Problem Statement

Takahashi's and Aoki's garden is covered with $N$ weeds, called Weed $1$, Weed $2$, $\ldots$, Weed $N$. The height of Weed $i$ is $A_i$. Takahashi and Aoki have decided to pull these weeds, as follows:

• First, Aoki will choose at most $K$ weeds and pull them.
• Then, Takahashi will repeat the following operation until all weeds are pulled.
• Let $H$ be the height of the tallest remaining weeds. Pull all weeds with heights above $\frac{H}{2}$ at once.

Aoki wants to minimize the number of operations done by Takahashi. Also, he wants to minimize it by pulling the minimum number of weeds needed. Find the number of operations done by Takahashi and the number of weeds Aoki pulls in this case.

Constraints

• $1 \leq N \leq 2\times 10^5$
• $0 \leq K \leq N$
• $1 \leq A_i \leq 10^9$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K
A_1 A_2 \ldots A_N

Output

Print the number of operations Takahashi will do and the number of weeds Aoki will pull, in this order, with a space in between.