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E. Freezing with Style

time limit per test

7 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThis 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.

Input

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}.

Output

Print two integers — numbers of the junctions, where to accommodate the participants and set up the contests, correspondingly. If there are multiple optimal variants, print any of them.

Examples

Input

6 3 4

1 2 1

2 3 1

3 4 1

4 5 1

5 6 1

Output

4 1

Input

6 3 4

1 2 1

2 3 1

3 4 1

4 5 2

5 6 2

Output

6 3

Input

5 1 4

1 2 1

1 3 4

3 4 7

3 5 2

Output

4 3

Input

8 3 6

1 2 9

2 3 7

3 4 7

4 5 8

5 8 2

3 6 3

2 7 4

Output

5 1

Note

In the first sample all roads have the same beauty. That means that all paths of the positive length have the same median. Thus, any path with length from 3 to 4, inclusive will be valid for us.

In the second sample the city looks like that: 1 - 2 - 3 - 4 - 5 - 6. Two last roads are more valuable and we should choose any path that contains both of them and has the suitable length. It is either the path between 2 and 6 or the path between 3 and 6.

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