This winter is so... well, you've got the idea :-) The Nvodsk road system can be represented as n junctions connected with n - 1 bidirectional roads so that there is a path between any two junctions. The organizers of some event want to choose a place to accommodate the participants (junction v ), and the place to set up the contests (junction u ). Besides, at the one hand, they want the participants to walk about the city and see the neighbourhood (that's why the distance between v and u should be no less than l ). On the other hand, they don't want the participants to freeze (so the distance between v and u should be no more than r ). Besides, for every street we know its beauty — some integer from 0 to 10 9 . Your task is to choose the path that fits in the length limits and has the largest average beauty. We shall define the average beauty as a median of sequence of the beauties of all roads along the path. We can put it more formally like that: let there be a path with the length k . Let a i be a non-decreasing sequence that contains exactly k elements. Each number occurs there exactly the number of times a road with such beauty occurs along on path. We will represent the path median as number a ⌊ k / 2⌋ , assuming that indexation starting from zero is used. ⌊ x ⌋ — is number х , rounded down to the nearest integer. For example, if a = {0, 5, 12} , then the median equals to 5 , and if a = {0, 5, 7, 12} , then the median is number 7 . It is guaranteed that there will be at least one path with the suitable quantity of roads. The first line contains three integers n , l , r ( 1 ≤ l ≤ r < n ≤ 10 5 ). Next n - 1 lines contain descriptions of roads of the Nvodsk, each line contains three integers a i , b i , c i ( 1 ≤ a i , b i ≤ n , 0 ≤ c i ≤ 10 9 , a i ≠ b i ) — junctions a i and b i are connected with a street whose beauty equals c i . Print two integers — numbers of the junctions, where to accommodate the participants and set up the contests, correspond