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D. Birthday

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputAli 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.

Input

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

Output *q* lines. In the *i*-th line print the value of *f*(*u*_{i}, *v*_{i}) modulo 10^{9} + 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

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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