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\leq N\leq 10^6~

~0\leq L\leq 10^{18}~

~1\leq w_i\leq 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