Marisa has $n$ flower pots arranged consecutively. Planting flowers in the $i$-th pot costs $a_i$. Marisa has a budget of $t$, so she cannot plant flowers in all pots. The "ugliness" of the flower pots is defined as the length of the longest contiguous segment of pots without flowers. Help Marisa find a way to plant flowers such that the ugliness is minimized while staying within the budget.
### Input
- The first line contains two positive integers $n$ and $t$.
- The second line contains $n$ integers $a_i$.
### Output
- Output a single integer representing the minimum possible ugliness.
### Constraints
- $1 \le n \le 5 \times 10^4$.
- $0 \le a_i \le 3000$.
- $1 \le t \le 10^8$.
### Example
Input:
```
17 11
6 4 5 2 5 3 4 5 2 3 4 5 2 3 6 3 5
```
Output:
```
3
```
Explanation: