Problem Statement

We have N gemstones. The color and beauty of the i-th gemstone are D_i and V_i, respectively.
Here, the color of each gemstone is one of $1, 2, \ldots, C$, and there is at least one gemstone of each color.
Out of the N gemstones, we will choose C with distinct colors and use them to make a necklace. (The order does not matter.)
The beautifulness of the necklace will be the bitwise $\rm$ XOR of the chosen gemstones.
Among all possible ways to make a necklace, find the beautifulness of the necklace made in the way with the K-th greatest beautifulness. (If there are multiple ways with the same beautifulness, we count all of them.)

What is bitwise $\rm$ XOR?

The bitwise $\rm$ XOR of 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 either A or B, but not both, has 1 in the 2^k's place, and 0 otherwise.

For example$, 3 \oplus 5 = 6.$ (In base two: $011 \oplus 101 = 110.)$

Input

Input is given from Standard Input in the following format:
N C K
D_1 V_1
$\vdots$
D_N V_N

Output

Print the answer.

Constraints

• $1 \leq C \leq N \leq 70$
• $1 \leq D_i \leq C$
• $0 \leq V_i < 2^{60}$
• $1 \leq K \leq 10^{18}$
• There are at least K ways to make a necklace.
• All values in input are integers.

Sample Input 1

4 2 3
2 4
2 6
1 2
1 3

Sample Output 1

5

There are four ways to make a necklace, as follows.

• Choose the 1-st and 3-rd gemstones to make a necklace with the beautifulness of 4\ ${\rm XOR}$\ 2 =6.
• Choose the 1-st and 4-th gemstones to make a necklace with the beautifulness of 4\ ${\rm XOR}$\ 3 =7.
• Choose the 2-nd and 3-rd gemstones to make a necklace with the beautifulness of 6\ ${\rm XOR}$\ 2 =4.
• Choose the 2-nd and 4-th gemstones to make a necklace with the beautifulness of 6\ ${\rm XOR}$\ 3 =5.

Thus, the necklace with the 3-rd greatest beautifulness has the beautifulness of 5.

Sample Input 2

3 1 2
1 0
1 0
1 0

Sample Output 2

0

There are three ways to make a necklace, all of which result in the beautifulness of 0.

Sample Input 3

10 3 11
1 414213562373095048
1 732050807568877293
2 236067977499789696
2 449489742783178098
2 645751311064590590
2 828427124746190097
3 162277660168379331
3 316624790355399849
3 464101615137754587
3 605551275463989293

Sample Output 3

766842905529259824

见题面 Input 部分

见题面 Output 部分