Score : $500$ points

Problem Statement

Seisu-ya, a store specializing in non-negative integers, sells $N$ non-negative integers. The $i$-th integer is $A_i$ and has a utility of $B_i$. There may be multiple equal integers with different utilities.

Takahashi will buy some integers in this store. He can buy a combination of integers whose bitwise OR is less than or equal to $K$. He wants the sum of utilities of purchased integers to be as large as possible.

Find the maximum possible sum of utilities of purchased integers.

Constraints

• $1 \leq N \leq 10^5$
• $0 \leq K < 2^{30}$
• $0 \leq A_i < 2^{30}(1\leq i\leq N)$
• $1 \leq B_i \leq 10^9(1\leq i\leq N)$
• All input values are integers.

Inputs

Input is given from Standard Input in the following format:

$N$ $K$

$A_1$ $B_1$

:

$A_N$ $B_N$

Outputs

Print the maximum possible sum of utilities of purchased integers.

3 5
3 3
4 4
2 5

8

Buy $2$ and $3$ to achieve the maximum possible total utility, $8$.

3 6
3 3
4 4
2 5

9

Buy $2$ and $4$ to achieve the maximum possible total utility, $9$.

7 14
10 5
7 4
11 4
9 8
3 6
6 2
8 9

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