Colorful Tree

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.

Example

Input

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

Output

130 200 60

inputFormat

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

outputFormat

Output

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

Example

Input

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

Output

130 200 60

样例

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

130
200
60

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