                const long X = 1000000000;
                foreach (var to in G[p.Key])
                {
                    var dx = to.Value * X;
                    var dy = 0;
                    if (dx < 0)
                    {
                        dx = -dx;
                        dy = 1;
                    }
                    if (dist[to.Key] > p.Value + dx + +dy)
                    {
                        dist[to.Key] = p.Value + dx + dy;
                        pq.Enqueue(new KeyValuePair<int, long>(to.Key, dist[to.Key]));
                    }
                }
            }
            return dist[t];
        }

        public IO.StreamScanner sc = new IO.StreamScanner(Console.OpenStandardInput());
        static T[] Enumerate<T>(int n, Func<int, T> f) { var a = new T[n]; for (int i = 0; i < n; ++i) a[i] = f(i); return a; }
        static public void Swap<T>(ref T a, ref T b) { var tmp = a; a = b; b = tmp; }
    }
}

#region main
static class Ex
{
    //static public string AsString(this IEnumerable<char> ie) { return new string(System.Linq.Enumerable.ToArray(ie)); }
    //static public string AsJoinedString<T>(this IEnumerable<T> ie, string st = " ") { return string.Join(st, ie); }
    static public void Main()
    {
        var solver = new Program.Solver();
        solver.Solve();
        Program.IO.Printer.Out.Flush();
    }
}
#endregion
#region Ex
namespace Program.IO
{
    using System.IO;
    using System.Text;
    using System.Globalization;
    public class Printer: StreamWriter
    {
        static Printer() { Out = new Printer(Console.OpenStandardOutput()) { AutoFlush = false }; }
        public static Printer Out { get; set; }
        public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } }
        public Printer(System.IO.Stream stream) : base(stream, new UTF8Encoding(false, true)) { }
        public Printer(System.IO.Stream stream, Encoding encoding) : base(stream, encoding) { }
        public void Write<T>(string format, T[] source) { base.Write(format, source.OfType<object>().ToArray()); }
        public void WriteLine<T>(string format, T[] source) { base.WriteLine(format, source.OfType<object>().ToArray()); }
    }
    public class StreamScanner
    {
        public StreamScanner(Stream stream) { str = stream; }
        public readonly Stream str;
        private readonly byte[] buf = new byte[1024];
        private int len, ptr;
        public bool isEof = false;
        public bool IsEndOfStream { get { return isEof; } }
        private byte read()
        {
            if (isEof) return 0;
            if (ptr >= len) { ptr = 0; if ((len = str.Read(buf, 0, 1024)) <= 0) { isEof = true; return 0; } }
            return buf[ptr++];
        }
        public char Char() { byte b = 0; do b = read(); while ((b < 33 || 126 < b) && !isEof); return (char)b; }

        public string Scan()
        {
            var sb = new StringBuilder();
            for (var b = Char(); b >= 33 && b <= 126; b = (char)read())
                sb.Append(b);
            return sb.ToString();
        }
        public string ScanLine()
        {
            var sb = new StringBuilder();
            for (var b = Char(); b != '\n'; b = (char)read())
                if (b == 0) break;
                else if (b != '\r') sb.Append(b);
            return sb.ToString();
        }
        public long Long()
        {
            if (isEof) return long.MinValue;
            long ret = 0; byte b = 0; var ng = false;
            do b = read();
            while (b != 0 && b != '-' && (b < '0' || '9' < b));
            if (b == 0) return long.MinValue;
            if (b == '-') { ng = true; b = read(); }
            for (; true; b = read())
            {
                if (b < '0' || '9' < b)
                    return ng ? -ret : ret;
                else ret = ret * 10 + b - '0';
            }
        }
        public int Integer() { return (isEof) ? int.MinValue : (int)Long(); }
        public double Double() { var s = Scan(); return s != "" ? double.Parse(s, CultureInfo.InvariantCulture) : double.NaN; }
        private T[] enumerate<T>(int n, Func<T> f)
        {
            var a = new T[n];
            for (int i = 0; i < n; ++i) a[i] = f();
            return a;
        }

        public char[] Char(int n) { return enumerate(n, Char); }
        public string[] Scan(int n) { return enumerate(n, Scan); }
        public double[] Double(int n) { return enumerate(n, Double); }
        public int[] Integer(int n) { return enumerate(n, Integer); }
        public long[] Long(int n) { return enumerate(n, Long); }
    }
}
#endregion

#region HashMap<K,V>
public class HashMap<K, V>: Dictionary<K, V>
//where V : new()
{
    public HashMap() : base() { }
    public HashMap(int cap) : base(cap) { }
    new public V this[K i]
    {
        get
        {
            V v;
            return TryGetValue(i, out v) ? v :
                base[i] = default(V);
            //base[i] = new V();
        }
        set { base[i] = value; }
    }
}
#endregion
#region PriorityQueue by BinaryHeap
public class BinaryHeapPriorityQueue<T>
{
    private readonly List<T> heap;
    private readonly Comparison<T> compare;
    private int size;
    public BinaryHeapPriorityQueue() : this(Comparer<T>.Default) { }
    public BinaryHeapPriorityQueue(IComparer<T> comparer) : this(16, comparer.Compare) { }
    public BinaryHeapPriorityQueue(Comparison<T> comparison) : this(16, comparison) { }
    public BinaryHeapPriorityQueue(int capacity, Comparison<T> comparison)
    {
        heap = new List<T>(capacity);
        compare = comparison;
    }
    public void Enqueue(T item)
    {

        heap.Add(item);
        var i = size++;
        while (i > 0)
        {
            var p = (i - 1) >> 1;
            if (compare(heap[p], item) <= 0)
                break;
            heap[i] = heap[p];
            i = p;
        }
        heap[i] = item;

    }
    public T Dequeue()
    {
        var ret = heap[0];
        var x = heap[--size];
        var i = 0;
        while ((i << 1) + 1 < size)
        {
            var a = (i << 1) + 1;
            var b = (i << 1) + 2;
            if (b < size && compare(heap[b], heap[a]) < 0) a = b;
            if (compare(heap[a], x) >= 0)
                break;
            heap[i] = heap[a];
            i = a;
        }
        heap[i] = x;
        heap.RemoveAt(size);
        return ret;

    }
    public T Peek() { return heap[0]; }
    public int Count { get { return size; } }
    public bool Any() { return size > 0; }
}
#endregion