In a magical world, pigs live under the constant threat of wolves. Thus, the pigs have developed an elevator to escape from the wolves.

One day, right before a wolf raid, there are $N$ pigs in a queue waiting for the elevator, with the $i^{\text{th}}$ pig having weight $w_i$. The elevator has a weight limit $L$.

Since the pigs have a bit of time before the wolf raid, at most one pig in the queue can step out and re-enter the queue at a different position.

What is the largest number of pigs that can fit onto the elevator without exceeding the weight limit?

Constraints

$1\le N\le {10}^6$

$0\le L\le {10}^{18}$

$1\le w_i\le {10}^9$

Input Specification

The first line contains two integers $N$ and $L$.

The second line of input consists of $N$ integers $w_i$.

Output Specification

Output the largest number of pigs that can fit on the elevator if at most one pig changes their place.

Sample Input 1

6 11
2 4 5 2 1 6

Sample Output 1

4

Explanation for Sample Output 1

If the second pig in the queue moves to the end of the queue, then $4$ pigs can enter the elevator, whose weight are $2$, $5$, $2$, and $1$, in order.

Sample Input 2

6 6
5 4 5 2 1 1

Sample Output 2

2

Sample Input 3

6 1000000000000
1 2 3 4 5 6

Sample Output 3

6