You have a lemon tree containing ~N~ lemons connected with ~N-1~ branches. Each lemon has a value. We call the floor of the arithmetic mean of the values on the path from ~u~ to ~v~ the relation between lemon ~u~ and lemon ~v~. Tommy can only eat the two lemons if their relation is not greater than ~M~; otherwise, Tommy will have syncope. Please help Tommy determine how many pairs of lemons he can eat.

Input Specification

The first line contains two integers, ~N~ ~(3 \le N \le 10^5)~ and ~M~ ~(1 \le M \le 10^3)~.

The next line contains ~N~ integers. The ~i^\text{th}~ integer, ~a_i~ ~(-10^3 \le a_i \le 10^3)~, represents the value of ~i^\text{th}~ lemon.

The next ~N-1~ lines will each contain two integers, ~u_i~ and ~v_i~ ~(1 \le u_i, v_i \le N)~, indicating that there is a branch between lemon ~u_i~ and ~v_i~.

Output Specification

Output the number of pairs of lemons Tommy can eat.

Constraints

Subtask	Points	Additional constraints
~1~	~40~	~3 \le N \le 10^3~
~2~	~60~	No additional constraints.

Sample Input 1

6 2
5 3 4 1 10 1
1 2
1 3
1 4
3 5
3 6

Sample Output 1

2

Explanation for Sample 1

The two pairs of lemons Tommy can eat are ~(3, 6)~ and ~(4, 6)~.

Sample Input 2

5 3
10 3 2 4 5
1 2
1 3
2 4
3 5

Sample Output 2

2