677. Maximize XOR

0

Easy

Given an array of N numbers, you need to select K elements from the array in order to maximize the XOR of all the chosen elements.

Input Format

The first line of input consists of two integers N and K, separated by a space.

The second line of input consists of N space-separated integers.

The second line of input consists of N space-separated integers.

Output Format

Print the maximum XOR.

Example

Input

5 3
1 2 3 4 5

Output

7

Constraints

1<=n<=20

1<=k<=n

1<= nums[i] <=10000

1<=k<=n

1<= nums[i] <=10000

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