CF494D.Birthday

Ali is Hamed's little brother and tomorrow is his birthday. Hamed wants his brother to earn his gift so he gave him a hard programming problem and told him if he can successfully solve it, he'll get him a brand new laptop. Ali is not yet a very talented programmer like Hamed and although he usually doesn't cheat but this time is an exception. It's about a brand new laptop. So he decided to secretly seek help from you. Please solve this problem for Ali.

An n-vertex weighted rooted tree is given. Vertex number 1 is a root of the tree. We define d(u, v) as the sum of edges weights on the shortest path between vertices u and v. Specifically we define d(u, u) = 0. Also let's define S(v) for each vertex v as a set containing all vertices u such that d(1, u) = d(1, v) + d(v, u). Function f(u, v) is then defined using the following formula:

The goal is to calculate f(u, v) for each of the q given pair of vertices. As the answer can be rather large it's enough to print it modulo 109 + 7.

阿里是哈米德的弟弟，明天是他的生日。哈米德希望弟弟通过自己的努力赢得生日礼物，因此给他出了一道难度较高的编程题，并告诉他：如果能成功解决，就送他一台崭新的笔记本电脑。阿里目前还远不如哥哥哈米德那样才华横溢；尽管他平时从不作弊，但这次是个例外——毕竟这关乎一台崭新的笔记本电脑！于是他决定悄悄向你求助。请帮阿里解决这道题。

给定一棵含 $ n $ 个顶点的带权有根树，其中顶点编号为 $ 1 $ 的节点为树的根。我们定义 $ d(u, v) $ 为顶点 $ u $ 与 $ v $ 之间最短路径上所有边的权值之和；特别地，定义 $ d(u, u) = 0 $。此外，对每个顶点 $ v $，定义集合 $ S(v) $ 为所有满足 $ d(1, u) = d(1, v) + d(v, u) $ 的顶点 $ u $ 所构成的集合。函数 $ f(u, v) $ 则按如下公式定义：

目标是对给定的 $ q $ 对顶点，分别计算 $ f(u, v) $。由于答案可能非常大，只需输出其对 $ 10^9 + 7 $ 取模的结果。

In the first line of input an integer n (1 ≤ n ≤ 105), number of vertices of the tree is given.

In each of the next n - 1 lines three space-separated integers a__i, b__i, c__i (1 ≤ a__i, b__i ≤ n, 1 ≤ c__i ≤ 109) are given indicating an edge between a__i and b__i with weight equal to c__i.

In the next line an integer q (1 ≤ q ≤ 105), number of vertex pairs, is given.

In each of the next q lines two space-separated integers u__i, v__i (1 ≤ u__i, v__i ≤ n) are given meaning that you must calculate f(u__i, v__i).

It is guaranteed that the given edges form a tree.

输入的第一行包含一个整数 $n$（$1 \leq n \leq 10^5$），表示树的顶点数。

接下来的 $n-1$ 行中，每行包含三个用空格分隔的整数 $a_i,\, b_i,\, c_i$（$1 \leq a_i,\, b_i \leq n$，$1 \leq c_i \leq 10^9$），表示在顶点 $a_i$ 与 $b_i$ 之间存在一条权重为 $c_i$ 的边。

下一行包含一个整数 $q$（$1 \leq q \leq 10^5$），表示顶点对的数量。

接下来的 $q$ 行中，每行包含两个用空格分隔的整数 $u_i,\, v_i$（$1 \leq u_i,\, v_i \leq n$），表示你需要计算 $f(u_i,\, v_i)$。

保证所给的边构成一棵树。

Output q lines. In the i-th line print the value of f(u__i, v__i) modulo 109 + 7.

输出 q 行。在第 i 行输出 f(u__i, v__i) 对 $10^9 + 7$ 取模的值。