There is an acyclic graph with n points and n-1 edges (we can also call it a tree). The number of the node is 1~n. Each edge has a weight  w. We know that there is a shortest path between the two nodes u, v. For this shortest path, we use:

    f(u,v) represents the average of all edge weights on the path
    d(u,v) represents the number of edges on the path

    s(u,v) represents the set of points passing on the path (including u, v)

Now there is a simple question, we only need to calculate

输入描述:

The first line enters two integers n, x, where n represents the number of nodes and x represents the value of x in the above formula.
Next n-1 lines, input three integers u, v, w for each line, represent that there is a path with a weight of w between node u and node v.
Data guarantee: 1 < n < = 1e5, 1<=x<n, 1 <= u, v <= n, 1 <= w < = 1e4.
Guaranteed input must be a tree

输出描述:

Output the result of the formula, accurate to three decimal places.
If there is no  value that satisfies the condition, directly output -1.

5 2
1 2 4
2 3 2
3 4 3
3 5 4

3.333

u=5, v=1 can get the maximum

5 2
1 2 2
2 3 4
3 4 3
3 5 4

4.000

u=5, v=2 can get the maximum

3 2
1 2 1
1 3 1

-1

Can't find u, v meets all of the above conditions