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