Brick towers

Young Peter has got a wonderful gift for his birthday --- the whole pack of wooden bricks. He has already made $n$ towers, with heights $a_1$, $a_2$, $\ldots$, $a_n$ bricks, correspondingly.

Peter's favorite number is $k$, so he likes towers with height exactly $k$ bricks. Peter finds a set of consecutive towers good if their average height is equal to exactly $k$ bricks. He wants to find a good set of towers containing as many consecutive towers as possible.

Help Peter to find the largest good set of towers.

The first line of input file contains two integer numbers $n$ and $k$ ($1 \le n \le 100000$; $1 \le k \le 10^9$). The second line of input file contains $n$ integer numbers $a_i$ ($1 \le a_i \le 10^9$) --- heights of the towers.

Output two integer numbers $l$ and $m$ --- amount of towers in the largest good set and number of the first tower in this set. Towers are numbered from $1$ in order of appearance in the input file. If there are multiple answers, output any of them. If there is no good set output single number $0$.