# Contemporary Art

If you've ever visited the contemporary art exhibition "Arsenal," you're aware of the immense cultural value of its displays. Not wanting to be outdone by the capital, Odesa has, with the help of its residents, created its own masterpiece of contemporary art: a sequence of towers made entirely from coffee cups!

This exhibit features n towers of varying heights, arranged in a sequence along the main street. Unfortunately, some vandals, who lack an appreciation for art (and happen to be competitive programmers), decided to indulge in a coffee spree, using m cups, thereby altering the heights of some towers. After their nocturnal activities, the height of the i-th tower is now A_i. It's crucial to restore the towers to ensure the exhibition's beauty is maximized. The beauty of this masterpiece is defined as the longest sequence of towers that are considered beautiful. A sequence of towers from l to r (1 ≤ l ≤ r ≤ n) is deemed beautiful if H_l=H_{l+1}=...=H_r, where H_i is the height of the i-th tower after adding the cups.

This task was assigned to the most diligent girls of Odesa, but they had to attend school, so it was turned into a problem for you to solve: determine the maximum beauty of the towers that can be achieved if no more than m cups are added to the existing ones. Note that new towers cannot be created, nor can any remaining cups be removed.

## Input

The first line contains two integers n (1 ≤ n ≤ 10^6) and m (0 ≤ m ≤ 10^9). The second line contains n integers A_{i }(1 ≤ A_{i }≤ 10^9), where the i-th integer represents the height of the i-th tower.

## Output

Output a single integer - the maximum beauty of the exhibit that can be achieved.