Number of pairs

Input

The first line contains two integers $n$ and $l$ ( $1 \leq n \leq 2 \cdot 1 0^{5}$ 1 \le n \le 2 \cdot 10^5, $1 \leq l \leq 1 0^{6}$ 1 \le l \le 10^6) — the number of vertices and the required distance.

Each of the next $n - 1$ n - 1 lines contains three integers $v_{i}$ v_i, $u_{i}$ u_i, and $t_{i}$ t_i ( $1 \leq u_{i}, v_{i} \leq n$ 1 \le u_i, v_i \le n, $v_{i} \neq = u_{i}$ v_i \ne u_i, $0 \leq t_{i} \leq 1 0^{6}$ 0 \le t_i \le 10^6), denoting a road with length $t_{i}$ t_i between cities $v_{i}$ v_i and $u_{i}$ u_i.

Output

Print the number of vertex pairs at a distance of exactly $l$ .

Examples

Example 1

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Example 2

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