This year Hablu wants to participate in ICPC. He studies in “Habagoba University” along with $n$ other students. Everyone in the University has a “Problem solving skill level”. Hablu needs 2 other members to make a team.

But Hablu is really dumb! He will select two students if and only if the summation of their “Problem solving skill level”s is less than his own (What?)!

Now your task is to calculate how many ways Hablu can make his team. Two teams are considered different if a student $x$ is on the first team but not on the second one.

Input

In the first line you will be given two integers $n$ and $k$ ($1 \leq n, k \leq 10^5$) representing the number of students other than Hablu and Hablu's “Problem solving skill level” respectively. Next line will contain $n$ integers $a_i$ ($1 \leq a_i \leq 10^5$) — the “Problem solving skill level”s of other students.

Output

Output a single integer — the number of ways Hablu can make his team.

Samples

Input

Output

4 10
1 1 2 7

6

Input

Output

5 1
1 2 3 4 5

0

Output may not fit into 32 bit integer. Use 64 bit integer.