Fu_L's Library

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:heavy_check_mark: verify/unit_test/math/lucas.test.cpp

Depends on

Code

#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#include "../../../src/template/template.hpp"
#include "../../../src/random/random_number_generator.hpp"
#include "../../../src/template/dynamic_modint.hpp"
#include "../../../src/math/lucas.hpp"
#include "../../../src/math/miller_rabin.hpp"
using mint = modint;
void test() {
    static Lucas<mint> binom;
    int n = rng(1, 200000), k = rng(0, n);
    mint ans = 1;
    int cnt = 0;
    rep(i, 1, k + 1) {
        int p = n - (i - 1), q = i;
        while(p % mint::mod() == 0) {
            cnt++;
            p /= mint::mod();
        }
        while(q % mint::mod() == 0) {
            cnt--;
            q /= mint::mod();
        }
        ans *= mint(p) / q;
    }
    if(cnt > 0) ans = 0;
    assert(binom(n, k).val() == ans.val());
}
int main(void) {
    int p = 1;
    while(!miller_rabin(p)) {
        p = rng(2, 200000);
    }
    mint::set_mod(p);
    constexpr int test_num = 1000;
    rep(_, 0, test_num) {
        test();
    }
    int a, b;
    cin >> a >> b;
    cout << a + b << '\n';
}
#line 1 "verify/unit_test/math/lucas.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#line 2 "src/template/template.hpp"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using P = pair<long long, long long>;
#define rep(i, a, b) for(long long i = (a); i < (b); ++i)
#define rrep(i, a, b) for(long long i = (a); i >= (b); --i)
constexpr long long inf = 4e18;
struct SetupIO {
    SetupIO() {
        ios::sync_with_stdio(0);
        cin.tie(0);
        cout << fixed << setprecision(30);
    }
} setup_io;
#line 3 "src/random/random_number_generator.hpp"
struct RandomNumberGenerator {
    RandomNumberGenerator()
        : mt(chrono::steady_clock::now().time_since_epoch().count()) {}
    template <typename T>
    inline T operator()(const T lower, const T upper) {
        static_assert(is_integral_v<T> or is_floating_point_v<T>);
        assert(lower <= upper);
        if constexpr(is_integral_v<T>) {
            uniform_int_distribution<T> dist(lower, upper);
            return dist(mt);
        } else if constexpr(is_floating_point_v<T>) {
            uniform_real_distribution<T> dist(lower, upper);
            return dist(mt);
        }
    }
    template <typename T>
    inline vector<T> vec(const int n, const T lower, const T upper, const bool dup = true) {
        static_assert(is_integral_v<T> or is_floating_point_v<T>);
        assert(0 <= n and n <= (int)1e8);
        assert(lower <= upper);
        if(n == 0) return {};
        vector<T> res(n);
        if(dup or is_floating_point_v<T>) {
            for(int i = 0; i < n; ++i) res[i] = this->operator()(lower, upper);
        } else {
            assert(upper - lower + 1 >= n);
            if(upper - lower + 1 >= 2 * n) {
                set<T> used;
                while((int)used.size() < n) {
                    const T a = this->operator()(lower, upper);
                    used.insert(a);
                }
                int i = 0;
                for(const T a : used) {
                    res[i] = a;
                    ++i;
                }
            } else {
                const vector<int> p = perm(upper - lower + 1, false);
                for(int i = 0; i < n; ++i) {
                    res[i] = p[i] + lower;
                }
            }
        }
        return res;
    }
    inline vector<int> perm(const int n, const bool one = true) {
        assert(0 <= n and n <= (int)1e8);
        vector<int> res(n);
        for(int i = 0; i < n; ++i) res[i] = i + one;
        for(int i = n - 1; i > 0; --i) {
            swap(res[i], res[this->operator()(0, i)]);
        }
        return res;
    }
    inline pair<vector<int>, vector<int>> tree(const int n, const bool one = true) {
        assert(0 <= n and n <= (int)1e8);
        if(n <= 1) return {{}, {}};
        if(n == 2) return {{0 + one}, {1 + one}};
        vector<int> u(n - 1), v(n - 1);
        const vector<int> pruefer = vec(n - 2, 0, n - 1);
        set<int> st;
        vector<int> cnt(n);
        for(int i = 0; i < n; ++i) st.insert(i);
        auto add = [&](const int x) -> void {
            if(x > n) return;
            if(cnt[x] == 0) st.erase(x);
            ++cnt[x];
        };
        auto del = [&](const int x) -> void {
            if(x > n) return;
            --cnt[x];
            if(cnt[x] == 0) st.insert(x);
        };
        for(int i = 0; i < n - 2; ++i) add(pruefer[i]);
        for(int i = 0; i < n - 2; ++i) {
            const int a = *st.begin();
            const int b = pruefer[i];
            u[i] = a + one;
            v[i] = b + one;
            del(b);
            add(a);
        }
        const int a = *st.begin();
        add(a);
        const int b = *st.begin();
        u[n - 2] = a + one;
        v[n - 2] = b + one;
        return {u, v};
    }
    template <typename T>
    inline tuple<vector<int>, vector<int>, vector<T>> weighted_tree(const int n, const T lower, const T upper, const bool one = true) {
        static_assert(is_integral_v<T> or is_floating_point_v<T>);
        assert(0 <= n and n <= (int)1e8);
        assert(lower <= upper);
        if(n == 0) return {{}, {}, {}};
        const auto [u, v] = tree(n, one);
        const vector<T> w = vec(n - 1, lower, upper, true);
        return {u, v, w};
    }
    inline pair<vector<int>, vector<int>> graph(const int n, const int m, const bool one = true) {
        assert(0 <= n and n <= (int)1e8);
        assert(0 <= m and m <= (int)min((ll)1e8, 1ll * n * (n - 1) / 2));
        vector<int> u, v;
        u.reserve(m);
        v.reserve(m);
        if(1ll * n * (n - 1) / 2 >= 2e6) {
            set<pair<int, int>> edge;
            while((int)edge.size() < m) {
                const int a = this->operator()(0, n - 1);
                const int b = this->operator()(0, n - 1);
                if(a >= b) continue;
                edge.insert({a, b});
            }
            for(const auto& [a, b] : edge) {
                u.push_back(a + one);
                v.push_back(b + one);
            }
        } else {
            vector<pair<int, int>> edge;
            edge.reserve(n * (n - 1) / 2);
            for(int i = 0; i < n; ++i) {
                for(int j = i + 1; j < n; ++j) {
                    edge.push_back({i, j});
                }
            }
            const vector<int> p = perm(n * (n - 1) / 2, false);
            for(int i = 0; i < m; ++i) {
                u.push_back(edge[p[i]].first + one);
                v.push_back(edge[p[i]].second + one);
            }
        }
        return {u, v};
    }
    template <typename T>
    inline tuple<vector<int>, vector<int>, vector<T>> weighted_graph(const int n, const int m, const T lower, const T upper, const bool one = true) {
        static_assert(is_integral_v<T> or is_floating_point_v<T>);
        assert(0 <= n and n <= (int)1e8);
        assert(0 <= m and m <= (int)min((ll)1e8, 1ll * n * (n - 1) / 2));
        assert(lower <= upper);
        const auto [u, v] = graph(n, m, one);
        const vector<T> w = vec(m, lower, upper, true);
        return {u, v, w};
    }
    inline pair<vector<int>, vector<int>> connected_graph(const int n, const int m, const bool one = true) {
        assert(0 <= n and n <= (int)1e8);
        assert(max(n - 1, 0) <= m and m <= (int)min((ll)1e8, 1ll * n * (n - 1) / 2));
        if(n <= 1) return {{}, {}};
        vector<int> u, v;
        u.reserve(m);
        v.reserve(m);
        auto [ut, vt] = tree(n, false);
        if(1ll * n * (n - 1) / 2 >= 2e6) {
            set<pair<int, int>> edge;
            for(int i = 0; i < n - 1; ++i) {
                edge.insert({min(ut[i], vt[i]), max(ut[i], vt[i])});
            }
            while((int)edge.size() < m) {
                const int a = this->operator()(0, n - 1);
                const int b = this->operator()(0, n - 1);
                if(a >= b) continue;
                edge.insert({a, b});
            }
            for(const auto& [a, b] : edge) {
                u.push_back(a + one);
                v.push_back(b + one);
            }
        } else {
            set<pair<int, int>> used;
            for(int i = 0; i < n - 1; ++i) {
                u.push_back(ut[i] + one);
                v.push_back(vt[i] + one);
                used.insert({min(ut[i], vt[i]), max(ut[i], vt[i])});
            }
            vector<pair<int, int>> edge;
            edge.reserve(n * (n - 1) / 2 - (n - 1));
            for(int i = 0; i < n; ++i) {
                for(int j = i + 1; j < n; ++j) {
                    if(used.find({i, j}) == used.end()) edge.push_back({i, j});
                }
            }
            const vector<int> p = perm(n * (n - 1) / 2 - (n - 1), false);
            for(int i = 0; i < m - (n - 1); ++i) {
                u.push_back(edge[p[i]].first + one);
                v.push_back(edge[p[i]].second + one);
            }
        }
        return {u, v};
    }
    template <typename T>
    inline tuple<vector<int>, vector<int>, vector<T>> weighted_connected_graph(const int n, const int m, const T lower, const T upper, const bool one = true) {
        static_assert(is_integral_v<T> or is_floating_point_v<T>);
        assert(0 <= n and n <= (int)1e8);
        assert(max(n - 1, 0) <= m and m <= (int)min((ll)1e8, 1ll * n * (n - 1) / 2));
        assert(lower <= upper);
        const auto [u, v] = connected_graph(n, m, one);
        const vector<T> w = vec(m, lower, upper, true);
        return {u, v, w};
    }
    inline string parenthesis(const int n) {
        assert(0 <= n and n <= 1e8);
        string res = "";
        int N = n, M = n;
        for(int i = 0; i < 2 * n; ++i) {
            if(this->operator()(0.0l, 1.0l) > 1.0l * (N - M) * (N + 1) / ((N - M + 1) * (N + M))) {
                res += "(";
                --M;
            } else {
                res += ")";
                --N;
            }
        }
        return res;
    }

   private:
    mt19937_64 mt;
} rng;
#line 3 "src/template/dynamic_modint.hpp"
struct Barrett {
    explicit Barrett(const unsigned int m)
        : _m(m), im((unsigned long long)(-1) / m + 1) {}
    inline unsigned int umod() const {
        return _m;
    }
    inline unsigned int mul(const unsigned int a, const unsigned int b) const {
        unsigned long long z = a;
        z *= b;
        const unsigned long long x = (unsigned long long)(((unsigned __int128)(z)*im) >> 64);
        unsigned int v = (unsigned int)(z - x * _m);
        if(_m <= v) v += _m;
        return v;
    }

   private:
    unsigned int _m;
    unsigned long long im;
};
template <int id>
struct DynamicModint {
    using mint = DynamicModint;
    static int mod() {
        return (int)bt.umod();
    }
    static void set_mod(const int m) {
        assert(1 <= m);
        bt = Barrett(m);
    }
    static mint raw(const int v) {
        mint a;
        a._v = v;
        return a;
    }
    DynamicModint()
        : _v(0) {}
    template <class T>
    DynamicModint(const T& v) {
        static_assert(is_integral_v<T>);
        if(is_signed_v<T>) {
            long long x = (long long)(v % (long long)(umod()));
            if(x < 0) x += umod();
            _v = (unsigned int)(x);
        } else _v = (unsigned int)(v % umod());
    }
    unsigned int val() const {
        return _v;
    }
    mint& operator++() {
        ++_v;
        if(_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if(_v == 0) _v = umod();
        --_v;
        return *this;
    }
    mint operator++(int) {
        mint res = *this;
        ++*this;
        return res;
    }
    mint operator--(int) {
        mint res = *this;
        --*this;
        return res;
    }
    mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if(_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v += mod() - rhs._v;
        if(_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        _v = bt.mul(_v, rhs._v);
        return *this;
    }
    mint& operator/=(const mint& rhs) {
        return *this *= rhs.inv();
    }
    mint operator+() const {
        return *this;
    }
    mint operator-() const {
        return mint() - *this;
    }
    mint pow(long long n) const {
        assert(0 <= n);
        if(n == 0) return 1;
        mint x = *this, r = 1;
        while(1) {
            if(n & 1) r *= x;
            n >>= 1;
            if(n == 0) return r;
            x *= x;
        }
    }
    mint inv() const {
        const auto eg = inv_gcd(_v, mod());
        assert(eg.first == 1);
        return eg.second;
    }
    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }
    friend istream& operator>>(istream& in, mint& x) {
        long long a;
        in >> a;
        x = a;
        return in;
    }
    friend ostream& operator<<(ostream& out, const mint& x) {
        return out << x.val();
    }

   private:
    unsigned int _v = 0;
    static Barrett bt;
    inline static unsigned int umod() {
        return bt.umod();
    }
    inline static pair<long long, long long> inv_gcd(const long long a, const long long b) {
        if(a == 0) return {b, 0};
        long long s = b, t = a, m0 = 0, m1 = 1;
        while(t) {
            const long long u = s / t;
            s -= t * u;
            m0 -= m1 * u;
            swap(s, t);
            swap(m0, m1);
        }
        if(m0 < 0) m0 += b / s;
        return {s, m0};
    }
};
template <int id>
Barrett DynamicModint<id>::bt(998244353);
using modint = DynamicModint<-1>;
#line 3 "src/math/lucas.hpp"
template <typename mint>
struct Lucas {
    Lucas()
        : mod(mint::mod()), fact(mint::mod()), ifact(mint::mod()) {
        fact[0] = 1;
        for(int i = 1; i < mod; ++i) fact[i] = fact[i - 1] * i;
        ifact[mod - 1] = fact[mod - 1].inv();
        for(int i = mod - 1; i >= 1; --i) ifact[i - 1] = ifact[i] * i;
    }
    mint operator()(long long n, long long k) const {
        if(n < 0 or n < k or k < 0) return 0;
        mint res = 1;
        while(n > 0) {
            const long long n0 = n % mod, k0 = k % mod;
            if(n0 < k0) return 0;
            res *= fact[n0] * ifact[k0] * ifact[n0 - k0];
            n /= mod;
            k /= mod;
        }
        return res;
    }

   private:
    int mod;
    vector<mint> fact, ifact;
};
#line 3 "src/math/miller_rabin.hpp"
constexpr __int128_t pow_mod_128(__int128_t x, __int128_t n, const __int128_t mod) {
    assert(n >= 0 and mod >= 1);
    x %= mod;
    if(x < 0) x += mod;
    __int128_t res = 1;
    while(n > 0) {
        if(n & 1) res = res * x % mod;
        x = x * x % mod;
        n >>= 1;
    }
    return res;
}
constexpr bool miller_rabin(const long long n) {
    if(n <= 2) return n == 2;
    if(n % 2 == 0) return false;
    constexpr long long bases[7] = {2, 325, 9375, 28178, 450775, 9780504, 1795265022};
    long long d = n - 1;
    while(d % 2 == 0) d /= 2;
    for(const long long base : bases) {
        if(base % n == 0) continue;
        long long t = d;
        long long y = pow_mod_128(base, t, n);
        while(t != n - 1 and y != 1 and y != n - 1) {
            y = (__int128_t)y * y % n;
            t *= 2;
        }
        if(y != n - 1 and t % 2 == 0) return false;
    }
    return true;
}
#line 7 "verify/unit_test/math/lucas.test.cpp"
using mint = modint;
void test() {
    static Lucas<mint> binom;
    int n = rng(1, 200000), k = rng(0, n);
    mint ans = 1;
    int cnt = 0;
    rep(i, 1, k + 1) {
        int p = n - (i - 1), q = i;
        while(p % mint::mod() == 0) {
            cnt++;
            p /= mint::mod();
        }
        while(q % mint::mod() == 0) {
            cnt--;
            q /= mint::mod();
        }
        ans *= mint(p) / q;
    }
    if(cnt > 0) ans = 0;
    assert(binom(n, k).val() == ans.val());
}
int main(void) {
    int p = 1;
    while(!miller_rabin(p)) {
        p = rng(2, 200000);
    }
    mint::set_mod(p);
    constexpr int test_num = 1000;
    rep(_, 0, test_num) {
        test();
    }
    int a, b;
    cin >> a >> b;
    cout << a + b << '\n';
}
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