The Nth Item (The 2019 Asia Nanchang First Round Online Programming Contest)

 

 

 

#include
#include
#include
#include
#include
#include

 

For a series $F$:

$\begin{array}{c}F(0)=0,F(1)=1\\ F(n)=3\ast F(n-1)+2\ast F(n-2),(n\ge 2)\end{array}$

 

We have some queries. For each query $N$, the answer $A$ is the value $F(N)$ modulo $998244353$.

Moreover, the input data is given in the form of encryption, only the number of queries $Q$ and the first query $N^1$are given. For the others, the query $N^i(2\le i\le Q)$ is defined as the xor of the previous $N^{i-1}$ and the square of the previous answer $A^{i-1}$. For example, if the first query $N^1$ is $2$, the answer $A^1$ is $3$, then the second query $N^2$ is $2xor(3\ast 3)=11$.

Finally, you don't need to output all the answers for every query, you just need to output the xor of each query's answer $A^{1}xor{A}^2...xor{A}^Q$.

Input

The input contains two integers, $Q,N$, $1\le Q\le 10^7,0\le N\le 10^{18}$. $Q$ representing the number of queries and $N$ representing the first query.

Output:

An integer representing the final answer.

样例输入复制

17 473844410

样例输出复制

903193081