You have an array of n integers. But n integers is too much for you, so you want to remove exactly k integers from them. You should select these k integers in such a way that bitwise OR of the remaining integers would be maximal possible.

It’s guaranteed that in any test either k ≤ 7, or all integers in the array are not greater than 10⁵.

The first line contains integers n and k (0 ≤ k ≤ 100; k + 1 ≤ n ≤ 10⁵). The second line describes the given array as a sequence of n integers. All integers in the array are from 0 to 10⁹.

Output maximal possible value of bitwise OR of the remaining integers.

To calculate a bitwise OR of two integers you should write them in the binary form and perform the OR operation for each pair of corresponding bits. If both bits are 0, then this bit of result is 0, otherwise this bit of result is 1.