#899050 (C++17) No.2406 Difference of Coordinate Squared

• 問題: No.2406 Difference of Coordinate Squared
• ユーザー: asaringo
• 提出日時: 2023-08-05 14:02:41
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 526 ms / 2,000 ms
• コード長: 10,096 bytes
• コンパイル時間: 2,088 ms
• コンパイル使用メモリ: 204,740 KB
• 最終ジャッジ日時: 2025-02-15 23:33:59
• ジャッジサーバーID （参考情報）: judge4 / judge2

ファイルパターン	結果
sample	AC * 2
other	AC * 55

ソースコード

#include <bits/stdc++.h>
using namespace std;
#define overload2(a, b, c, ...) c
#define overload3(a, b, c, d, ...) d
#define overload4(a, b, c, d, e ...) e
#define overload5(a, b, c, d, e, f ...) f
#define overload6(a, b, c, d, e, f, g ...) g
#define fast_io ios::sync_with_stdio(false); cin.tie(nullptr);
#pragma GCC optimize("Ofast,no-stack-protector,unroll-loops,fast-math")
typedef long long ll;
typedef long double ld;
#define chmin(a,b) a = min(a,b);
#define chmax(a,b) a = max(a,b);
#define bit_count(x) __builtin_popcountll(x)
#define leading_zero_count(x) __builtin_clz(x)
#define trailing_zero_count(x) __builtin_ctz(x)
#define gcd(a,b) __gcd(a,b)
#define lcm(a,b) a / gcd(a,b) * b
#define rep(...) overload3(__VA_ARGS__, rrep, rep1)(__VA_ARGS__)
#define rep1(i,n) for(int i = 0 ; i < n ; i++)
#define rrep(i,a,b) for(int i = a ; i < b ; i++)
#define repi(it,S) for(auto it = S.begin() ; it != S.end() ; it++)
#define pt(a) cout << a << endl;
#define print(...) printall(__VA_ARGS__);
#define debug(a) cout << #a << " " << a << endl;
#define all(a) a.begin(), a.end()
#define endl "\n";
#define v1(T,n,a) vector<T>(n,a)
#define v2(T,n,m,a) vector<vector<T>>(n,v1(T,m,a))
#define v3(T,n,m,k,a) vector<vector<vector<T>>>(n,v2(T,m,k,a))
#define v4(T,n,m,k,l,a) vector<vector<vector<vector<T>>>>(n,v3(T,m,k,l,a))
template<typename T,typename U>istream &operator>>(istream&is,pair<T,U>&p){is>>p.first>>p.second;return is;}
template<typename T,typename U>ostream &operator<<(ostream&os,const pair<T,U>&p){os<<p.first<<" "<<p.second;return os;}
template<typename T>istream &operator>>(istream&is,vector<T>&v){for(T &in:v){is>>in;}return is;}
template<typename T>ostream &operator<<(ostream&os,const vector<T>&v){for(auto it=v.begin();it!=v.end();){os<<*it<<((++it)!=v.end()?" ":"");}return os;}
template<typename T>istream &operator>>(istream&is,vector<vector<T>>&v){for(T &in:v){is>>in;}return is;}
template<typename T>ostream &operator<<(ostream&os,const vector<vector<T>>&v){for(auto it=v.begin();it!=v.end();){os<<*it<<((++it)!=v.end()?"\n":"");}return os;}
template<typename T>ostream &operator<<(ostream&os,const set<T>&v){for(auto it=v.begin();it!=v.end();){os<<*it<<((++it)!=v.end()?" ":"");}return os;}
template<typename T>ostream &operator<<(ostream&os,const multiset<T>&v){for(auto it=v.begin();it!=v.end();){os<<*it<<((++it)!=v.end()?" ":"");}return os;}
template<class... Args> void printall(Args... args){for(auto i:initializer_list<common_type_t<Args...>>{args...}) cout<<i<<" ";cout<<endl;}

const int mod = 998244353 ;

template< int mod >
struct ModInt {
    int x;

    ModInt() : x(0) {}

    ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

    ModInt &operator+=(const ModInt &p) {
        if((x += p.x) >= mod) x -= mod;
        return *this;
    }

    ModInt &operator-=(const ModInt &p) {
        if((x += mod - p.x) >= mod) x -= mod;
        return *this;
    }

    ModInt &operator*=(const ModInt &p) {
        x = (int) (1LL * x * p.x % mod);
        return *this;
    }

    ModInt &operator/=(const ModInt &p) {
        *this *= p.inverse();
        return *this;
    }

    ModInt operator-() const { return ModInt(-x); }

    ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }

    ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }

    ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }

    ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }

    bool operator==(const ModInt &p) const { return x == p.x; }

    bool operator!=(const ModInt &p) const { return x != p.x; }

    ModInt inverse() const {
        int a = x, b = mod, u = 1, v = 0, t;
        while(b > 0) {
            t = a / b;
            swap(a -= t * b, b);
            swap(u -= t * v, v);
        }
        return ModInt(u);
    }

    ModInt pow(int64_t n) const {
        ModInt ret(1), mul(x);
        while(n > 0) {
            if(n & 1) ret *= mul;
            mul *= mul;
            n >>= 1;
        }
        return ret;
    }

    friend ostream &operator<<(ostream &os, const ModInt &p) {
        return os << p.x;
    }

    friend istream &operator>>(istream &is, ModInt &a) {
        int64_t t;
        is >> t;
        a = ModInt< mod >(t);
        return (is);
    }

    static int get_mod() { return mod; }
};

using modint = ModInt< mod >;

const int MAX_N = 3030303;

modint inv[MAX_N+1] ; // (n!)^(p-2) (mod p) を格納
modint fac[MAX_N+1] ; // (n!) (mod p) を格納

modint powmod(modint x , ll n){
    modint res = 1 ;
    while(n > 0){
        if(n & 1) res *= x;
        x *= x;
        n >>= 1 ;
    }
    return res ;
}

// 階乗の逆元(n!)^(-1)のmodを配列に格納
void f(){
    inv[0] = 1 ; inv[1] = 1 ;
    for(ll i = 2 ; i <= MAX_N ; i++){
        inv[i] = powmod(i,mod-2) * inv[i-1];
    }
}

// 階乗のmodを配列に格納
void g(){
    fac[0] = 1 ; fac[1] = 1 ;
    for(ll i = 2 ; i <= MAX_N ; i++){
        fac[i] = fac[i-1] * i;
    }
}

//nCrの計算
modint combination(ll n , ll r){
    if(n < 0 || r < 0 || n < r) return 0 ;
    return fac[n] * inv[n-r] * inv[r];
}

modint permutation(ll n , ll r){
    if(n < 0 || r < 0 || n < r) return 0 ;
    return fac[n] * inv[n-r];
}

void init(){ f() ; g() ; }

struct NTT{
    private:
        int n , logn = 0;
        modint BASE = 3 ;
        vector<modint> vec , X , Y ;
        vector<vector<modint>> ROOT , INV_ROOT ;

        // ビルドする（畳み込み→逆変換） 
        void build(){
            // 畳み込み
            vector<modint> V = convolution(X,Y) ;
            // 逆変換
            vec = ifft(V) ;
        }
        // バタフライ演算を行うために配置を変換
        inline void arrangeIndexForBatafly(vector<modint> &A , int logn){
            for (int i = 0; i < n; i++) {
                int j = 0;
                for (int k = 0; k < logn; k++) j |= (i >> k & 1) << (logn - 1 - k);
                if (i < j) swap(A[i], A[j]);
            }
        }
        // FFT, IFFT のロジック
        inline vector<modint> sub_fft(vector<modint> A , bool inverse){
            // バタフライ演算
            arrangeIndexForBatafly(A,logn) ;
            int lg = 1 ;
            for(int block = 1 ; block < n ; block *= 2){
                // block内 の j 番目に対する処理
                for(int j = 0 ; j < block ; j++){
                    // w , v : 重み
                    modint w = inverse ? ROOT[lg][j] : INV_ROOT[lg][j] ;
                    modint v = inverse ? ROOT[lg][j+block] : INV_ROOT[lg][j+block] ;
                    for(int i = 0 ; i < n ; i += 2 * block){
                        modint s = A[j+i] ;
                        modint t = A[j+i+block] ;
                        A[j + i] = s + t * w ;
                        A[j + i + block] = s + t * v ;
                    }
                }
                lg++ ;
            }
            if(inverse) for(int i = 0 ; i < n ; i++) A[i] /= n ;
            return A ;
        }
        // 高速数論変換（NTT）
        inline vector<modint>  fft(vector<modint> A) { return sub_fft(A,false)  ; }
        // 逆高速数論変換（INTT）
        inline vector<modint> ifft(vector<modint> A) { return sub_fft(A,true) ; }
        // 畳み込み（Comvolution）を行う
        inline vector<modint> convolution(vector<modint> A , vector<modint> B){
            X = fft(A) , Y = fft(B) ;
            vector<modint> V(n,0) ;
            for(int i = 0 ; i < n ; i++) V[i] = X[i] * Y[i] ;
            return V ;
        }

    public:
        NTT(vector<modint> A , vector<modint> B){
            BASE = BASE.pow(119) ;
            int n1 = A.size() , n2 = B.size() , n_ = n1 + n2 - 1 ;
            n = 1 ;
            while(n < n_) n *= 2 , logn++ ;
            X.resize(n,0) , Y.resize(n,0) ;
            for(int i = 0 ; i < n1 ; i++) X[i] = A[i] ;
            for(int i = 0 ; i < n2 ; i++) Y[i] = B[i] ;

            rep(i,logn+1) {
                vector<modint> pwr , ipwr ;
                modint POW = BASE.pow(1<<(23-i)) ;
                modint INV_POW = POW.inverse() ;
                modint powval = 1 , inv_powval = 1 ;
                rep(j,(1<<i)+1) {
                    pwr.push_back(powval) ;
                    powval *= POW ;
                }
                rep(j,(1<<i)+1) {
                    ipwr.push_back(inv_powval) ;
                    inv_powval *= INV_POW ;
                }
                ROOT.push_back(pwr) ;
                INV_ROOT.push_back(ipwr) ;
            }
            build() ;
        }
        inline modint operator [] (int i) { return vec[i] ; }
        size_t fft_size() { return n ; } // 2の冪乗が返ってくる
        vector<modint> get_fft() { return vec ; }
};

ll n, m;

void solve(){
    init();
    cin >> n >> m;
    m = abs(m);
    if(m == 0){
        if(n % 2) {
            pt(0)
            return;
        }
        modint res = 0;
        rep(x,n+1) {
            ll y = x;
            ll diff = n - (x + y);
            if(diff < 0) continue;
            if((n+x-y)%2) continue;
            if((n-x-y)%2) continue;
            modint t = 4;
            if(x == 0) t /= 2;
            if(y == 0) t /= 2;
            res += combination(n,(n+x-y)/2) * combination(n,(n-x-y)/2) * t;
        }
        pt(res/powmod(4,n))
        return;
    }
    vector<ll> V;
    for(ll x = 1; x * x <= m; x++){
        if(m % x != 0) continue;
        V.push_back(x);
    }
    modint res = 0;
    for(ll b : V){
        ll a = m / b;
        if((a + b) % 2 != 0) continue;
        ll x = (a + b) / 2;
        ll y = (a - b) / 2;
        x = abs(x);
        y = abs(y);
        if(x < y) swap(x,y);
        ll diff = n - (x + y);
        if(diff < 0) continue;
        if((n+x-y)%2) continue;
        if((n-x-y)%2) continue;
        modint t = 4;
        if(x == 0) t /= 2;
        if(y == 0) t /= 2;
        res += combination(n,(n+x-y)/2) * combination(n,(n-x-y)/2) * t;
    }
    pt(res / powmod(4,n))
}

int main(){
    // fast_io
    int t = 1;
    // cin >> t;
    rep(i,t) solve();
}