## Task

You are given an array with $n$ natural numbers, which is **sorted in increasing order**. The task is to find the subarray with a sum of at least $k$ that has the minimum difference between the maximum and minimum values in the subarray. If there are multiple such subarrays, find the one with the minimum length.

## Input data

The first line contains two integers, $n$ and $k$, representing the number of numbers in the array, and the sum we want to achieve.

The next line contains $n$ numbers **sorted in increasing order**, representing the values in the array.

## Output data

The first line will contain two numbers, representing the minimum difference required and the minimum length of a subarray that meets the given property.

## Constraints and clarifications

- $1 \leq n \leq 200 \ 000$
- $1 \leq k \leq 10^9$
- $1 \leq v_1 \leq v_2 \leq \dots \leq v_n \leq 1 \ 000 \ 000$
- A subarray represents values in the array of some consecutive indices.
- It is guaranteed that there is at least one subarray with a sum of at least $k$.

## Example 1

`stdin`

```
7 10
2 3 3 4 4 5 7
```

`stdout`

```
1 3
```

### Explanation

The minimum difference is obtained if we take the subarray $(3, 3, 4)$, the sum being $10$, the difference between the maximum and minimum values being $1$, and the minimum length being $3$.

## Example 2

`stdin`

```
15 85
1 5 6 7 7 7 8 8 9 9 11 13 15 16 17
```

`stdout`

```
7 10
```

### Explanation

$6 + 7 + 7 + 7 + 8 + 8 + 9 + 9 + 11 + 13 = 85$