# fulger

Time limit: 0.2s Memory limit: 16MB Input: Output:

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

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