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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)



import java.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        // 整数の入力
        int N = sc.nextInt();
        int Q = sc.nextInt();
        int nodes[] = new int[N];
        Branch branches[] = new Branch[N-1];

        Map<Integer, List<Integer>> bMap = new HashMap<>();

        ArrayList<Integer> a,b;
        for(int i=0;i<N-1;i++) {
            branches[i] = new Branch();
            branches[i].left = sc.nextInt();
            branches[i].right = sc.nextInt();
            branches[i].color = sc.nextInt();
            branches[i].distance = sc.nextInt();

            a = (ArrayList<Integer>) bMap.get(branches[i].left);
            if (a==null) { a = new ArrayList<>(); }
            a.add(branches[i].right);
            bMap.put(branches[i].left, a);

            a = (ArrayList<Integer>) bMap.get(branches[i].right);
            if (a==null) { a = new ArrayList<>(); }
            a.add(branches[i].left);
            bMap.put(branches[i].right, a);
        }

//        for(int i=1;i<=N;i++) {
//            a = (ArrayList<Integer>) bMap.get(i);
////            System.out.print(i + " : ");
//            if (a != null) {
//                for (Iterator itr = a.iterator(); itr.hasNext(); ) {
////                    System.out.print(itr.next() + " ");
//                }
//            }
//
////            System.out.println();
//        }
////        System.out.println();

//        for (Branch br:branches) {
//            Branch.dump(br);
//        }
//        System.out.println();

        for(int i=0;i<Q;i++) {
            int x = sc.nextInt();
            int y = sc.nextInt();
            int u = sc.nextInt();
            int v = sc.nextInt();

//            System.out.println(x + " " + y + " " + u + " " + v);
            for (Branch br:branches) {
                if (br.color == x) {
                    br.tmp_distance = y;
                } else {
                    br.tmp_distance = br.distance;
                }
            }

            int result = -1;
            for (Branch br:branches) {
                if ((br.left == u) || (br.right == u)) {
                    result = calc(branches, br, u, v);
                }
                if (result != -1) {
                    break;
                }
            }
            System.out.println(result);
//            System.out.println();
        }
//        System.out.println();
    }

    private static int calc(Branch[] branches, Branch b, int source, int destination) {
        int result = -1;
        if ((b.left == 0) || (b.right == 0)) {
//            Branch.dump(b);
//            System.out.println("==");
            return -1;
        }

        if ((b.right == destination) || (b.left == destination)) {
            result = b.tmp_distance;
//            Branch.dump(b);
//            System.out.println("<>");
        } else if (b.right == source) {
//            Branch.dump(b);
//            System.out.println(" >");

            for (Branch br:branches) {
                if (!br.equals(b) && ((br.left == b.left) || (br.right == b.left))) {
                    result = calc(branches, br, b.left, destination);
                }
                if (result != -1) {
                    break;
                }
            }

            if (result != -1) {
                result += b.tmp_distance;
            }
        } else if(b.left == source) {
//            Branch.dump(b);
//            System.out.println("< ");

            for (Branch br : branches) {
                if (!br.equals(b) && ((br.left == b.right) || (br.right == b.right))) {
                    result = calc(branches, br, b.right, destination);
                }
                if (result != -1) {
                    break;
                }
            }

            if (result != -1) {
                result += b.tmp_distance;
            }
        }
        return result;
    }

    private static class Branch {
        int left;
        int right;
        int color;
        int distance;
        int tmp_distance;

        static void dump(Branch b) {
            System.out.println("(" + b.left + ", " + b.right + ", " + b.color + ", " + b.tmp_distance + ")");
        }

    }
}