Problem:
Score : 600 points

Problem Statement

There is a tree with N vertices numbered 1 to N.
The i-th edge in this tree connects Vertex a_i and Vertex b_i, and the color and length of that edge are c_i and d_i, respectively.
Here the color of each edge is represented by an integer between 1 and N-1 (inclusive). The same integer corresponds to the same color, and different integers correspond to different colors.

Answer the following Q queries:

Query j (1 \leq j \leq Q): assuming that the length of every edge whose color is x_j is changed to y_j, find the distance between Vertex u_j and Vertex v_j. (The changes of the lengths of edges do not affect the subsequent queries.)

Constraints

2 \leq N \leq 10^5

1 \leq Q \leq 10^5

1 \leq a_i, b_i \leq N

1 \leq c_i \leq N-1

1 \leq d_i \leq 10^4

1 \leq x_j \leq N-1

1 \leq y_j \leq 10^4

1 \leq u_j < v_j \leq N

The given graph is a tree.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N Q
a_1 b_1 c_1 d_1
:
a_{N-1} b_{N-1} c_{N-1} d_{N-1}
x_1 y_1 u_1 v_1
:
x_Q y_Q u_Q v_Q

Output

Print Q lines. The j-th line (1 \leq j \leq Q) should contain the answer to Query j.

Sample Input 1

5 3
1 2 1 10
1 3 2 20
2 4 4 30
5 2 1 40
1 100 1 4
1 100 1 5
3 1000 3 4

Sample Output 1

130
200
60

The graph in this input is as follows:

Here the edges of Color 1 are shown as solid red lines, the edge of Color 2 is shown as a bold green line, and the edge of Color 4 is shown as a blue dashed line.

Query 1: Assuming that the length of every edge whose color is 1 is changed to 100, the distance between Vertex 1 and Vertex 4 is 100 + 30 = 130.

Query 2: Assuming that the length of every edge whose color is 1 is changed to 100, the distance between Vertex 1 and Vertex 5 is 100 + 100 = 200.

Query 3: Assuming that the length of every edge whose color is 3 is changed to 1000 (there is no such edge), the distance between Vertex 3 and Vertex 4 is 20 + 10 + 30 = 60. Note that the edges of Color 1 now have their original lengths.

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

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Runtime.CompilerServices;
using static System.Math;
using System.Text;

namespace Program
{
    public static class ABC133F
    {
        static List<Tuple<int, int, int>>[] path;
        class LCA
        {
            public int V, logV;
            public List<int> depth;
            public List<Dictionary<int, Tuple<int, long>>> len;
            public List<List<int>> parent;

            public LCA(int v)
            {
                V = v;
                logV = 0;
                while (V > (1 << logV)) logV++;
                depth = Repeat(0, V).ToList();
                len = Repeat(0, V).Select(_ => new Dictionary<int, Tuple<int, long>>()).ToList();
                parent = Repeat(0, logV).Select(_ => Repeat(0, V).ToList()).ToList();
            }
            public void init(int v, int par, int d, Dictionary<int, Tuple<int, long>> l)
            {
                depth[v] = d;
                parent[0][v] = par;
                len[v] = l;
                for (var i = 0; i < path[v].Count; i++)
                {
                    int w = path[v][i].Item1;
                    var lc = new Dictionary<int, Tuple<int, long>>(l);
                    if (!lc.ContainsKey(path[v][i].Item2))
                    {
                        lc[path[v][i].Item2] = Tuple.Create(0, 0L);
                    }
                    lc[path[v][i].Item2] = Tuple.Create(lc[path[v][i].Item2].Item1 + 1, lc[path[v][i].Item2].Item2 + path[v][i].Item3);
                    if (w == par) continue;
                    init(w, v, d + 1, lc);
                }
            }
            public void build()
            {
                for (var k = 0; k + 1 < logV; k++)
                {
                    for (var v = 0; v < V; v++)
                    {
                        if (parent[k][v] < 0) parent[k + 1][v] = -1;
                        else parent[k + 1][v] = parent[k][parent[k][v]];
                    }
                }
            }
            public int query(int u, int v)
            {
                if (depth[u] > depth[v])
                {
                    var tmp = u;
                    u = v;
                    v = tmp;
                }
                for (var k = 0; k < logV; k++)
                {
                    if ((((depth[v] - depth[u]) >> k) & 1) != 0)
                    {
                        v = parent[k][v];
                    }
                }
                if (u == v) return u;
                for (int k = logV - 1; k >= 0; k--)
                {
                    if (parent[k][u] != parent[k][v])
                    {
                        u = parent[k][u];
                        v = parent[k][v];
                    }
                }
                return parent[0][u];
            }
        }

        static public void Solve()
        {
            var N = NN;
            var Q = NN;
            var abcd = Repeat(0, N - 1).Select(_ => new { a = (int)NN - 1, b = (int)NN - 1, c = (int)NN, d = (int)NN }).ToArray();
            var xyuv = Repeat(0, Q).Select(_ => new { x = NN, y = NN, u = NN - 1, v = NN - 1 }).ToArray();

            path = Repeat(0, N).Select(_ => new List<Tuple<int, int, int>>()).ToArray();
            foreach (var item in abcd)
            {
                path[item.a].Add(Tuple.Create(item.b, item.c, item.d));
                path[item.b].Add(Tuple.Create(item.a, item.c, item.d));
            }

            var lca = new LCA((int)N);
            lca.init(0, -1, 0, new Dictionary<int, Tuple<int, long>>());
            lca.build();

            foreach (var item in xyuv)
            {
                var z = lca.query((int)item.u, (int)item.v);
                var iroDic = new Dictionary<int, Tuple<int, long>>();
                for (var i = 1; i < N; i++)
                {
                    iroDic[i] = Tuple.Create(0, 0L);
                }
                foreach (var item2 in lca.len[(int)item.u])
                {
                    iroDic[item2.Key] = Tuple.Create(iroDic[item2.Key].Item1 + item2.Value.Item1, iroDic[item2.Key].Item2 + item2.Value.Item2);
                }
                foreach (var item2 in lca.len[(int)item.v])
                {
                    iroDic[item2.Key] = Tuple.Create(iroDic[item2.Key].Item1 + item2.Value.Item1, iroDic[item2.Key].Item2 + item2.Value.Item2);
                }
                foreach (var item2 in lca.len[z])
                {
                    iroDic[item2.Key] = Tuple.Create(iroDic[item2.Key].Item1 - item2.Value.Item1 * 2, iroDic[item2.Key].Item2 - item2.Value.Item2 * 2);
                }
                var sum = 0L;
                foreach (var item2 in iroDic)
                {
                    if (item2.Key == item.x)
                    {
                        sum += item2.Value.Item1 * item.y;
                    }
                    else
                    {
                        sum += item2.Value.Item2;
                    }
                }
                Console.WriteLine(sum);

            }
        }

        //_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/
        //                    TEST                    _/
        //_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/
        class BT<T> where T : IComparable
        {
            private class Node
            {
                public Node left;
                public Node right;
                public T val;
                public bool isBlack;
            }
            private Comparison<T> c;
            private Node root;
            private bool change;
            public BT(Comparison<T> _c) { c = _c; }
            public BT() : this((x, y) => x.CompareTo(y)) { }
            private bool Red(Node n) => n != null && !n.isBlack;
            private bool Black(Node n) => n != null && n.isBlack;
            private Node RotateL(Node n)
            {
                Node m = n.right, t = m.left;
                m.left = n; n.right = t;
                return m;
            }
            private Node RotateR(Node n)
            {
                Node m = n.left, t = m.right;
                m.right = n; n.left = t;
                return m;
            }
            private Node RotateLR(Node n)
            {
                n.left = RotateL(n.left);
                return RotateR(n);
            }
            private Node RotateRL(Node n)
            {
                n.right = RotateR(n.right);
                return RotateL(n);
            }
            public void Add(T x)
            {
                root = Add(root, x);
                root.isBlack = true;
            }
            private Node Add(Node n, T x)
            {
                if (n == null)
                {
                    change = true;
                    return new Node() { val = x };
                }
                var r = c(x, n.val);
                if (r < 0)
                {
                    n.left = Add(n.left, x);
                    return Balance(n);
                }
                if (r > 0)
                {
                    n.right = Add(n.right, x);
                    return Balance(n);
                }
                change = false;
                return n;
            }

            private Node Balance(Node n)
            {
                if (!change) return n;
                if (!Black(n)) return n;
                if (Red(n.left) && Red(n.left.left))
                {
                    n = RotateR(n);
                    n.left.isBlack = true;
                }
                else if (Red(n.left) && Red(n.left.right))
                {
                    n = RotateLR(n);
                    n.left.isBlack = true;
                }
                else if (Red(n.right) && Red(n.right.left))
                {
                    n = RotateRL(n);
                    n.right.isBlack = true;
                }
                else if (Red(n.right) && Red(n.right.right))
                {
                    n = RotateL(n);
                    n.right.isBlack = true;
                }
                else
                {
                    change = false;
                }
                return n;
            }

            public void Remove(T x)
            {
                root = Remove(root, x);
                if (root != null) root.isBlack = true;
            }
            private Node Remove(Node n, T x)
            {
                if (n == null)
                {
                    change = false;
                    return n;
                }
                var r = c(x, n.val);
                if (r < 0)
                {
                    n.left = Remove(n.left, x);
                    return BalanceL(n);
                }
                if (r > 0)
                {
                    n.right = Remove(n.right, x);
                    return BalanceR(n);
                }
                if (n.left == null)
                {
                    change = n.isBlack;
                    return n.right;
                }
                n.left = RemoveMax(n.left);
                n.val = lmax;
                return BalanceL(n);
            }
            private T lmax;
            private Node RemoveMax(Node n)
            {
                if (n.right != null)
                {
                    n.right = RemoveMax(n.right);
                    return BalanceR(n);
                }
                lmax = n.val;
                change = n.isBlack;
                return n.left;
            }
            private Node BalanceL(Node n)
            {
                if (!change) return n;
                if (Black(n.right) && Red(n.right.left))
                {
                    var b = n.isBlack;
                    n = RotateRL(n);
                    n.isBlack = b;
                    n.left.isBlack = true;
                    change = false;
                }
                else if (Black(n.right) && Red(n.right.right))
                {
                    var b = n.isBlack;
                    n = RotateL(n);
                    n.isBlack = b;
                    n.right.isBlack = true;
                    n.left.isBlack = true;
                    change = false;
                }
                else if (Black(n.right))
                {
                    change = n.isBlack;
                    n.isBlack = true;
                    n.right.isBlack = false;
                }
                else
                {
                    n = RotateL(n);
                    n.isBlack = true;
                    n.left.isBlack = false;
                    n.left = BalanceL(n.left);
                    change = false;
                }
                return n;
            }
            private Node BalanceR(Node n)
            {
                if (!change) return n;
                if (Black(n.left) && Red(n.left.right))
                {
                    var b = n.isBlack;
                    n = RotateLR(n);
                    n.isBlack = b;
                    n.right.isBlack = true;
                    change = false;
                }
                else if (Black(n.left) && Red(n.left.left))
                {
                    var b = n.isBlack;
                    n = RotateR(n);
                    n.isBlack = b;
                    n.left.isBlack = true;
                    n.right.isBlack = true;
                    change = false;
                }
                else if (Black(n.left))
                {
                    change = n.isBlack;
                    n.isBlack = true;
                    n.left.isBlack = false;
                }
                else
                {
                    n = RotateR(n);
                    n.isBlack = true;
                    n.right.isBlack = false;
                    n.right = BalanceR(n.right);
                    change = false;
                }
                return n;
            }
            public bool Have(T x)
            {
                var t = FindUpper(x);
                return t.Item1 && t.Item2.CompareTo(x) == 0;
            }
            public Tuple<bool, T> FindUpper(T x)
            {
                var v = FindUpper(root, x);
                if (v == null) return Tuple.Create(false, default(T));
                return v;
            }
            private Tuple<bool, T> FindUpper(Node n, T x)
            {
                if (n == null) return null;
                var r = c(x, n.val);
                if (r < 0)
                {
                    var v = FindUpper(n.left, x);
                    if (v == null) return Tuple.Create(true, n.val);
                    return v;
                }
                else if (r > 0) return FindUpper(n.right, x);
                else return Tuple.Create(true, x);
            }
            public Tuple<bool, T> FindLower(T x)
            {
                var v = FindLower(root, x);
                if (v == null) return Tuple.Create(false, default(T));
                return v;
            }
            private Tuple<bool, T> FindLower(Node n, T x)
            {
                if (n == null) return null;
                var r = c(x, n.val);
                if (r < 0) return FindLower(n.left, x);
                else if (r > 0)
                {
                    var v = FindLower(n.right, x);
                    if (v == null) return Tuple.Create(true, n.val);
                    return v;
                }
                else return Tuple.Create(true, x);
            }
            public T Min()
            {
                Node n = root, p = null;
                while (n != null) { p = n; n = n.left; }
                return p == null ? default(T) : p.val;
            }
            public T Max()
            {
                Node n = root, p = null;
                while (n != null) { p = n; n = n.right; }
                return p == null ? default(T) : p.val;
            }
            public bool Any() => root != null;
            public int CountSlow() => List(root).Count();
            public IEnumerable<T> List() => List(root);
            private IEnumerable<T> List(Node n)
            {
                if (n == null) yield break;
                foreach (var i in List(n.left)) yield return i;
                yield return n.val;
                foreach (var i in List(n.right)) yield return i;
            }
        }
        //_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/
        //                  TEST END                  _/
        //_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/

        static public void Main(string[] args)
        {
            if (args.Length == 0) { var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false }; Console.SetOut(sw); }
            Solve();
            Console.Out.Flush();
        }
        static Random rand = new Random();
        static class Console_
        {
            private static Queue<string> param = new Queue<string>();
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            public static string NextString() { if (param.Count == 0) foreach (var item in Console.ReadLine().Split(' ')) param.Enqueue(item); return param.Dequeue(); }
        }
        static long NN => long.Parse(Console_.NextString());
        static double ND => double.Parse(Console_.NextString());
        static string NS => Console_.NextString();
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static long[] NNList(long N) => Repeat(0, N).Select(_ => NN).ToArray();
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static double[] NDList(long N) => Repeat(0, N).Select(_ => ND).ToArray();
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static string[] NSList(long N) => Repeat(0, N).Select(_ => NS).ToArray();
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static IEnumerable<T> OrderByRand<T>(this IEnumerable<T> x) => x.OrderBy(_ => rand.Next());
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static IEnumerable<T> Repeat<T>(T v, long n) => Enumerable.Repeat<T>(v, (int)n);
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static IEnumerable<int> Range(long s, long c) => Enumerable.Range((int)s, (int)c);
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static void RevSort<T>(T[] l) where T : IComparable { Array.Sort(l, (x, y) => y.CompareTo(x)); }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static void RevSort<T>(T[] l, Comparison<T> comp) where T : IComparable { Array.Sort(l, (x, y) => comp(y, x)); }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static IEnumerable<long> Primes(long x) { if (x < 2) yield break; yield return 2; var halfx = x / 2; var table = new bool[halfx + 1]; var max = (long)(Math.Sqrt(x) / 2); for (long i = 1; i <= max; ++i) { if (table[i]) continue; var add = 2 * i + 1; yield return add; for (long j = 2 * i * (i + 1); j <= halfx; j += add) table[j] = true; } for (long i = max + 1; i <= halfx; ++i) if (!table[i] && 2 * i + 1 <= x) yield return 2 * i + 1; }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static IEnumerable<long> Factors(long x) { if (x < 2) yield break; while (x % 2 == 0) { x /= 2; yield return 2; } var max = (long)Math.Sqrt(x); for (long i = 3; i <= max; i += 2) while (x % i == 0) { x /= i; yield return i; } if (x != 1) yield return x; }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static IEnumerable<long> Divisor(long x) { if (x < 1) yield break; var max = (long)Math.Sqrt(x); for (long i = 1; i <= max; ++i) { if (x % i != 0) continue; yield return i; if (i != x / i) yield return x / i; } }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static long GCD(long a, long b) { while (b > 0) { var tmp = b; b = a % b; a = tmp; } return a; }
        static long LCM(long a, long b) => a * b / GCD(a, b);
        class PQ<T> where T : IComparable
        {
            private List<T> h;
            private Comparison<T> c;
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            public PQ(int cap, Comparison<T> c, bool asc = true) { h = new List<T>(cap); this.c = asc ? c : (x, y) => c(y, x); }
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            public PQ(Comparison<T> c, bool asc = true) { h = new List<T>(); this.c = asc ? c : (x, y) => c(y, x); }
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            public PQ(int cap, bool asc = true) : this(cap, (x, y) => x.CompareTo(y), asc) { }
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            public PQ(bool asc = true) : this((x, y) => x.CompareTo(y), asc) { }
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            public void Push(T v) { var i = h.Count; h.Add(v); while (i > 0) { var ni = (i - 1) / 2; if (c(v, h[ni]) >= 0) break; h[i] = h[ni]; i = ni; } h[i] = v; }
            public T Peek => h[0];
            public int Count => h.Count;
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            public T Pop() { var r = h[0]; var v = h[h.Count - 1]; h.RemoveAt(h.Count - 1); if (h.Count == 0) return r; var i = 0; while (i * 2 + 1 < h.Count) { var i1 = i * 2 + 1; var i2 = i * 2 + 2; if (i2 < h.Count && c(h[i1], h[i2]) > 0) i1 = i2; if (c(v, h[i1]) <= 0) break; h[i] = h[i1]; i = i1; } h[i] = v; return r; }
        }
        class PQ<TKey, TValue> where TKey : IComparable
        {
            private PQ<Tuple<TKey, TValue>> q;
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            public PQ(int cap, Comparison<TKey> c, bool asc = true) { q = new PQ<Tuple<TKey, TValue>>(cap, (x, y) => c(x.Item1, y.Item1), asc); }
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            public PQ(Comparison<TKey> c, bool asc = true) { q = new PQ<Tuple<TKey, TValue>>((x, y) => c(x.Item1, y.Item1), asc); }
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            public PQ(int cap, bool asc = true) : this(cap, (x, y) => x.CompareTo(y), asc) { }
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            public PQ(bool asc = true) : this((x, y) => x.CompareTo(y), asc) { }
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            public void Push(TKey k, TValue v) => q.Push(Tuple.Create(k, v));
            public Tuple<TKey, TValue> Peek => q.Peek;
            public int Count => q.Count;
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            public Tuple<TKey, TValue> Pop() => q.Pop();
        }
        public class UF
        {
            private long[] d;
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            public UF(long s) { d = Repeat(-1L, s).ToArray(); }
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            public bool Unite(long x, long y) { x = Root(x); y = Root(y); if (x != y) { if (d[y] < d[x]) { var t = y; y = x; x = t; } d[x] += d[y]; d[y] = x; } return x != y; }
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            public bool IsSame(long x, long y) => Root(x) == Root(y);
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            public long Root(long x) => d[x] < 0 ? x : d[x] = Root(d[x]);
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            public long Count(long x) => -d[Root(d[x])];
        }
        struct Mod : IEquatable<object>
        {
            static public long _mod = 1000000007;
            private long _val;
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            public Mod(long x) { if (x < _mod && x >= 0) _val = x; else if ((_val = x % _mod) < 0) _val += _mod; }
            static public implicit operator Mod(long x) => new Mod(x);
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            static public implicit operator long(Mod x) => x._val;
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            static public Mod operator +(Mod x, Mod y) => x._val + y._val;
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            static public Mod operator -(Mod x, Mod y) => x._val - y._val;
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            static public Mod operator *(Mod x, Mod y) => x._val * y._val;
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            static public Mod operator /(Mod x, Mod y) => x._val * Inverse(y._val);
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            static public bool operator ==(Mod x, Mod y) => x._val == y._val;
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            static public bool operator !=(Mod x, Mod y) => x._val != y._val;
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            static public long Inverse(long x) { long b = _mod, r = 1, u = 0, t = 0; while (b > 0) { var q = x / b; t = u; u = r - q * u; r = t; t = b; b = x - q * b; x = t; } return r < 0 ? r + _mod : r; }
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            bool IEquatable<object>.Equals(object obj) => obj == null ? false : Equals((Mod)obj);
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            public override bool Equals(object obj) => obj == null ? false : Equals((Mod)obj);
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            public bool Equals(Mod obj) => obj == null ? false : _val == obj._val;
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            public override int GetHashCode() => _val.GetHashCode();
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            public override string ToString() => _val.ToString();
            static private List<Mod> _fact = new List<Mod>() { 1 };
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            static private void Build(long n) { if (n >= _fact.Count) for (int i = _fact.Count; i <= n; ++i) _fact.Add(_fact[i - 1] * i); }
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            static public Mod Comb(long n, long k) { Build(n); if (n == 0 && k == 0) return 1; if (n < k || n < 0) return 0; return _fact[(int)n] / _fact[(int)(n - k)] / _fact[(int)k]; }
        }
        struct Mat<T>
        {
            private T[,] m;
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            public Mat(T[,] v) { m = (T[,])v.Clone(); }
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            static public implicit operator Mat<T>(T[,] v) => new Mat<T>(v);
            public T this[int r, int c] { get { return m[r, c]; } set { m[r, c] = value; } }
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            static public Mat<T> operator +(Mat<T> a, T x) { var tm = (T[,])a.m.Clone(); for (int r = 0; r < tm.GetLength(0); ++r) for (int c = 0; c < tm.GetLength(1); ++c) tm[r, c] += (dynamic)x; return tm; }
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            static public Mat<T> operator +(Mat<T> a, Mat<T> b) { var tm = (T[,])a.m.Clone(); for (int r = 0; r < tm.GetLength(0); ++r) for (int c = 0; c < tm.GetLength(1); ++c) tm[r, c] += (dynamic)b[r, c]; return tm; }
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            static public Mat<T> operator -(Mat<T> a, T x) { var tm = (T[,])a.m.Clone(); for (int r = 0; r < tm.GetLength(0); ++r) for (int c = 0; c < tm.GetLength(1); ++c) tm[r, c] -= (dynamic)x; return tm; }
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            static public Mat<T> operator -(Mat<T> a, Mat<T> b) { var tm = (T[,])a.m.Clone(); for (int r = 0; r < tm.GetLength(0); ++r) for (int c = 0; c < tm.GetLength(1); ++c) tm[r, c] -= (dynamic)b[r, c]; return tm; }
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            static public Mat<T> operator *(Mat<T> a, T x) { var tm = (T[,])a.m.Clone(); for (int r = 0; r < tm.GetLength(0); ++r) for (int c = 0; c < tm.GetLength(1); ++c) tm[r, c] *= (dynamic)x; return tm; }
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            static public Mat<T> operator *(Mat<T> a, Mat<T> b) { var nr = a.m.GetLength(0); var nc = b.m.GetLength(1); var tm = new T[nr, nc]; for (int i = 0; i < nr; ++i) for (int j = 0; j < nc; ++j) tm[i, j] = (dynamic)0; for (int r = 0; r < nr; ++r) for (int c = 0; c < nc; ++c) for (int i = 0; i < a.m.GetLength(1); ++i) tm[r, c] += a[r, i] * (dynamic)b[i, c]; return tm; }
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            static public Mat<T> Pow(Mat<T> x, long y) { var n = x.m.GetLength(0); var t = (Mat<T>)new T[n, n]; for (int i = 0; i < n; ++i) for (int j = 0; j < n; ++j) t[i, j] = (dynamic)(i == j ? 1 : 0); while (y != 0) { if ((y & 1) == 1) t *= x; x *= x; y >>= 1; } return t; }
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static Mat<T> Pow<T>(Mat<T> x, long y) => Mat<T>.Pow(x, y);
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static T Pow<T>(T x, long y) { T a = (dynamic)1; while (y != 0) { if ((y & 1) == 1) a *= (dynamic)x; x *= (dynamic)x; y >>= 1; } return a; }
        static List<long> _fact = new List<long>() { 1 };
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static void _Build(long n) { if (n >= _fact.Count) for (int i = _fact.Count; i <= n; ++i) _fact.Add(_fact[i - 1] * i); }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static long Comb(long n, long k) { _Build(n); if (n == 0 && k == 0) return 1; if (n < k || n < 0) return 0; return _fact[(int)n] / _fact[(int)(n - k)] / _fact[(int)k]; }
    }
}