結果

問題 No.1973 Divisor Sequence
ユーザー yuto1115yuto1115
提出日時 2022-06-10 22:46:10
言語 C++17
(gcc 13.2.0 + boost 1.83.0)
結果
AC  
実行時間 330 ms / 2,000 ms
コード長 16,112 bytes
コンパイル時間 3,919 ms
コンパイル使用メモリ 246,888 KB
実行使用メモリ 178,900 KB
最終ジャッジ日時 2023-10-21 06:21:48
合計ジャッジ時間 7,148 ms
ジャッジサーバーID
（参考情報） 		judge10 / judge12
このコードへのチャレンジ
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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
4,348 KB
testcase_01 AC 2 ms
4,348 KB
testcase_02 AC 165 ms
29,940 KB
testcase_03 AC 9 ms
5,416 KB
testcase_04 AC 97 ms
18,864 KB
testcase_05 AC 22 ms
16,480 KB
testcase_06 AC 102 ms
25,396 KB
testcase_07 AC 19 ms
6,924 KB
testcase_08 AC 55 ms
14,752 KB
testcase_09 AC 85 ms
16,820 KB
testcase_10 AC 92 ms
24,980 KB
testcase_11 AC 15 ms
5,368 KB
testcase_12 AC 83 ms
20,952 KB
testcase_13 AC 22 ms
9,540 KB
testcase_14 AC 62 ms
17,724 KB
testcase_15 AC 145 ms
21,888 KB
testcase_16 AC 140 ms
25,924 KB
testcase_17 AC 77 ms
21,284 KB
testcase_18 AC 6 ms
4,524 KB
testcase_19 AC 113 ms
27,228 KB
testcase_20 AC 20 ms
6,132 KB
testcase_21 AC 125 ms
30,388 KB
testcase_22 AC 117 ms
22,032 KB
testcase_23 AC 280 ms
178,900 KB
testcase_24 AC 330 ms
54,080 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 # 

#include<bits/stdc++.h>
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>
#include<ext/pb_ds/tag_and_trait.hpp>
#define overload4(_1, _2, _3, _4, name, ...) name
#define rep1(i, n) for (ll i = 0; i < ll(n); ++i)
#define rep2(i, s, n) for (ll i = ll(s); i < ll(n); ++i)
#define rep3(i, s, n, d) for(ll i = ll(s); i < ll(n); i+=d)
#define rep(...) overload4(__VA_ARGS__,rep3,rep2,rep1)(__VA_ARGS__)
#define rrep1(i, n) for (ll i = ll(n)-1; i >= 0; i--)
#define rrep2(i, n, t) for (ll i = ll(n)-1; i >= (ll)t; i--)
#define rrep3(i, n, t, d) for (ll i = ll(n)-1; i >= (ll)t; i-=d)
#define rrep(...) overload4(__VA_ARGS__,rrep3,rrep2,rrep1)(__VA_ARGS__)
#define all(a) a.begin(),a.end()
#define rall(a) a.rbegin(),a.rend()
#define SUM(a) accumulate(all(a),0LL)
#define MIN(a) *min_element(all(a))
#define MAX(a) *max_element(all(a))
#define SORT(a) sort(all(a));
#define REV(a) reverse(all(a));
#define SZ(a) int(a.size())
#define popcount(x) __builtin_popcountll(x)
#define pf push_front
#define pb push_back
#define ef emplace_front
#define eb emplace_back
#define ppf pop_front
#define ppb pop_back
#ifdef __LOCAL
#define debug(...) { cout << #__VA_ARGS__; cout << ": "; print(__VA_ARGS__); cout << flush; }
#else
#define debug(...) void(0);
#endif
#define INT(...) int __VA_ARGS__;scan(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__;scan(__VA_ARGS__)
#define STR(...) string __VA_ARGS__;scan(__VA_ARGS__)
#define CHR(...) char __VA_ARGS__;scan(__VA_ARGS__)
#define DBL(...) double __VA_ARGS__;scan(__VA_ARGS__)
#define LD(...) ld __VA_ARGS__;scan(__VA_ARGS__)
using namespace std;
using namespace __gnu_pbds;
using ll = long long;
using ld = long double;
using P = pair<int, int>;
using LP = pair<ll, ll>;
using vi = vector<int>;
using vvi = vector<vi>;
using vvvi = vector<vvi>;
using vl = vector<ll>;
using vvl = vector<vl>;
using vvvl = vector<vvl>;
using vd = vector<double>;
using vvd = vector<vd>;
using vs = vector<string>;
using vc = vector<char>;
using vvc = vector<vc>;
using vb = vector<bool>;
using vvb = vector<vb>;
using vp = vector<P>;
using vvp = vector<vp>;
template<class T>
using PQ = priority_queue<pair<T, int>, vector<pair<T, int>>, greater<pair<T, int>>>;

template<class S, class T>
istream &operator>>(istream &is, pair<S, T> &p) { return is >> p.first >> p.second; }

template<class S, class T>
ostream &operator<<(ostream &os, const pair<S, T> &p) { return os << '{' << p.first << ", " << p.second << '}'; }

template<class S, class T, class U>
istream &operator>>(istream &is, tuple<S, T, U> &t) { return is >> get<0>(t) >> get<1>(t) >> get<2>(t); }

template<class S, class T, class U>
ostream &operator<<(ostream &os, const tuple<S, T, U> &t) {
    return os << '{' << get<0>(t) << ", " << get<1>(t) << ", " << get<2>(t) << '}';
}

template<class T>
istream &operator>>(istream &is, vector<T> &v) {
    for (T &t: v) { is >> t; }
    return is;
}

template<class T>
ostream &operator<<(ostream &os, const vector<T> &v) {
    os << '[';
    rep(i, v.size()) os << v[i] << (i == int(v.size() - 1) ? "" : ", ");
    return os << ']';
}

template<class T>
ostream &operator<<(ostream &os, const deque<T> &v) {
    os << '[';
    rep(i, v.size()) os << v[i] << (i == int(v.size() - 1) ? "" : ", ");
    return os << ']';
}

template<class T>
ostream &operator<<(ostream &os, const set<T> &st) {
    os << '{';
    auto it = st.begin();
    while (it != st.end()) {
        os << (it == st.begin() ? "" : ", ") << *it;
        it++;
    }
    return os << '}';
}

template<class T>
ostream &operator<<(ostream &os, const multiset<T> &st) {
    os << '{';
    auto it = st.begin();
    while (it != st.end()) {
        os << (it == st.begin() ? "" : ", ") << *it;
        it++;
    }
    return os << '}';
}

template<class T, class U>
ostream &operator<<(ostream &os, const map<T, U> &mp) {
    os << '{';
    auto it = mp.begin();
    while (it != mp.end()) {
        os << (it == mp.begin() ? "" : ", ") << *it;
        it++;
    }
    return os << '}';
}

template<class T>
void vecout(const vector<T> &v, char div = '\n') {
    rep(i, v.size()) cout << v[i] << (i == int(v.size() - 1) ? '\n' : div);
}

template<class T>
bool constexpr chmin(T &a, T b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}

template<class T>
bool constexpr chmax(T &a, T b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}

void scan() {}

template<class Head, class... Tail>
void scan(Head &head, Tail &... tail) {
    cin >> head;
    scan(tail...);
}

template<class T>
void print(const T &t) { cout << t << '\n'; }

template<class Head, class... Tail>
void print(const Head &head, const Tail &... tail) {
    cout << head << ' ';
    print(tail...);
}

template<class... T>
void fin(const T &... a) {
    print(a...);
    exit(0);
}

template<class T>
vector<T> &operator+=(vector<T> &v, T x) {
    for (T &t: v) t += x;
    return v;
}

template<class T>
vector<T> &operator-=(vector<T> &v, T x) {
    for (T &t: v) t -= x;
    return v;
}

template<class T>
vector<T> &operator*=(vector<T> &v, T x) {
    for (T &t: v) t *= x;
    return v;
}

template<class T>
vector<T> &operator/=(vector<T> &v, T x) {
    for (T &t: v) t /= x;
    return v;
}

struct Init_io {
    Init_io() {
        ios::sync_with_stdio(false);
        cin.tie(nullptr);
        cout.tie(nullptr);
        cout << boolalpha << fixed << setprecision(15);
        cerr << boolalpha << fixed << setprecision(15);
    }
} init_io;

const string yes[] = {"no", "yes"};
const string Yes[] = {"No", "Yes"};
const string YES[] = {"NO", "YES"};
const int inf = 1001001001;
const ll linf = 1001001001001001001;

void rearrange(const vi &) {}

template<class T, class... Tail>
void rearrange(const vi &ord, vector<T> &head, Tail &...tail) {
    assert(ord.size() == head.size());
    vector<T> ori = head;
    rep(i, ord.size()) head[i] = ori[ord[i]];
    rearrange(ord, tail...);
}

template<class T, class... Tail>
void sort_by(vector<T> &head, Tail &... tail) {
    vi ord(head.size());
    iota(all(ord), 0);
    sort(all(ord), [&](int i, int j) { return head[i] < head[j]; });
    rearrange(ord, head, tail...);
}

template<class T, class S>
vector<T> cumsum(const vector<S> &v, bool shift_one = true) {
    int n = v.size();
    vector<T> res;
    if (shift_one) {
        res.resize(n + 1);
        rep(i, n) res[i + 1] = res[i] + v[i];
    } else {
        res.resize(n);
        if (n) {
            res[0] = v[0];
            rep(i, 1, n) res[i] = res[i - 1] + v[i];
        }
    }
    return res;
}

vvi graph(int n, int m, bool directed = false, int origin = 1) {
    vvi G(n);
    rep(_, m) {
        INT(u, v);
        u -= origin, v -= origin;
        G[u].pb(v);
        if (!directed) G[v].pb(u);
    }
    return G;
}

template<class T>
vector<vector<pair<int, T>>> weighted_graph(int n, int m, bool directed = false, int origin = 1) {
    vector<vector<pair<int, T>>> G(n);
    rep(_, m) {
        int u, v;
        T w;
        scan(u, v, w);
        u -= origin, v -= origin;
        G[u].eb(v, w);
        if (!directed) G[v].eb(u, w);
    }
    return G;
}

template<int mod>
class modint {
    ll x;
public:
    constexpr modint(ll x = 0) : x((x % mod + mod) % mod) {}
    
    static constexpr int get_mod() { return mod; }
    
    constexpr int val() const { return x; }
    
    constexpr modint operator-() const { return modint(-x); }
    
    constexpr modint &operator+=(const modint &a) {
        if ((x += a.val()) >= mod) x -= mod;
        return *this;
    }
    
    constexpr modint &operator++() { return *this += 1; }
    
    constexpr modint &operator-=(const modint &a) {
        if ((x += mod - a.val()) >= mod) x -= mod;
        return *this;
    }
    
    constexpr modint &operator--() { return *this -= 1; }
    
    constexpr modint &operator*=(const modint &a) {
        (x *= a.val()) %= mod;
        return *this;
    }
    
    constexpr modint operator+(const modint &a) const {
        modint res(*this);
        return res += a;
    }
    
    constexpr modint operator-(const modint &a) const {
        modint res(*this);
        return res -= a;
    }
    
    constexpr modint operator*(const modint &a) const {
        modint res(*this);
        return res *= a;
    }
    
    constexpr modint pow(ll t) const {
        modint res = 1, a(*this);
        while (t > 0) {
            if (t & 1) res *= a;
            t >>= 1;
            a *= a;
        }
        return res;
    }
    
    template<int m>
    friend istream &operator>>(istream &, modint<m> &);
    
    // for prime mod
    constexpr modint inv() const { return pow(mod - 2); }
    
    constexpr modint &operator/=(const modint &a) { return *this *= a.inv(); }
    
    constexpr modint operator/(const modint &a) const {
        modint res(*this);
        return res /= a;
    }
    
    // constraints : mod = 2 or val = 0 or val^((mod-1)/2) ≡ 1
    //               mod is prime
    // time complexity : O(log^2 p)
    // reference : https://nyaannyaan.github.io/library/modulo/mod-sqrt.hpp
    modint sqrt() const {
        if (x < 2) return x;
        assert(this->pow((mod - 1) >> 1).val() == 1);
        modint b = 1;
        while (b.pow((mod - 1) >> 1).val() == 1) b += 1;
        ll m = mod - 1, e = 0;
        while (~m & 1) m >>= 1, e += 1;
        modint X = this->pow((m - 1) >> 1);
        modint Y = (*this) * X * X;
        X *= *this;
        modint Z = b.pow(m);
        while (Y.val() != 1) {
            ll j = 0;
            modint t = Y;
            while (t.val() != 1) {
                j += 1;
                t *= t;
            }
            Z = Z.pow(1LL << (e - j - 1));
            X *= Z;
            Z *= Z;
            Y *= Z;
            e = j;
        }
        return X;
    }
};

using modint998244353 = modint<998244353>;
using modint1000000007 = modint<1000000007>;

template<int mod>
istream &operator>>(istream &is, modint<mod> &a) { return is >> a.x; }

template<int mod>
constexpr ostream &operator<<(ostream &os, const modint<mod> &a) { return os << a.val(); }

template<int mod>
constexpr bool operator==(const modint<mod> &a, const modint<mod> &b) { return a.val() == b.val(); }

template<int mod>
constexpr bool operator!=(const modint<mod> &a, const modint<mod> &b) { return a.val() != b.val(); }

template<int mod>
constexpr modint<mod> &operator++(modint<mod> &a) { return a += 1; }

template<int mod>
constexpr modint<mod> &operator--(modint<mod> &a) { return a -= 1; }

using mint = modint1000000007;

using vm = vector<mint>;
using vvm = vector<vm>;

// reference : https://nyaannyaan.github.io/library/misc/rng.hpp
// [0, 2^64 - 1)
uint64_t rng() {
    static uint64_t x_ =
        uint64_t(chrono::duration_cast<chrono::nanoseconds>(
            chrono::high_resolution_clock::now().time_since_epoch())
                     .count()) *
        10150724397891781847ULL;
    x_ ^= x_ << 7;
    return x_ ^= x_ >> 9;
}

// [l, r)
template<class T>
T randint(T l, T r) {
    assert(l < r);
    return l + rng() % (r - l);
}

// choose n numbers from [l, r) without overlapping
template<class T>
vector<T> randset(T l, T r, T n) {
    assert(1 <= n and n <= r - l);
    unordered_set<T> st;
    for (T i = n; i > 0; --i) {
        T m = randint(l, r + 1 - i);
        if (st.count(m)) m = r - i;
        st.insert(m);
    }
    vector<T> res;
    for (T x: st) res.pb(x);
    return res;
}

// [0.0, 1.0)
double rnd() {
    union raw_cast {
        double t;
        uint64_t u;
    };
    constexpr uint64_t p = uint64_t(1023 - 64) << 52;
    return rng() * ((raw_cast *) (&p))->t;
}

template<typename T>
void randshf(vector<T> &v) {
    int n = v.size();
    rep(_, 2) rep(i, n) swap(v[i], v[randint(0, n)]);
}

// reference : https://nyaannyaan.github.io/library/prime/fast-factorize.hpp.html
template<typename T>
class prime {
    vector<T> as;
    
    constexpr T add(T a, T b, T m) {
        return (a + b >= m ? a + b - m : a + b);
    }
    
    constexpr T sub(T a, T b, T m) {
        return (a - b < 0 ? a - b + m : a - b);
    }
    
    constexpr T mul(T a, T b, T m) {
        return T((__int128) a * (__int128) b % m);
    }
    
    constexpr T mod_pow(T a, T t, T m) {
        T res = 1;
        while (t > 0) {
            if (t & 1) res = mul(res, a, m);
            t >>= 1;
            a = mul(a, a, m);
        }
        return res;
    }
    
    constexpr bool miller_rabin(T n) {
        T d = n - 1;
        while (~d & 1) d >>= 1;
        for (T a: as) {
            a %= n;
            if (!a) return true;
            T t = d;
            T y = mod_pow(a, t, n);
            while (t != n - 1 and y != 1 and y != n - 1) {
                y = mul(y, y, n);
                t *= 2;
            }
            if (y != n - 1 and t % 2 == 0) return false;
        }
        return true;
    }
    
    T pollard_rho(T n) {
        assert(n >= 2);
        if (~n & 1) return 2;
        if (miller_rabin(n)) return n;
        T R;
        auto f = [&](T x) { return add(mul(x, x, n), R, n); };
        auto rnd_ = [&]() { return rng() % (n - 2) + 2; };
        while (true) {
            T x = 0, y = 0, ys = 0, q = 1;
            R = rnd_(), y = rnd_();
            T g = 1;
            constexpr int m = 128;
            for (int r = 1; g == 1; r <<= 1) {
                x = y;
                rep(i, r) y = f(y);
                for (int k = 0; g == 1 and k < r; k += m) {
                    ys = y;
                    for (int i = 0; i < m and i < r - k; ++i) q = mul(q, sub(x, y = f(y), n), n);
                    g = gcd(q, n);
                }
            }
            if (g == n)
                do
                    g = gcd(sub(x, ys = f(ys), n), n);
                while (g == 1);
            if (g != n) return g;
        }
        assert(false);
    }
    
    vector<T> factorize(T n) {
        assert(n >= 2);
        T p = pollard_rho(n);
        if (p == n) return {p};
        auto l = factorize(p);
        auto r = factorize(n / p);
        copy(all(r), back_inserter(l));
        return l;
    }

public:
    constexpr prime() {
        static_assert(is_same<T, int>::value or is_same<T, ll>::value);
        if (is_same<T, int>::value) as = {2, 7, 61};
        else as = {2, 325, 9375, 28178, 450775, 9780504, 1795265022};
    }
    
    constexpr bool is_prime(T n) {
        assert(n >= 1);
        if (n == 1) return false;
        if (~n & 1) return n == 2;
        return miller_rabin(n);
    }
    
    map<T, int> factor_list(T n) {
        assert(n >= 1);
        if (n == 1) return {};
        map<T, int> mp;
        for (T x: factorize(n)) ++mp[x];
        return mp;
    }
    
    vector<T> unique_factor(T n) {
        assert(n >= 1);
        if (n == 1) return {};
        auto res = factorize(n);
        sort(all(res));
        res.erase(unique(all(res)), res.end());
        return res;
    };
    
    T count_divisor(T n) {
        assert(n >= 1);
        T res = 1;
        for (auto p: factor_list(n)) res *= p.second + 1;
        return res;
    };
    
    vector<T> enum_divisors(T n) {
        assert(n >= 1);
        vector<pair<T, int>> v;
        for (auto p: factor_list(n)) v.pb(p);
        vector<T> res;
        auto f = [&](auto &f, int i, T x) -> void {
            if (i == SZ(v)) {
                res.pb(x);
                return;
            }
            rep(j, v[i].second + 1) {
                f(f, i + 1, x);
                if (j == v[i].second) break;
                x *= v[i].first;
            }
        };
        f(f, 0, 1);
        sort(all(res));
        return res;
    }
};

int main() {
    INT(n);
    LL(m);
    prime<ll> pr;
    auto mp = pr.factor_list(m);
    mint ans = 1;
    for (auto[_, c]: mp) {
        vvm dp(n + 1, vm(c + 2));
        dp[0][0] = 1;
        rep(i, n) {
            rep(j, c + 1) {
                dp[i + 1][0] += dp[i][j];
                dp[i + 1][c - j + 1] -= dp[i][j];
            }
            rep(j, c + 1) dp[i + 1][j + 1] += dp[i + 1][j];
        }
        ans *= accumulate(all(dp[n]), mint(0));
    }
    fin(ans);
}
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