Problem C
Taking Out the Trash

Peter has way too much trash and he needs to take it all out.

Specifically, there are $n$ bags of trash each with a specific weight. Peter can hold either one or two bags of trash per trip, and he can carry a maximum total of $m$ milligrams of trash in a single trip. What is the minimum number of trips Peter needs to take to take out all the trash?

Input

The input starts with two integers $n$ $(1\le n\le 5\cdot {10}^5)$ and $m$ $(1\le m\le {10}^9)$, the number of bags of trash and the maximum weight of trash Peter can carry.

The next line contains $n$ integers, $w_i$ $(1\le w_i\le m)$, the weight of each bag of trash in milligrams.

Output

Output the minimum number of trips Peter needs to make to take out all the trash.

4 1000
100 900 200 900

3

4 10
1 2 3 4

2