Problem Statement

There are $N$ cards numbered $1, \dots, N$. Card $i \, (1 \leq i \leq N)$ has an integer $A_i$ written on the front and an integer $B_i$ written on the back.

Consider choosing one or more cards so that the exclusive logical sum of the integers written on the front of the chosen cards is at most $K$. Find the maximum possible exclusive logical sum of the integers written on the back of the chosen cards.

What is the exclusive logical sum? The exclusive logical sum $a \oplus b$ of two integers $a$ and $b$ is defined as follows. The $2^k$'s place ($k \geq 0$) in the binary notation of $a \oplus b$ is $1$ if exactly one of the $2^k$'s places in the binary notation of $a$ and $b$ is $1$; otherwise, it is $0$. For example, $3 \oplus 5 = 6$ (In binary notation: $011 \oplus 101 = 110$). In general, the exclusive logical sum of $k$ integers $p_1, \dots, p_k$ is defined as $(\cdots ((p_1 \oplus p_2) \oplus p_3) \oplus \cdots \oplus p_k)$. We can prove that it is independent of the order of $p_1, \dots, p_k$.

Constraints

• $1 \leq N \leq 1000$
• $0 \leq K \lt 2^{30}$
• $0 \leq A_i, B_i \lt 2^{30} \, (1 \leq i \leq N)$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K
A_1 B_1
\vdots
A_N B_N

Output

Print the maximum possible exclusive logical sum of the integers written on the back of the chosen cards when choosing one or more cards so that the exclusive logical sum of the integers written on the front of the chosen cards is at most $K$. If it is impossible to choose cards in such way, print $-1$ instead.