For her birthday, Mimi received a set of pencil crayons. Mimi loves her beautiful pencil crayons. In fact, she loves them so much that she assigned each of them individual names, a backstory, and also a *cuteness number*, .

One day, Mimi lent out her pencil crayons for an art class assignment. When the class ended, her friend returned the pencil crayons in a neat row. Mimi then asked her a curious question:

What is the longest contiguous subsequence where the sum of the

cuteness numbers is strictly less than ?

Can you answer her question?

#### Constraints

For all subtasks,

##### Subtask 1 [10%]

##### Subtask 2 [20%]

##### Subtask 3 [70%]

#### Input Specification

The first line of input will contain two space-separated integers, and .

The second line of input will contain space-separated integers, .

#### Output Specification

A single integer, the length of the longest subarray where the sum of the cuteness numbers is strictly less than .

#### Sample Input

```
5 3
1 1 1 2 3
```

#### Sample Output

`2`

## Comments