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

The Nth Item
ideas:
the first formula is obtained by leading eigenvalue method, and then leading to the emergence of the formula \ (\ sqrt {}. 17 \) , the quadratic residue can find out, then O ( \ (log ( the n-) \) ) is obtained.
But not enough, we first \ (n \) Euler descending, and then seek to base \ (\ sqrt {1e9} \ ) fast power, pretreatment something similar can be O (1) to obtain a.
Code:

#pragma GCC optimize(2)
#pragma GCC optimize(3)
#pragma GCC optimize(4)
#include<bits/stdc++.h>
using namespace std;
#define y1 y11
#define fi first
#define se second
#define pi acos(-1.0)
#define LL long long
//#define mp make_pair
#define pb push_back
#define ls rt<<1, l, m
#define rs rt<<1|1, m+1, r
#define ULL unsigned LL
#define pll pair<LL, LL>
#define pli pair<LL, int>
#define pii pair<int, int>
#define piii pair<pii, int>
#define pdd pair<double, double>
#define mem(a, b) memset(a, b, sizeof(a))
#define debug(x) cerr << #x << " = " << x << "\n";
#define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
//head

const int MOD = 998244353;
const LL fsqrt17 = 473844410;
const LL sqrt17 = MOD-fsqrt17;
const LL inv2 = (MOD+1)/2;
const LL invsqrt17 = 438914993;
const int N = 4e4 + 5;
LL p[N], pp[N], P[N], PP[N], q, n;
LL f(LL n) {
    return (p[n%(N-1)]*P[n/(N-1)])%MOD;
}
LL F(LL n) {
    return (pp[n%(N-1)]*PP[n/(N-1)])%MOD;
}
int main() {
    p[0] = pp[0] = 1;
    for (int i = 1; i < N; ++i) p[i] = p[i-1]*(3+sqrt17)%MOD*inv2%MOD, pp[i] = pp[i-1]*(3+fsqrt17)%MOD*inv2%MOD;
    P[0] = PP[0] = 1;
    for (int i = 1; i < N; ++i) {
        P[i] = P[i-1]*p[N-1]%MOD;
        PP[i] = PP[i-1]*pp[N-1]%MOD;
    }
    scanf("%lld %lld", &q, &n);
    LL res = 0;
    for (int i = 1; i <= q; ++i) {
        LL ans = -(f(n%(MOD-1))-F(n%(MOD-1)))*invsqrt17%MOD;
        ans = (ans + MOD) % MOD;
        res ^= ans;
        n ^= ans*ans;
    }
    printf("%lld\n", res);
    return 0;
}