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 $p_1, p_2, p_3, \dots, p_k$.
  

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.

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.

Sample Input 1

2 2
10 30

Sample Output 1

40

There are four sequences to consider: (X_1,X_2)=(1,1),(1,2),(2,1),(2,2), for which A_{X_1}+A_{X_2} is 20,40,40,60, respectively. Thus, the answer is $20 \oplus 40 \oplus 40 \oplus 60=40$.

Sample Input 2

4 10
0 0 0 0

Sample Output 2

0

Sample Input 3

11 998244353
314 159 265 358 979 323 846 264 338 327 950

Sample Output 3

236500026047

见题面 Input 部分

见题面 Output 部分