Suppose we have $n$ cities with integer coordinate on a line. First, we have to select a city to be the capital. Then in each operation, we have to choose a non-capital city and change it's coordinate by $1$ ($-1$ or $+1$). We have to pick the capital and do the operations exactly $k$ time so that the sum of distances from cities to the capital is minimized. Print the index of the selected capital and the desired sum after exactly $k$ operations. If there are multiple such choices, output the smallest index of an optimal capital. 

You are required to print the index of the selected capital and required sum after $k$ operations. If there are multiple such choices, print the smallest index of an optimal capital.

Input format

• First line: Two integers $n$ and $k$ $1 \le n \le 300\ 000$
• Second line: $n$ integers where the $i^{th}$ integer that contains the coordinate of the $i^{th}$ city

Output format

Print two integers that represent the index of the capital and the minimized required sum respectively.

Constraints

$1 \le n \le 300\ 000$

$0 \le k, A_i \le 10^9$

Sample input #2

5 47019
19912129 5 7138912 913 200134

Sample output #2

5 27003104