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: Accepted)

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

class F
{
	struct R
	{
		public int P, C, D;
	}

	struct P
	{
		public int Id, Order, Sign, Depth, Distance, ColorDistance, ColorCount;
	}

	class Context
	{
		public int[] P2 = Enumerable.Range(0, 20).Select(i => (int)Math.Pow(2, i)).ToArray();
		public int Distance;
		public List<int> Stack = new List<int>();
		public List<R>[] Map;
		public List<int>[] Parents;

		public int Order;
		public P[] Points;
		public int[] ColorDistances;
		public int[] ColorCounts;
		public List<P>[] ColorTours;
	}

	static void Main()
	{
		Func<int[]> read = () => Console.ReadLine().Split().Select(int.Parse).ToArray();
		var h = read();
		var n = h[0];

		var c = new Context
		{
			Parents = new int[n + 1].Select(_ => new List<int>()).ToArray(),
			Points = new P[n + 1],
			ColorDistances = new int[n],
			ColorCounts = new int[n],
			ColorTours = new int[n].Select(_ => new List<P>()).ToArray(),
			Map = new int[n + 1].Select(_ => new List<R>()).ToArray(),
		};
		foreach (var r in new int[n - 1].Select(_ => read()))
		{
			c.Map[r[0]].Add(new R { P = r[1], C = r[2], D = r[3] });
			c.Map[r[1]].Add(new R { P = r[0], C = r[2], D = r[3] });
		}

		c.Map[0].Add(new R { P = 1 });
		Dfs(0, 0, c);

		Console.WriteLine(string.Join("\n", new int[h[1]].Select(_ => Answer(read(), c))));
	}

	static void Dfs(int p, int parent, Context c)
	{
		foreach (var r in c.Map[p])
		{
			if (r.P == parent) continue;

			for (int i = 0; c.P2[i] <= c.Stack.Count; i++)
				c.Parents[r.P].Add(c.Stack[c.Stack.Count - c.P2[i]]);

			c.Stack.Add(r.P);
			c.Distance += r.D;
			c.ColorDistances[r.C] += r.D;
			c.ColorCounts[r.C]++;

			var pd = new P
			{
				Id = r.P,
				Order = ++c.Order,
				Sign = 1,
				Depth = c.Stack.Count,
				Distance = c.Distance,
				ColorDistance = c.ColorDistances[r.C],
				ColorCount = c.ColorCounts[r.C],
			};
			c.ColorTours[r.C].Add(pd);
			c.Points[r.P] = pd;

			Dfs(r.P, p, c);

			c.Stack.RemoveAt(c.Stack.Count - 1);
			c.Distance -= r.D;
			c.ColorDistances[r.C] -= r.D;
			c.ColorCounts[r.C]--;

			var pu = new P
			{
				Id = r.P,
				Order = ++c.Order,
				Sign = -1,
				Depth = c.Stack.Count,
				Distance = c.Distance,
				ColorDistance = c.ColorDistances[r.C],
				ColorCount = c.ColorCounts[r.C],
			};
			c.ColorTours[r.C].Add(pu);
		}
	}

	static int Answer(int[] q, Context c)
	{
		var p1 = c.Points[q[2]];
		var p2 = c.Points[q[3]];

		var r1 = p1.Depth < p2.Depth ? p1 : p2;
		var r2 = p1.Depth < p2.Depth ? p2 : p1;

		while (r1.Depth < r2.Depth)
			r2 = c.Points[c.Parents[r2.Id][(int)Math.Log(r2.Depth - r1.Depth, 2)]];
		while (r1.Id != r2.Id)
		{
			var k = 0;
			while (k < c.Parents[r1.Id].Count && c.Parents[r1.Id][k] != c.Parents[r2.Id][k]) k++;
			if (k > 0) k--;
			r1 = c.Points[c.Parents[r1.Id][k]];
			r2 = c.Points[c.Parents[r2.Id][k]];
		}

		return Replace(p1, q[0], q[1], c) + Replace(p2, q[0], q[1], c) - 2 * Replace(r1, q[0], q[1], c);
	}

	static int Replace(P p, int x, int y, Context c)
	{
		var k = SearchLast(i => c.ColorTours[x][i].Order <= p.Order, -1, c.ColorTours[x].Count - 1);
		return p.Distance - (k == -1 ? 0 : c.ColorTours[x][k].ColorDistance) + (k == -1 ? 0 : c.ColorTours[x][k].ColorCount) * y;
	}

	static int SearchLast(Func<int, bool> f, int l, int r)
	{
		int m;
		while (l < r) if (f(m = (l + r + 1) / 2)) l = m; else r = m - 1;
		return r;
	}
}