IOI — Eolymp

Input

The first line contains two integers $n$ and $l$ ( $1 \leq n \leq 2 \cdot 1 0^{5}$ 1 \leq n \leq 2 \cdot 10^5, $1 \leq l \leq 1 0^{6}$ 1 \leq l \leq 10^6): the number of cities and the required path length.

Each of the following $n - 1$ n - 1 lines contains three integers $v_{i}$ v_i, $u_{i}$ u_i, and $t_{i}$ t_i ( $1 \leq v_{i}, u_{i} \leq n$ 1 \leq v_i, u_i \leq n, $v_{i} \neq = u_{i}$ v_i \neq u_i, $1 \leq t_{i} \leq 1 0^{6}$ 1 \leq t_i \leq 10^6), indicating that there is a road of length $t_{i}$ t_i between cities $v_{i}$ v_i and $u_{i}$ u_i.

Output

Print the minimal $k$ , or $- 1$ if no such path exists.

Examples

Example 1

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Example 2

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Example 3

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Note

In the first example, you can select the sequence of cities $1, 2, 3$ .
In the second example, it is impossible to find such a path.
In the third example, you can select the sequence $11, 9, 7$ .