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 $j$.