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.

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.

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