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 $p_1, p_2, p_3, \dots, p_k$.
  

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.

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.

Sample Input 1

1 15 0 1
8 2

Sample Output 1

5

You can make X equal to T in the following manner:

• Choose i=1 and replace X with $X \oplus 8$ to get X=7. This has a cost of 2.
• Add 1 to X to get X=8. This has a cost of 1.
• Choose i=1 and replace X with $X \oplus 8$ to get X=0. This has a cost of 2.

Sample Input 2

3 21 10 100
30 1
12 1
13 1

Sample Output 2

3

Sample Input 3

1 2 0 1
1 1

Sample Output 3

-1

Sample Input 4

8 352217 670575 84912
239445 2866
537211 16
21812 6904
50574 8842
380870 5047
475646 8924
188204 2273
429397 4854

Sample Output 4

563645

见题面 Input 部分

见题面 Output 部分