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 (GCC 5.4.1) (judge verdict: Runtime Error)

#include <stdio.h>
#define min(x,y) (x<y)?x:y
#define max(x,y) (x>y)?x:y
#define BIG 9999999
typedef struct{
	int m;
	int md;
	int mc;
	int d;
} tree;

int main(void) {
	tree t[100001];
	int N,Q,a[4],x[4];
	scanf("%d%d",&N,&Q);
	t[1].m = BIG;
	t[1].d = 0;
	for(int i=0; i<N-1; i++){
		scanf("%d%d%d%d",&a[0],&a[1],&a[2],&a[3]);
		if(t[a[0]].m == 0){
			t[a[0]].m = a[1];
			t[a[0]].mc = a[2];
			t[a[0]].md = a[3];
		}else{
			t[a[1]].m = a[0];
			t[a[1]].mc = a[2];
			t[a[1]].md = a[3];
		}
	}
	for(int i=2; i<=N; i++) t[i].d = -1;
	for(int i=2; i<=N; i++){
		int count=0,x=i;
		while(1){
			count++;
			if(t[t[x].m].d!=-1){
				t[i].d = count + t[t[x].m].d;
				break;
			}
			x = t[x].m;
		}
		count = 0;
	}
	for(int i=0; i<Q; i++){
		scanf("%d%d%d%d",&x[0],&x[1],&x[2],&x[3]);
		int ans = 0,tem1=x[2],tem2=x[3];
		if(t[x[2]].d!=t[x[3]].d){
			tem1 = (t[x[2]].d>t[x[3]].d)?x[2]:x[3];
			tem2 = (t[x[2]].d<t[x[3]].d)?x[2]:x[3];
			while(t[tem1].d != t[tem2].d){
				if(t[tem1].mc == x[0]){
					ans += x[1];
				}else{
					ans += t[tem1].md;
				}
				tem1 = t[tem1].m;
			}
		}
		while(t[tem1].m != t[tem2].m){
			if(t[tem1].mc == x[0]){
				ans += x[1];
			}else{
				ans += t[tem1].md;
			}
			if(t[tem2].mc == x[0]){
				ans += x[1];
			}else{
				ans += t[tem2].md;
			}
			tem1 = t[tem1].m;
			tem2 = t[tem2].m;
		}
		ans += (t[tem1].md + t[tem2].md);
		printf("%d\n",ans);
		ans = 0;
	}
	return 0;
}