Fish

Kuching the cat likes eating fish. He accidentally bought a fish that is far too large and does not want to eat all of it. He cut the fish into $N$ segments from head to tail, numbered 1 to $N$, and gave every segment a satisfaction rating. The higher the rating, the more Kuching enjoys that segment. Fish only tastes good when it is eaten as a chunk. A chunk is one or more segments with consecutive numbers.

Kuching is picky and does not enjoy a chunk whose satisfaction ratings sum to less than $K$, so the sum has to be at least $K$. Count the ways to cut a single chunk out of the fish that Kuching would enjoy eating. Segments outside the chunk are thrown away.

A chunk holds at least 1 segment and at most $N$ segments, which is the whole fish.

The first line contains two 32-bit signed integers $N$ and $K$. $N$ is always positive, while $K$ may be positive, zero, or negative. ($1 \le N \le 200{,}000$)

The second line contains the satisfaction ratings of the $N$ segments in order. The $i$-th integer is the rating of the $i$-th segment. Every rating fits in a 32-bit signed integer and may be positive, zero, or negative.

Print a single integer, the number of ways to cut out one chunk whose satisfaction ratings sum to at least $K$.

In the first example Kuching cut the fish into 5 segments with ratings 1, -2, 3, -4, 5, and he only enjoys chunks whose sum is at least 2. The six chunks he enjoys are (1, -2, 3), (1, -2, 3, -4, 5), (-2, 3, -4, 5), (3), (3, -4, 5) and (5). Every other chunk sums to less than $K$. Segments 1, 3 and 5 are not consecutive, so (1, 3, 5) is not a chunk.