#1168782 (C++17) No.3478 XOR-Folding Primes

• 問題: No.3478 XOR-Folding Primes
• ユーザー: akua
• 提出日時: 2026-06-10 05:01:53
• 言語: C++17 (gcc 15.2.0 + boost 1.89.0)
• 結果: AC
• 実行時間: 1,571 ms / 4,000 ms
• コード長: 6,930 bytes
• コンパイル時間: 4,551 ms
• コンパイル使用メモリ: 263,564 KB
• 実行使用メモリ: 46,736 KB
• 最終ジャッジ日時: 2026-06-10 05:02:15
• 合計ジャッジ時間: 18,065 ms
• ジャッジサーバーID （参考情報）: judge2_0 / judge3_0

ファイルパターン	結果
sample	AC * 1
other	AC * 8

ソースコード

# pragma GCC target("avx2")
# pragma GCC optimize("O3")
# pragma GCC optimize("unroll-loops")
#include<atcoder/all>

#include <iostream> // cout, endl, cin
#include <string> // string, to_string, stoi
#include <vector> // vector
#include <algorithm> // min, max, swap, sort, reverse, lower_bound, upper_bound
#include <utility> // pair, make_pair
#include <tuple> // tuple, make_tuple
#include <cstdint> // int64_t, int*_t
#include <cstdio> // printf
#include <map> // map
#include <queue> // queue, priority_queue
#include <set> // set
#include <stack> // stack
#include <deque> // deque #include <unordered_map> // unordered_map #include <unordered_set> // unordered_set #include <bitset> // bitset
#include <cctype> // isupper, islower, isdigit, toupper, tolower
#include <math.h>
#include <iomanip>
#include <functional>
#include<unordered_map>
#include <random>
#include<bitset>
#include<cassert>
#include<chrono>
using namespace std;  
using namespace atcoder;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define repi(i, a, b) for (int i = (int)(a); i < (int)(b); i++)
#define endl '\n'
#define all(x) (x).begin(),(x).end()
#define arr(x) (x).rbegin(),(x).rend()
typedef long long ll;
typedef unsigned long long ull;
const ll inf=4e18;  
using graph = vector<vector<int> > ;
using vi=vector<int>;
using P= pair<ll,ll>;  
using pii=pair<int,int>;
using pll=pair<ll,ll>;
using vvi=vector<vi>;
using vvvi=vector<vvi>;
using vll=vector<ll>; 
using vvll=vector<vll>;
using vvvll=vector<vvll>;
using vp=vector<P>;
using vvp=vector<vp>;
using vvvp=vector<vvp>;
using vd=vector<double>;
using vvd =vector<vd>;
//using vs=vector<string>;
//string T="ABCDEFGHIJKLMNOPQRSTUVWXYZ";
//string S="abcdefghijklmnopqrstuvwxyz";
//g++ main.cpp -std=c++17 -I .  
//cout <<setprecision(20);
//cout << fixed << setprecision(10);
//cin.tie(0); ios::sync_with_stdio(false);

const double PI = acos(-1);
int vx[]={0,1,0,-1,-1,1,1,-1},vy[]={1,0,-1,0,1,1,-1,-1};
void putsYes(bool f){cout << (f?"Yes":"No") << endl;}
void putsYES(bool f){cout << (f?"YES":"NO") << endl;}
void putsFirst(bool f){cout << (f?"First":"Second") << endl;}
void debug(int test){cout << "TEST" << " " << test << endl;}
ll pow_pow(ll x,ll n,ll mod){
    if(n==0) return 1; 
    x%=mod;
    ll res=pow_pow(x*x%mod,n/2,mod);
    if(n&1)res=res*x%mod;
    return res;
}
ll gcdll(ll x,ll y){
    if(y==0)return x;
    return gcdll(y,x%y);
}
ll INFF=1000100100100100100;
ll lcmll(ll x,ll y){
    ll X=(x/gcdll(x,y)),Y=y;
    if(X<=INFF/Y)return X*Y;
    else return INFF;
}
template<class T> bool chmin(T& a, T b) {
    if (a > b) {
        a = b;
        return true;
    }
    else return false;
}
template<class T> bool chmax(T& a, T b) {
    if (a < b) {
        a = b;
        return true;
    }
    else return false;
}
struct edge{
  int to; ll cost;int id;
  edge(int to,ll cost,int id) : to(to),cost(cost),id(id) {}
};
using ve=vector<edge>;
using vve=vector<ve>;
int mod=998244353;
using mint=modint998244353;
using vm=vector<mint>;
using vvm=vector<vm>;
using vvvm=vector<vvm>;
constexpr int MAX = 10;
ll fact[MAX],finv[MAX],invv[MAX];
void initcomb(){
  fact[0]=fact[1]=1;
  finv[0]=finv[1]=1;
  invv[1]=1;
  for(int i=2;i<MAX;i++){
    fact[i]=fact[i-1]*i%mod;
    invv[i]=mod-invv[mod%i]*(mod/i)%mod;
    finv[i]=finv[i-1]*invv[i]%mod;
  }
}
ll comb(ll n,ll k){
  if(n<k) return 0;
  if(n<0||k<0) return 0;
  return fact[n]*(finv[k]*finv[n-k]%mod)%mod;
}
struct Compress{
   vll a;
   int cnt;
   Compress() :cnt(0) {}
   void add(ll x){a.push_back(x);}
   void init(){
       sort(all(a));
       a.erase(unique(all(a)),a.end());
       cnt=a.size();
   }
   ll to(ll x){
       int index=lower_bound(all(a),x)-a.begin();
       return index;
   } //変換先
   ll from(ll x){return a[x];}//逆引き
   int size(){return cnt;}
};
struct UnionFind { 
    vector<int> par, siz; 
    UnionFind(int n) : par(n, -1) , siz(n, 1) { } 
    int root(int x) { 
        if (par[x] == -1) return x;
        else return par[x] = root(par[x]);
    }
    bool issame(int x, int y) {
        return root(x) == root(y);
    }
    bool unite(int x, int y) {
        x = root(x), y = root(y);
        if (x == y) return false; 
        if (siz[x] < siz[y]) swap(x, y);
        par[y] = x;
        siz[x] += siz[y];
        return true;
    }
    int size(int x) {
        return siz[root(x)];
    }
};

// https://youtu.be/ylWYSurx10A?t=2352
template<typename T>
struct Matrix {
  int h, w;
  vector<vector<T>> d;
  Matrix() {}
  Matrix(int h, int w, T val=0): h(h), w(w), d(h, vector<T>(w,val)) {}
  Matrix& unit() {
   // assert(h == w);
    rep(i,h) d[i][i] = 1;
    return *this;
  }
  const vector<T>& operator[](int i) const { return d[i];}
  vector<T>& operator[](int i) { return d[i];}
  Matrix operator*(const Matrix& a) const {
 //   assert(w == a.h);
    Matrix r(h, a.w);
    rep(i,h)rep(k,w)rep(j,a.w) {
      r[i][j] += d[i][k]*a[k][j];
    }
    return r;
  }
  Matrix pow(long long t) const {
  //  assert(h == w);
    if (!t) return Matrix(h,h).unit();
    if (t == 1) return *this;
    Matrix r = pow(t>>1);
    r = r*r;
    if (t&1) r = r*(*this);
    return r;
  }
  // https://youtu.be/-j02o6__jgs?t=11273
  /* mint only
  mint det() {
    assert(h == w);
    mint res = 1;
    rep(k,h) {
      for (int i = k; i < h; ++i) {
        if (d[i][k] == 0) continue;
        if (i != k) {
          swap(d[i],d[k]);
          res = -res;
        }
      }
      if (d[k][k] == 0) return 0;
      res *= d[k][k];
      mint inv = mint(1)/d[k][k];
      rep(j,h) d[k][j] *= inv;
      for (int i = k+1; i < h; ++i) {
        mint c = d[i][k];
        for (int j = k; j < h; ++j) d[i][j] -= d[k][j]*c;
      }
    }
    return res;
  }
  //*/
};

vll anss; 
vi isprime;
vi prime;
void getPrime(int N){
  isprime.resize(N+1);
  rep(i,N+1)isprime[i]=1;
  isprime[0]=0;isprime[1]=0;
  for(int i=2; i<=N; i++){
    if(isprime[i])prime.push_back(i);
    for(int j=2*i; j<=N; j+=i){
      isprime[j]=0;
    }
  }
}
vi vs;


void solve(int test){
    int n,m; cin >> n >> m;
    if(n==1){
        int index=upper_bound(all(prime),m)-prime.begin();
        cout<< index << endl;
        return;
    }
    int index=upper_bound(all(vs),m)-vs.begin();
    int cnt=index;
    Matrix<mint> M(2,2);
    Matrix<mint> X(1,2);
    M[0][0]=0;
    M[0][1]=2*cnt;
    M[1][0]=1;
    M[1][1]=1;
    X[0][0]=1,X[0][1]=2*cnt;
    auto Y=X*M.pow(n-1);
    mint ans=Y[0][0]+Y[0][1];
    //cout << test+1 << " " << cnt << endl;
    cout << ans.val() << endl;
}
//cat cf.cpp | pbcopy
//g++ cf.cpp -std=c++17 -I .  
int main(){cin.tie(0);ios::sync_with_stdio(false);
    {
        int N=10000000;
        getPrime(N);
        rep(i,prime.size()-1){
            if((prime[i]^prime[i+1])==2){
                vs.push_back(prime[i+1]);
            }
        }
    }
    //initcomb();
    int t=1;cin >>t;
    rep(test,t)solve(test);
    for(auto ans:anss){
        cout<< ans << endl;
    }
}