結果

問題 No.2406 Difference of Coordinate Squared
ユーザー siro53siro53
提出日時 2023-08-04 23:35:19
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 64 ms / 2,000 ms
コード長 8,261 bytes
コンパイル時間 2,796 ms
コンパイル使用メモリ 212,512 KB
実行使用メモリ 13,792 KB
最終ジャッジ日時 2024-05-05 01:41:59
合計ジャッジ時間 4,250 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge4
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 2 ms
5,248 KB
testcase_01 AC 33 ms
13,764 KB
testcase_02 AC 32 ms
13,792 KB
testcase_03 AC 64 ms
13,632 KB
testcase_04 AC 31 ms
13,600 KB
testcase_05 AC 11 ms
5,376 KB
testcase_06 AC 14 ms
8,512 KB
testcase_07 AC 16 ms
8,516 KB
testcase_08 AC 6 ms
5,376 KB
testcase_09 AC 25 ms
13,620 KB
testcase_10 AC 23 ms
13,656 KB
testcase_11 AC 11 ms
5,376 KB
testcase_12 AC 11 ms
5,376 KB
testcase_13 AC 26 ms
13,752 KB
testcase_14 AC 25 ms
13,760 KB
testcase_15 AC 25 ms
13,756 KB
testcase_16 AC 24 ms
13,632 KB
testcase_17 AC 2 ms
5,376 KB
testcase_18 AC 9 ms
5,376 KB
testcase_19 AC 10 ms
5,376 KB
testcase_20 AC 22 ms
13,764 KB
testcase_21 AC 25 ms
13,632 KB
testcase_22 AC 24 ms
8,512 KB
testcase_23 AC 25 ms
13,628 KB
testcase_24 AC 7 ms
6,080 KB
testcase_25 AC 3 ms
5,376 KB
testcase_26 AC 2 ms
5,376 KB
testcase_27 AC 2 ms
5,376 KB
testcase_28 AC 1 ms
5,376 KB
testcase_29 AC 1 ms
5,376 KB
testcase_30 AC 1 ms
5,376 KB
testcase_31 AC 2 ms
5,376 KB
testcase_32 AC 1 ms
5,376 KB
testcase_33 AC 1 ms
5,376 KB
testcase_34 AC 2 ms
5,376 KB
testcase_35 AC 2 ms
5,376 KB
testcase_36 AC 2 ms
5,376 KB
testcase_37 AC 2 ms
5,376 KB
testcase_38 AC 2 ms
5,376 KB
testcase_39 AC 1 ms
5,376 KB
testcase_40 AC 2 ms
5,376 KB
testcase_41 AC 1 ms
5,376 KB
testcase_42 AC 2 ms
5,376 KB
testcase_43 AC 2 ms
5,376 KB
testcase_44 AC 2 ms
5,376 KB
testcase_45 AC 1 ms
5,376 KB
testcase_46 AC 2 ms
5,376 KB
testcase_47 AC 1 ms
5,376 KB
testcase_48 AC 1 ms
5,376 KB
testcase_49 AC 2 ms
5,376 KB
testcase_50 AC 2 ms
5,376 KB
testcase_51 AC 1 ms
5,376 KB
testcase_52 AC 1 ms
5,376 KB
testcase_53 AC 2 ms
5,376 KB
testcase_54 AC 1 ms
5,376 KB
testcase_55 AC 1 ms
5,376 KB
testcase_56 AC 1 ms
5,376 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#line 1 "combined.cpp"
#pragma region Macros
#include <bits/stdc++.h>
using namespace std;
template <class T> inline bool chmax(T &a, T b) {
    if(a < b) {
        a = b;
        return 1;
    }
    return 0;
}
template <class T> inline bool chmin(T &a, T b) {
    if(a > b) {
        a = b;
        return 1;
    }
    return 0;
}
#ifdef DEBUG
template <class T, class U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
    os << '(' << p.first << ',' << p.second << ')';
    return os;
}
template <class T> ostream &operator<<(ostream &os, const vector<T> &v) {
    os << '{';
    for(int i = 0; i < (int)v.size(); i++) {
        if(i) { os << ','; }
        os << v[i];
    }
    os << '}';
    return os;
}
void debugg() { cerr << endl; }
template <class T, class... Args>
void debugg(const T &x, const Args &... args) {
    cerr << " " << x;
    debugg(args...);
}
#define debug(...)                                                             \
    cerr << __LINE__ << " [" << #__VA_ARGS__ << "]: ", debugg(__VA_ARGS__)
#define dump(x) cerr << __LINE__ << " " << #x << " = " << (x) << endl
#else
#define debug(...) (void(0))
#define dump(x) (void(0))
#endif

struct Setup {
    Setup() {
        cin.tie(0);
        ios::sync_with_stdio(false);
        cout << fixed << setprecision(15);
    }
} __Setup;

using ll = long long;
#define OVERLOAD3(_1, _2, _3, name, ...) name
#define ALL(v) (v).begin(), (v).end()
#define RALL(v) (v).rbegin(), (v).rend()
#define REP1(i, n) for(int i = 0; i < int(n); i++)
#define REP2(i, a, b) for(int i = (a); i < int(b); i++)
#define REP(...) OVERLOAD3(__VA_ARGS__, REP2, REP1)(__VA_ARGS__)
#define UNIQUE(v) sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end())
#define REVERSE(v) reverse(ALL(v))
#define SZ(v) ((int)(v).size())
const int INF = 1 << 30;
const ll LLINF = 1LL << 60;
constexpr int MOD = 1000000007;
constexpr int MOD2 = 998244353;
const int dx[4] = {1, 0, -1, 0};
const int dy[4] = {0, 1, 0, -1};

void Case(int i) { cout << "Case #" << i << ": "; }
int popcount(int x) { return __builtin_popcount(x); }
ll popcount(ll x) { return __builtin_popcountll(x); }
#pragma endregion Macros

#line 2 "/Users/siro53/kyo-pro/compro_library/modint/modint.hpp"

#line 6 "/Users/siro53/kyo-pro/compro_library/modint/modint.hpp"

template <int mod> class ModInt {
  public:
    ModInt() : x(0) {}
    ModInt(long long y)
        : x(y >= 0 ? y % umod() : (umod() - (-y) % umod()) % umod()) {}
    unsigned int val() const { return x; }
    ModInt &operator+=(const ModInt &p) {
        if((x += p.x) >= umod()) x -= umod();
        return *this;
    }
    ModInt &operator-=(const ModInt &p) {
        if((x += umod() - p.x) >= umod()) x -= umod();
        return *this;
    }
    ModInt &operator*=(const ModInt &p) {
        x = (unsigned int)(1ULL * x * p.x % umod());
        return *this;
    }
    ModInt &operator/=(const ModInt &p) {
        *this *= p.inv();
        return *this;
    }
    ModInt operator-() const { return ModInt(-(long long)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 inv() const {
        long long a = x, b = mod, u = 1, v = 0, t;
        while(b > 0) {
            t = a / b;
            std::swap(a -= t * b, b);
            std::swap(u -= t * v, v);
        }
        return ModInt(u);
    }
    ModInt pow(unsigned long long n) const {
        ModInt ret(1), mul(x);
        while(n > 0) {
            if(n & 1) ret *= mul;
            mul *= mul;
            n >>= 1;
        }
        return ret;
    }
    friend std::ostream &operator<<(std::ostream &os, const ModInt &p) {
        return os << p.x;
    }
    friend std::istream &operator>>(std::istream &is, ModInt &a) {
        long long t;
        is >> t;
        a = ModInt<mod>(t);
        return (is);
    }
    static constexpr int get_mod() { return mod; }

  private:
    unsigned int x;
    static constexpr unsigned int umod() { return mod; }
};
#line 78 "combined.cpp"
using mint = ModInt<MOD2>;
#line 2 "/Users/siro53/kyo-pro/compro_library/math/binom.hpp"

#line 6 "/Users/siro53/kyo-pro/compro_library/math/binom.hpp"

template <class mint> class Binomial {
  public:
    explicit Binomial(): Binomial(1) {}
    explicit Binomial(int MAX) : f(MAX, mint(1)), f_inv(MAX, mint(1)) {
        for(int i = 1; i < MAX; i++) f[i] = f[i-1] * mint(i);
        f_inv[MAX - 1] = f[MAX - 1].inv();
        for(int i = MAX - 2; i >= 1; i--) {
            f_inv[i] = f_inv[i + 1] * mint(i + 1);
        } 
    }
    void extend() {
        int n = (int)f.size();
        f.resize(n * 2);
        f_inv.resize(n * 2);
        for(int i = n; i < n * 2; i++) f[i] = f[i - 1] * mint(i);
        f_inv[n * 2 - 1] = f[n * 2 - 1].inv();
        for(int i = n * 2 - 2; i >= n; i--) {
            f_inv[i] = f_inv[i + 1] * mint(i + 1);
        }
    }
    mint fac(int n) {
        if(n < 0) return mint(0);
        while(n >= (int)f.size()) extend();
        return f[n];
    }
    mint fac_inv(int n) {
        if(n < 0) return mint(0);
        while(n >= (int)f_inv.size()) extend();
        return f_inv[n];
    }
    mint inv(int n) {
        if(n < 0) return -mint(-n);
        assert(n != 0);
        while(n >= (int)f_inv.size()) extend();
        return (f_inv[n] * f[n - 1]);
    }
    mint binom(int n, int k) {
        if(n < k || n < 0 || k < 0) return mint(0);
        return (fac(n) * fac_inv(k) * fac_inv(n - k));
    }
    mint binom_naive(long long n, long long k) {
        if(n < k || n < 0 || k < 0) return mint(0);
        mint res(1);
        k = std::min(k, n - k);
        for(int i = 0; i < k; i++) res *= inv(i + 1) * mint(n - i);
        return res;
    }
    mint perm(int n, int k) {
        if(n < k || n < 0 || k < 0) return mint(0);
        return (fac(n) * fac_inv(n - k));
    }
    mint hom(int n, int k) {
        if(n < 0 || k < 0) return mint(0);
        return (k == 0 ? mint(1) : binom(n + k - 1, k));
    }

  private:
    std::vector<mint> f, f_inv;
};
#line 2 "/Users/siro53/kyo-pro/compro_library/math/divisor.hpp"

#line 5 "/Users/siro53/kyo-pro/compro_library/math/divisor.hpp"

template<typename T>
std::vector<T> divisor(T n) {
    static_assert(std::is_integral<T>::value == true, "type 'T' should be integer.");
    std::vector<T> ret;
    for(T i = 1; i * i <= n; i++) {
        if(n % i == 0) {
            ret.push_back(i);
            if(i * i != n) ret.push_back(n / i);
        }
    }
    std::sort(ret.begin(), ret.end());
    return ret;
}
#line 81 "combined.cpp"

int main() {
    ll N, M;
    cin >> N >> M;
    Binomial<mint> comb;
    auto calc = [&](ll a, ll b) -> mint {
        if(abs(a + b + N) & 1) return 0;
        ll j = (a + b + N) / 2;
        ll i = j - b;
        if(i < 0 or i > N or j < 0 or j > N) return 0;
        return comb.binom(N, i) * comb.binom(N, j);
    };
    mint ans = 0;
    if(M == 0) {
        for(ll a = -N; a <= N; a++) {
            ans += calc(a, a);
            if(a != 0) ans += calc(a, -a);
        }
        ans *= mint(4).inv().pow(N);
        cout << ans << endl;
        return 0;
    }
    auto divs = divisor<ll>(abs(M));
    for(ll d1 : divs) {
        ll d2 = M / d1;
        if(M > 0) {
            if((d1 + d2) % 2 == 0) {
                ll a = (d1 + d2) / 2;
                ll b = d1 - a;
                ans += calc(a, b);
            }
            if(abs(- d1 - d2) % 2 == 0) {
                ll a = (- d1 - d2) / 2;
                ll b = - d1 - a;
                ans += calc(a, b);
            }
        } else {
            if(abs(-d1 + d2) % 2 == 0) {
                ll a = (-d1 + d2) / 2;
                ll b = -d1 - a;
                ans += calc(a, b);
            }
            if(abs(d1 - d2) % 2 == 0) {
                ll a = (d1 - d2) / 2;
                ll b = d1 - a;
                ans += calc(a, b);
            }
        }
    } 
    ans *= mint(4).inv().pow(N);
    cout << ans << endl;
}
0