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 10 9 + 7 . In the first line of input an integer n ( 1 ≤ n ≤ 10 5 ), 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 ≤ 10 9 ) 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 ≤ 10 5 ), 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. Output q lines. In the i -th line print the value of f ( u i , v i ) modulo 10 9 + 7 .