Few people know, but a long time ago a developed state existed on Mars. It
consisted of n cities, numbered by integers from 1 to n, the capital had
the number 1. Some pairs of cities were connected by a road. The residents
of the state were very prudent, therefore, between any two cities, there
was exactly one path (possibly consisting of several roads).
Due to the fact that the state was developed, its residents loved
traveling. Tourist route on Mars was described by two numbers L and
R. This meant that the tourist started the route in the city L, then
went to the city L + 1 (without going into the cities, that did not lie on
the path between L and L + 1), then went to the city L + 2, and so
on. The last city on the route was the city R. A city that was the
closest to the capital among all cities visited on this route (if to count
a distance between the cities by the roads) was considered the main
attraction of the route.
Knowing the map of the Martian state and all the tourist routes, find for
each route its main attraction.
The first line contains an integer n that is the number of cities (1
≤ n ≤ 2 · 105).
The following n − 1 lines describe the roads. Each road is described by
two numbers of cities that are connected by it (1 ≤ vi, ui ≤ n; vi ≠ ui).
The (n + 1)-th line contains an integer q that is the number of
tourist routes (0 ≤ q ≤ 106).
Then q lines describe the routes themselves. Each route is described by
a pair of integers Li, Ri (1 ≤ Li ≤ Ri ≤ n).
Output q integers, one per line — for each route the number of its
main attraction. These numbers should be output in the same order in which
the respective routes were described.
This problem has a big input and output data size and a strict Time Limit. If you write your solution in C++ we recommend you to use Visual C++ 2013 compiler.
Problem Author: Vladimir Leskov
Problem Source: Ural FU Junior Championship 2016