Ahano loves pretty places and pretty paths.

Her city has ~N~ places, each with a prettiness ~p_i~. The places are connected by a network of ~N-1~ bidirectional roads, in which any two places are connected by some sequence of roads.

A path from place ~a~ to place ~b~ is defined as the sequence of places visited on the traversal from ~a~ to ~b~, where ~a < b~. The average prettiness of a path is defined as the numerical median of the ~p_i~ in the path. For example, if the path from ~a~ to ~b~ visits places with the following ~p_i~: ~[3, 2, 8, 4, 6]~, then the average prettiness of the path is the numerical median, ~4~.

Ahano likes a path if the number of places on the path is odd and the average prettiness of the path is greater than or equal to ~K~. How many paths does Ahano like?

Input Specification

The first line of input contains two space-separated integers, ~N (1 \le N \le 2\times10^{5})~ and ~K (0 \le K \le 10^{5})~.

The next line contains ~N~ space separated integers, ~p_i (0 \le p_i \le 10^{5})~.

Each of the next ~N-1~ lines contains two space-separated integers, representing a bidirectional road between two places.

Output Specification

Output a single integer, the number of paths Ahano likes.

Subtasks

Subtask 1 [40%]

~(1 \le N \le 10^{3})~

Subtask 2 [60%]

~(1 \le N \le 2\times10^{5})~

Sample Input 1

5 3
6 2 8 1 2
1 2
2 3
2 4
1 5

Sample Output 1

1

Explanation

The path from ~1~ to ~3~ consists of the prettiness values ~[6, 2, 8]~. Ahano likes the path since it contains an odd number of places, and the numerical median is ~6~ which is greater than ~K~.

Sample Input 2

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

Sample Output 2

2

Explanation

The path from ~3~ to ~5~ consists of the prettiness values ~[1, 6, 4]~. Ahano likes the path since it contains an odd number of places, and the numerical median is ~4~ which is greater than ~K~.

The path from ~1~ to ~5~ consists of the prettiness values ~[3, 2, 1, 6, 4]~. Ahano likes the path since it contains an odd number of places, and the numerical median is ~3~ which is equal to ~K~.