IOI

Find a path that meets the following criteria:

1. The path is a sequence of distinct cities $a_1$, $a_2$, ..., $a_k$, where there is a direct road connecting each pair of consecutive cities.

2. The total length of this path must be exactly $l$.

Your task is to select such a sequence of cities that minimizes $k$.

Input Format

The first line contains two integers $n$ and $l$ ($1\le n\le 2\cdot 10^5$, $1\le l\le 10^6$) — representing the number of cities and the required path length, respectively.

Each of the following $n-1$ lines contains three integers $v_i$, $u_i$, and $t_i$ ($1\le u_i,v_i\le n,v_i\ne u_i,1\le t_i\le 10^6$), indicating there is a road of length $t_i$ between cities $v_i$ and $u_i$.

Output Format

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

Examples

Note

• In the first example, you can select the sequence of cities $1,2,3$.

• In the second example, it is not possible to find such a path.

• In the third example, you can choose the sequence $11,9,7$.