Problem Statement

You are given a sequence of $N$ non-negative integers: $A=(A_1,A_2,\dots,A_N)$. You may perform the following operation at most $M$ times (possibly zero):

• choose an integer $i$ such that $1 \le i \le N$ and add $1$ to $A_i$.

Then, you will choose $K$ of the elements of $A$.

Find the maximum possible value of the bitwise $\mathrm{AND}$ of the elements you choose.

What is bitwise ${\rm AND}$? The bitwise ${\rm AND}$ of non-negative integers $A$ and $B$, $A\ \mathrm{AND}\ B$, is defined as follows: When $A\ {\rm AND}\ B$ is written in base two, the digit in the $2^k$'s place ($k \geq 0$) is $1$ if both of the digits in that place of $A$ and $B$ are $1$, and $0$ otherwise. For example, $3\ {\rm AND}\ 5 = 1$. (In base two, $011\ {\rm AND}\ 101 = 001$.) Generally, the bitwise ${\rm AND}$ of $k$ non-negative integers $p_1, p_2, p_3, \dots, p_k$ is defined as $(\dots ((p_1\ \mathrm{AND}\ p_2)\ \mathrm{AND}\ p_3)\ \mathrm{AND}\ \dots\ \mathrm{AND}\ p_k)$. We can prove that this value does not depend on the order of $p_1, p_2, p_3, \dots, p_k$.

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Constraints

• $1 \le K \le N \le 2 \times 10^5$
• $0 \le M < 2^{30}$
• $0 \le A_i < 2^{30}$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M K
A_1 A_2 \dots A_N

Output

Print the answer.