Problem Statement

There is a non-negative integer $X$ initially equal to $S$. One can perform the following operations, in any order, any number of times:

• Add $1$ to $X$. This has a cost of $A$.
• Choose $i$ between $1$ and $N$, and replace $X$ with $X \oplus Y_i$. This has a cost of $C_i$. Here, $\oplus$ denotes bitwise $\mathrm{XOR}$.

Find the smallest total cost to make $X$ equal to a given non-negative integer $T$, or report that this is impossible.

What is bitwise $\mathrm{XOR}$? The bitwise $\mathrm{XOR}$ of non-negative integers $A$ and $B$, $A \oplus B$, is defined as follows: When $A \oplus B$ is written in base two, the digit in the $2^k$'s place ($k \geq 0$) is $1$ if exactly one of the digits in that place of $A$ and $B$ is $1$, and $0$ otherwise. For example, we have $3 \oplus 5 = 6$ (in base two: $011 \oplus 101 = 110$). Generally, the bitwise $\mathrm{XOR}$ of $k$ non-negative integers $p_1, p_2, p_3, \dots, p_k$ is defined as $(\dots ((p_1 \oplus p_2) \oplus p_3) \oplus \dots \oplus p_k)$. We can prove that this value does not depend on the order of $p_1, p_2, p_3, \dots, p_k$.

Constraints

• $1 \leq N \leq 8$
• $0 \leq S, T < 2^{40}$
• $0 \leq A \leq 10^5$
• $0 \leq Y_i < 2^{40}$ ($1 \leq i \leq N$)
• $0 \leq C_i \leq 10^{16}$ ($1 \leq i \leq N$)
• All values in the input are integers.

Input

Input is given from Standard Input in the following format:

N S T A
Y_1 C_1
\vdots
Y_N C_N

Output

If the task is impossible, print -1. Otherwise, print the smallest total cost.