RNG 2

Consider every array of length $N$ whose elements are integers between $0$ and $K$, inclusive. Count how many of those arrays have a bitwise XOR of all their elements greater than $0$.

A value may appear more than once, and two arrays that hold the same values in a different order count as different arrays.

The first line contains $N$ and $K$, separated by a space. ($1 \le N \le 20000$, $1 \le K \le 50000$)

Print the number of arrays that satisfy the condition, modulo $30011$, on the first line.