# ICPC Cricket Challenge

Limits 1s, 512 MB

In the ICPC World Cup cricket match, Bangladesh won the toss and chose to field first. To secure a victory, Bangladesh needs to strategically break the partnerships at crucial moments to minimize the total runs scored by opponent.

The strategy is as follows,

Hathurusingha provided a threshold $K$ to Bangladeshi bowlers, instructed them to take a wicket when the sum of runs scored in exactly two consecutive balls exceed the given threshold $K$.

Now, you are provided with the total number of balls $N$, played in the first innings, along with the runs scored in each ball. Your task is to calculate the number of wickets taken by Bangladesh team if they play strategically.

## Input

The first line contains two integers $N$ and $K$ — representing total number of balled played and threshold provided by Hathurusingha respectively.

The second line contains $N$ integers $a_0,a_1,…,a_{n−1}, a_n$ — representing the runs scored in each ball.

$1 \leq N \leq 350$

$1 \leq K \leq 12$

$0 \leq a_i \leq 6$

## Output

A single integer representing the number of wickets taken by Bangladesh team if they play strategically.

## Sample

InputOutput
10 4
0 1 0 2 6 1 2 0 4 1

3