5401: Birthday
内存限制：256 MB
时间限制：2 S
题面：传统
评测方式：文本比较
上传者：
提交：1
通过：1
题目描述
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.
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.
Input
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 ai,bi,ci (1≤ai,bi≤n, 1≤ci≤109) are given indicating an edge between ai and bi with weight equal to ci.
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 ui,vi (1≤ui,vi≤n) are given meaning that you must calculate f(ui,vi).
It is guaranteed that the given edges form a tree.
Output
Output q lines. In the i-th line print the value of f(ui,vi) modulo 109+7.
Examples
Input
5 1 2 1 4 3 1 3 5 1 1 3 1 5 1 1 1 5 2 4 2 1 3 5
Output
10 1000000005 1000000002 23 1000000002
Input
8 1 2 100 1 3 20 2 4 2 2 5 1 3 6 1 3 7 2 6 8 5 6 1 8 2 3 5 8 2 6 4 7 6 1
Output
999968753 49796 999961271 999991235 999958569 45130
输入样例 复制
输出样例 复制