#1153120 (C++17) No.3478 XOR-Folding Primes

• 問題: No.3478 XOR-Folding Primes
• ユーザー: GOTKAKO
• 提出日時: 2026-03-20 22:13:41
• 言語: C++17 (gcc 15.2.0 + boost 1.89.0)
• 結果: AC
• 実行時間: 749 ms / 4,000 ms
• コード長: 4,399 bytes
• コンパイル時間: 1,568 ms
• コンパイル使用メモリ: 229,248 KB
• 実行使用メモリ: 10,016 KB
• 最終ジャッジ日時: 2026-03-20 22:13:50
• 合計ジャッジ時間: 4,477 ms
• ジャッジサーバーID （参考情報）: judge2_1 / judge3_0

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

ソースコード

#include <bits/stdc++.h>
using namespace std;

//入力が必ず-mod<=a<modの時.
template<const int mod> //mod<2^30.
struct modint{ //mod変更が不可能.
    public:
    long long v;
    static void setmod(int m){} //飾り.
    static constexpr long long getmod(){return mod;}
    modint():v(0){}
    template<typename T>
    modint(T a):v(a){if(v < 0) v += mod;}
    long long val()const{return v;}
 
    modint &operator=(const modint &b) = default;
    modint &operator+()const{return (*this);}
    modint operator-()const{return modint(0)-(*this);}
    modint operator+(const modint b)const{return modint(v)+=b;}
    modint operator-(const modint b)const{return modint(v)-=b;}
    modint operator*(const modint b)const{return modint(v)*=b;}
    modint operator/(const modint b)const{return modint(v)/=b;}
    modint &operator+=(const modint b){
        v += b.v; if(v >= mod) v -= mod;
        return *this;
    }
    modint &operator-=(const modint b){
        v -= b.v; if(v < 0) v += mod; 
        return *this;
    }   
    modint &operator*=(const modint b){v = v*b.v%mod; return *this;}
    modint &operator/=(modint b){ //b!=0 mod素数が必須.
        assert(b.v != 0);
        (*this) *= b.pow(mod-2);
        return *this;
    }
    modint pow(long long n)const{
        modint ret = 1,p = v;
        if(n < 0) p = p.inv(),n = -n;
        while(n){
            if(n&1) ret *= p;
            p *= p; n >>= 1;
        }
        return ret;
    }
    modint inv()const{return pow(mod-2);} //素数mod必須.
 
    modint &operator++(){*this += 1; return *this;}
    modint &operator--(){*this -= 1; return *this;}
    modint operator++(int){modint ret = *this; *this += 1; return ret;}
    modint operator--(int){modint ret = *this; *this -= 1; return ret;}
    friend bool operator==(const modint a,const modint b){return a.v==b.v;}
    friend bool operator!=(const modint a,const modint b){return a.v!=b.v;}
    friend bool operator<(const modint a,const modint b){return a.v<b.v;}
    friend bool operator<=(const modint a,const modint b){return a.v<=b.v;}
    friend bool operator>=(const modint a,const modint b){return a.v>=b.v;}
    friend bool operator>(const modint a,const modint b){return a.v>b.v;}
    friend ostream &operator<<(ostream &os,const modint a){return os<<a.v;}
    friend istream &operator>>(istream &is,modint &a){ //入力はmodをとってくれる.
        long long x; is >> x; x %= mod;
        a = modint(x); return is;
    }
};
using mint = modint<998244353>; const long long mod = 998244353;

template<typename T>
vector<vector<T>> multima(vector<vector<T>> &A,vector<vector<T>> &B){
    assert(A.at(0).size() == B.size() && B.size());
    int H = A.size(),W = B.at(0).size();
    vector<vector<T>> ret(H,vector<T>(W));
    for(int i=0; i<H; i++) for(int k=0; k<W; k++){
        for(int l=0; l<A.at(i).size(); l++){
            ret.at(i).at(k) += A.at(i).at(l)*B.at(l).at(k);
        }
    }
    return ret; //計算できる行列のみ.
}
template<typename T>
vector<vector<T>> Powmat(vector<vector<T>> A,vector<vector<T>> B,long long N){ //return A^N*B ABは行列;
    //n*n行列A n*1行列Bと想定 O(n^3*logN).
    assert(A.size() && A.size() == A.at(0).size() && N >= 0);
    while(N){
        if(N&1) B = multima(A,B);
        A = multima(A,A); N >>= 1;
    }
    return B;
}

int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);

    int n = 1'000'000'0;
    vector<bool> prime(n+1,true);
    prime.at(0) = false; prime.at(1) = false;
    for(int i=2; i*i<=n; i++){
        if(!prime.at(i)) continue;
        for(int k=i*i; k<=n; k+=i) prime.at(k) = false;
    }
    vector<int> twin,allp = {2};
    for(int i=3; i<=n; i+=2){
        if(prime.at(i)) allp.push_back(i);
        if(prime.at(i) && prime.at(i-2) && ((i-2)^2) == i) twin.push_back(i);
    }
    int T; cin >> T;
    while(T--){
        int N,M; cin >> N >> M;
        if(N == 1){
            int pos = upper_bound(allp.begin(),allp.end(),M)-allp.begin();
            cout << pos << "\n"; continue;
        }
        int mul = upper_bound(twin.begin(),twin.end(),M)-twin.begin();
        
        vector<vector<mint>> A = {
            {0,1,1},
            {mul,0,1},
            {mul,1,0}
        },B = {{1},{mul},{mul}};
        B = Powmat(A,B,N-1);
        mint answer = B.at(0).at(0)+B.at(1).at(0)+B.at(2).at(0);
        cout << answer << "\n";
   }
}