Problem Statement

You are given a sequence of $N$ non-negative integers $A=(A_1,A_2,\dots,A_N)$ and a positive integer $K$.

Find the bitwise $\mathrm{XOR}$ of $\displaystyle \sum_{i=1}^{K} A_{X_i}$ over all $N^K$ sequences of $K$ positive integer sequences $X=(X_1,X_2,\dots,X_K)$ such that $1 \leq X_i \leq N\ (1\leq i \leq K)$.

What is bitwise $\mathrm{XOR}$? The bitwise $\mathrm{XOR}$ of non-negative 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 exactly one of the digits in that place of $A$ and $B$ is $1$, and $0$ otherwise. For example, we have $3 \oplus 5 = 6$ (in base two: $011 \oplus 101 = 110$). Generally, the bitwise $\mathrm{XOR}$ of $k$ non-negative integers $p_1, p_2, p_3, \dots, p_k$ is defined as $(\dots ((p_1 \oplus p_2) \oplus p_3) \oplus \dots \oplus p_k)$. We can prove that this value does not depend on the order of $p_1, p_2, p_3, \dots, p_k$.

Constraints

• $1 \leq N \leq 1000$
• $1 \leq K \leq 10^{12}$
• $0 \leq A_i \leq 1000$
• All values in the input are integers.

Input

The input is given from Standard Input in the following format:

N K
A_1 A_2 \dots A_N

Output

Print the answer.