{"raw_statement":[{"iden":"problem statement","content":"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.\nAnswer the following $Q$ queries:\n\n*   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.)"},{"iden":"constraints","content":"*   $2 \\leq N \\leq 10^5$\n*   $1 \\leq Q \\leq 10^5$\n*   $1 \\leq a_i, b_i \\leq N$\n*   $1 \\leq c_i \\leq N-1$\n*   $1 \\leq d_i \\leq 10^4$\n*   $1 \\leq x_j \\leq N-1$\n*   $1 \\leq y_j \\leq 10^4$\n*   $1 \\leq u_j < v_j \\leq N$\n*   The given graph is a tree.\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $Q$\n$a_1$ $b_1$ $c_1$ $d_1$\n$:$\n$a_{N-1}$ $b_{N-1}$ $c_{N-1}$ $d_{N-1}$\n$x_1$ $y_1$ $u_1$ $v_1$\n$:$\n$x_Q$ $y_Q$ $u_Q$ $v_Q$"},{"iden":"sample input 1","content":"5 3\n1 2 1 10\n1 3 2 20\n2 4 4 30\n5 2 1 40\n1 100 1 4\n1 100 1 5\n3 1000 3 4"},{"iden":"sample output 1","content":"130\n200\n60\n\nThe graph in this input is as follows:\n![image](https://img.atcoder.jp/ghi/ca75688b08f73eb63a30ce6daa54a781.png)\nHere 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.\n\n*   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 $100 + 30 = 130$.\n*   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 $100 + 100 = 200$.\n*   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."}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}