結果

問題 No.1261 数字集め
ユーザー hitonanodehitonanode
提出日時 2020-10-16 23:52:01
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 4,644 ms / 8,000 ms
コード長 17,133 bytes
コンパイル時間 5,736 ms
コンパイル使用メモリ 258,368 KB
実行使用メモリ 106,148 KB
最終ジャッジ日時 2024-07-21 04:57:57
合計ジャッジ時間 42,095 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge3
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 4,644 ms
105,892 KB
testcase_01 AC 76 ms
41,508 KB
testcase_02 AC 154 ms
77,988 KB
testcase_03 AC 155 ms
78,888 KB
testcase_04 AC 107 ms
53,540 KB
testcase_05 AC 170 ms
101,284 KB
testcase_06 AC 96 ms
59,812 KB
testcase_07 AC 158 ms
81,320 KB
testcase_08 AC 96 ms
48,932 KB
testcase_09 AC 98 ms
61,732 KB
testcase_10 AC 20 ms
10,148 KB
testcase_11 AC 194 ms
99,880 KB
testcase_12 AC 174 ms
90,276 KB
testcase_13 AC 143 ms
82,468 KB
testcase_14 AC 27 ms
15,784 KB
testcase_15 AC 87 ms
44,320 KB
testcase_16 AC 151 ms
81,440 KB
testcase_17 AC 106 ms
67,364 KB
testcase_18 AC 88 ms
45,088 KB
testcase_19 AC 122 ms
79,136 KB
testcase_20 AC 32 ms
17,700 KB
testcase_21 AC 204 ms
105,384 KB
testcase_22 AC 203 ms
105,128 KB
testcase_23 AC 205 ms
105,208 KB
testcase_24 AC 176 ms
105,252 KB
testcase_25 AC 207 ms
105,124 KB
testcase_26 AC 208 ms
105,252 KB
testcase_27 AC 206 ms
105,128 KB
testcase_28 AC 201 ms
105,252 KB
testcase_29 AC 196 ms
105,252 KB
testcase_30 AC 206 ms
105,252 KB
testcase_31 AC 182 ms
105,252 KB
testcase_32 AC 207 ms
105,376 KB
testcase_33 AC 190 ms
105,248 KB
testcase_34 AC 195 ms
105,204 KB
testcase_35 AC 173 ms
105,128 KB
testcase_36 AC 193 ms
105,256 KB
testcase_37 AC 189 ms
105,252 KB
testcase_38 AC 174 ms
105,376 KB
testcase_39 AC 167 ms
105,380 KB
testcase_40 AC 167 ms
105,248 KB
testcase_41 AC 184 ms
105,252 KB
testcase_42 AC 186 ms
105,252 KB
testcase_43 AC 200 ms
105,124 KB
testcase_44 AC 360 ms
94,240 KB
testcase_45 AC 232 ms
27,808 KB
testcase_46 AC 82 ms
54,952 KB
testcase_47 AC 239 ms
40,992 KB
testcase_48 AC 191 ms
80,168 KB
testcase_49 AC 191 ms
93,092 KB
testcase_50 AC 351 ms
84,512 KB
testcase_51 AC 84 ms
29,760 KB
testcase_52 AC 80 ms
9,632 KB
testcase_53 AC 224 ms
30,240 KB
testcase_54 AC 357 ms
33,828 KB
testcase_55 AC 150 ms
20,004 KB
testcase_56 AC 295 ms
23,588 KB
testcase_57 AC 278 ms
76,652 KB
testcase_58 AC 203 ms
28,192 KB
testcase_59 AC 410 ms
96,036 KB
testcase_60 AC 245 ms
32,548 KB
testcase_61 AC 204 ms
42,400 KB
testcase_62 AC 480 ms
87,076 KB
testcase_63 AC 61 ms
21,668 KB
testcase_64 AC 399 ms
102,560 KB
testcase_65 AC 225 ms
70,564 KB
testcase_66 AC 131 ms
60,320 KB
testcase_67 AC 151 ms
87,080 KB
testcase_68 AC 167 ms
57,508 KB
testcase_69 AC 138 ms
56,228 KB
testcase_70 AC 294 ms
46,756 KB
testcase_71 AC 319 ms
83,108 KB
testcase_72 AC 206 ms
35,752 KB
testcase_73 AC 203 ms
40,356 KB
testcase_74 AC 136 ms
23,464 KB
testcase_75 AC 362 ms
53,796 KB
testcase_76 AC 259 ms
76,708 KB
testcase_77 AC 255 ms
87,716 KB
testcase_78 AC 106 ms
8,356 KB
testcase_79 AC 226 ms
90,788 KB
testcase_80 AC 167 ms
9,636 KB
testcase_81 AC 125 ms
16,936 KB
testcase_82 AC 261 ms
73,120 KB
testcase_83 AC 312 ms
37,540 KB
testcase_84 AC 502 ms
106,024 KB
testcase_85 AC 553 ms
106,020 KB
testcase_86 AC 502 ms
106,020 KB
testcase_87 AC 505 ms
106,020 KB
testcase_88 AC 514 ms
106,024 KB
testcase_89 AC 457 ms
106,016 KB
testcase_90 AC 543 ms
105,892 KB
testcase_91 AC 459 ms
106,024 KB
testcase_92 AC 490 ms
106,020 KB
testcase_93 AC 459 ms
106,148 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>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T, typename V>
void ndarray(vector<T>& vec, const V& val, int len) { vec.assign(len, val); }
template <typename T, typename V, typename... Args> void ndarray(vector<T>& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); }
template <typename T> bool chmax(T &m, const T q) { if (m < q) {m = q; return true;} else return false; }
template <typename T> bool chmin(T &m, const T q) { if (m > q) {m = q; return true;} else return false; }
template <typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }
template <typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }
template <typename T> vector<T> srtunq(vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <typename T> istream &operator>>(istream &is, vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
#if __cplusplus >= 201703L
template <typename... T> istream &operator>>(istream &is, tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <typename... T> ostream &operator<<(ostream &os, const tuple<T...> &tpl) { std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os; }
#endif
template <typename T> ostream &operator<<(ostream &os, const deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T, typename TH> ostream &operator<<(ostream &os, const unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; }
template <typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <typename TK, typename TV, typename TH> ostream &operator<<(ostream &os, const unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
#define dbg(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl
#else
#define dbg(x) {}
#endif

template <int mod>
struct ModInt
{
    using lint = long long;
    static int get_mod() { return mod; }
    static int get_primitive_root() {
        static int primitive_root = 0;
        if (!primitive_root) {
            primitive_root = [&](){
                std::set<int> fac;
                int v = mod - 1;
                for (lint i = 2; i * i <= v; i++) while (v % i == 0) fac.insert(i), v /= i;
                if (v > 1) fac.insert(v);
                for (int g = 1; g < mod; g++) {
                    bool ok = true;
                    for (auto i : fac) if (ModInt(g).power((mod - 1) / i) == 1) { ok = false; break; }
                    if (ok) return g;
                }
                return -1;
            }();
        }
        return primitive_root;
    }
    int val;
    constexpr ModInt() : val(0) {}
    constexpr ModInt &_setval(lint v) { val = (v >= mod ? v - mod : v); return *this; }
    constexpr ModInt(lint v) { _setval(v % mod + mod); }
    explicit operator bool() const { return val != 0; }
    constexpr ModInt operator+(const ModInt &x) const { return ModInt()._setval((lint)val + x.val); }
    constexpr ModInt operator-(const ModInt &x) const { return ModInt()._setval((lint)val - x.val + mod); }
    constexpr ModInt operator*(const ModInt &x) const { return ModInt()._setval((lint)val * x.val % mod); }
    constexpr ModInt operator/(const ModInt &x) const { return ModInt()._setval((lint)val * x.inv() % mod); }
    constexpr ModInt operator-() const { return ModInt()._setval(mod - val); }
    constexpr ModInt &operator+=(const ModInt &x) { return *this = *this + x; }
    constexpr ModInt &operator-=(const ModInt &x) { return *this = *this - x; }
    constexpr ModInt &operator*=(const ModInt &x) { return *this = *this * x; }
    constexpr ModInt &operator/=(const ModInt &x) { return *this = *this / x; }
    friend constexpr ModInt operator+(lint a, const ModInt &x) { return ModInt()._setval(a % mod + x.val); }
    friend constexpr ModInt operator-(lint a, const ModInt &x) { return ModInt()._setval(a % mod - x.val + mod); }
    friend constexpr ModInt operator*(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.val % mod); }
    friend constexpr ModInt operator/(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.inv() % mod); }
    constexpr bool operator==(const ModInt &x) const { return val == x.val; }
    constexpr bool operator!=(const ModInt &x) const { return val != x.val; }
    bool operator<(const ModInt &x) const { return val < x.val; }  // To use std::map<ModInt, T>
    friend std::istream &operator>>(std::istream &is, ModInt &x) { lint t; is >> t; x = ModInt(t); return is; }
    friend std::ostream &operator<<(std::ostream &os, const ModInt &x) { os << x.val;  return os; }
    constexpr lint power(lint n) const {
        lint ans = 1, tmp = this->val;
        while (n) {
            if (n & 1) ans = ans * tmp % mod;
            tmp = tmp * tmp % mod;
            n /= 2;
        }
        return ans;
    }
    constexpr ModInt pow(lint n) const {
        return power(n);
    }
    constexpr lint inv() const { return this->power(mod - 2); }
    constexpr ModInt operator^(lint n) const { return ModInt(this->power(n)); }
    constexpr ModInt &operator^=(lint n) { return *this = *this ^ n; }

    inline ModInt fac() const {
        static std::vector<ModInt> facs;
        int l0 = facs.size();
        if (l0 > this->val) return facs[this->val];

        facs.resize(this->val + 1);
        for (int i = l0; i <= this->val; i++) facs[i] = (i == 0 ? ModInt(1) : facs[i - 1] * ModInt(i));
        return facs[this->val];
    }

    ModInt doublefac() const {
        lint k = (this->val + 1) / 2;
        if (this->val & 1) return ModInt(k * 2).fac() / ModInt(2).power(k) / ModInt(k).fac();
        else return ModInt(k).fac() * ModInt(2).power(k);
    }

    ModInt nCr(const ModInt &r) const {
        if (this->val < r.val) return ModInt(0);
        return this->fac() / ((*this - r).fac() * r.fac());
    }

    ModInt sqrt() const {
        if (val == 0) return 0;
        if (mod == 2) return val;
        if (power((mod - 1) / 2) != 1) return 0;
        ModInt b = 1;
        while (b.power((mod - 1) / 2) == 1) b += 1;
        int e = 0, m = mod - 1;
        while (m % 2 == 0) m >>= 1, e++;
        ModInt x = power((m - 1) / 2), y = (*this) * x * x;
        x *= (*this);
        ModInt z = b.power(m);
        while (y != 1) {
            int j = 0;
            ModInt t = y;
            while (t != 1) j++, t *= t;
            z = z.power(1LL << (e - j - 1));
            x *= z, z *= z, y *= z;
            e = j;
        }
        return ModInt(std::min(x.val, mod - x.val));
    }
};
using mint = ModInt<1000000007>;

// Sieve of Eratosthenes
// (*this)[i] = (divisor of i, greater than 1)
// Example: [0, 1, 2, 3, 2, 5, 3, 7, 2, 3, 2, 11, ...]
// Complexity: Space O(MAXN), Time (construction) O(MAXNloglogMAXN)
struct SieveOfEratosthenes : std::vector<int>
{
    std::vector<int> primes;
    SieveOfEratosthenes(int MAXN) : std::vector<int>(MAXN + 1) {
        std::iota(begin(), end(), 0);
        for (int i = 2; i <= MAXN; i++) {
            if ((*this)[i] == i) {
                primes.push_back(i);
                for (int j = i; j <= MAXN; j += i) (*this)[j] = i;
            }
        }
    }
    using T = long long int;
    // Prime factorization for x <= MAXN^2
    // Complexity: O(log x)          (x <= MAXN)
    //             O(MAXN / logMAXN) (MAXN < x <= MAXN^2)
    std::map<T, int> Factorize(T x) {
        assert(x <= 1LL * (int(size()) - 1) * (int(size()) - 1));
        std::map<T, int> ret;
        if (x < int(size())) {
            while (x > 1) {
                ret[(*this)[x]]++;
                x /= (*this)[x];
            }
        }
        else {
            for (auto p : primes) {
                while (!(x % p)) x /= p, ret[p]++;
                if (x == 1) break;
            }
            if (x > 1) ret[x]++;
        }
        return ret;
    }
    std::vector<T> Divisors(T x) {
        std::vector<T> ret{1};
        for (auto p : Factorize(x)) {
            int n = ret.size();
            for (int i = 0; i < n; i++) {
                for (T a = 1, d = 1; d <= p.second; d++) {
                    a *= p.first;
                    ret.push_back(ret[i] * a);
                }
            }
        }
        return ret; // Not sorted
    }
    // Moebius function Table
    // return: [0=>0, 1=>1, 2=>-1, 3=>-1, 4=>0, 5=>-1, 6=>1, 7=>-1, 8=>0, ...]
    std::vector<int> GenerateMoebiusFunctionTable() {
        std::vector<int> ret(size());
        for (int i = 1; i < int(size()); i++) {
            if (i == 1) ret[i] = 1;
            else if ((i / (*this)[i]) % (*this)[i] == 0) ret[i] = 0;
            else ret[i] = -ret[i / (*this)[i]];
        }
        return ret;
    }
};
SieveOfEratosthenes sieve(1000000);

// Integer convolution for arbitrary mod
// with NTT (and Garner's algorithm) for ModInt / ModIntRuntime class.
// We skip Garner's algorithm if `skip_garner` is true or mod is in `nttprimes`.
// input: a (size: n), b (size: m)
// return: vector (size: n + m - 1)
template <typename MODINT>
std::vector<MODINT> nttconv(std::vector<MODINT> a, std::vector<MODINT> b, bool skip_garner = false);

constexpr int nttprimes[3] = {998244353, 167772161, 469762049};

// Integer FFT (Fast Fourier Transform) for ModInt class
// (Also known as Number Theoretic Transform, NTT)
// is_inverse: inverse transform
// ** Input size must be 2^n **
template <typename MODINT>
void ntt(std::vector<MODINT> &a, bool is_inverse = false)
{
    int n = a.size();
    if (n == 1) return;
    static const int mod = MODINT::get_mod();
    static const MODINT root = MODINT::get_primitive_root();
    assert(__builtin_popcount(n) == 1 and (mod - 1) % n == 0);

    static std::vector<MODINT> w{1}, iw{1};
    for (int m = w.size(); m < n / 2; m *= 2) {
        MODINT dw = root.power((mod - 1) / (4 * m)), dwinv = 1 / dw;
        w.resize(m * 2), iw.resize(m * 2);
        for (int i = 0; i < m; i++) w[m + i] = w[i] * dw, iw[m + i] = iw[i] * dwinv;
    }

    if (!is_inverse) {
        for (int m = n; m >>= 1;) {
            for (int s = 0, k = 0; s < n; s += 2 * m, k++) {
                for (int i = s; i < s + m; i++) {
                    MODINT x = a[i], y = a[i + m] * w[k];
                    a[i] = x + y, a[i + m] = x - y;
                }
            }
        }
    }
    else {
        for (int m = 1; m < n; m *= 2) {
            for (int s = 0, k = 0; s < n; s += 2 * m, k++) {
                for (int i = s; i < s + m; i++) {
                    MODINT x = a[i], y = a[i + m];
                    a[i] = x + y, a[i + m] = (x - y) * iw[k];
                }
            }
        }
        int n_inv = MODINT(n).inv();
        for (auto &v : a) v *= n_inv;
    }
}
template <int MOD>
std::vector<ModInt<MOD>> nttconv_(const std::vector<int> &a, const std::vector<int> &b) {
    int sz = a.size();
    assert(a.size() == b.size() and __builtin_popcount(sz) == 1);
    std::vector<ModInt<MOD>> ap(sz), bp(sz);
    for (int i = 0; i < sz; i++) ap[i] = a[i], bp[i] = b[i];
    ntt(ap, false);
    if (a == b) bp = ap;
    else ntt(bp, false);
    for (int i = 0; i < sz; i++) ap[i] *= bp[i];
    ntt(ap, true);
    return ap;
}
long long garner_ntt_(int r0, int r1, int r2, int mod)
{
    using mint2 = ModInt<nttprimes[2]>;
    static const long long m01 = 1LL * nttprimes[0] * nttprimes[1];
    static const long long m0_inv_m1 = ModInt<nttprimes[1]>(nttprimes[0]).inv();
    static const long long m01_inv_m2 = mint2(m01).inv();

    int v1 = (m0_inv_m1 * (r1 + nttprimes[1] - r0)) % nttprimes[1];
    auto v2 = (mint2(r2) - r0 - mint2(nttprimes[0]) * v1) * m01_inv_m2;
    return (r0 + 1LL * nttprimes[0] * v1 + m01 % mod * v2.val) % mod;
}
template <typename MODINT>
std::vector<MODINT> nttconv(std::vector<MODINT> a, std::vector<MODINT> b, bool skip_garner)
{
    int sz = 1, n = a.size(), m = b.size();
    while (sz < n + m) sz <<= 1;
    if (sz <= 16) {
        std::vector<MODINT> ret(n + m - 1);
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) ret[i + j] += a[i] * b[j];
        }
        return ret;
    }
    int mod = MODINT::get_mod();
    if (skip_garner or std::find(std::begin(nttprimes), std::end(nttprimes), mod) != std::end(nttprimes))
    {
        a.resize(sz), b.resize(sz);
        if (a == b) { ntt(a, false); b = a; }
        else ntt(a, false), ntt(b, false);
        for (int i = 0; i < sz; i++) a[i] *= b[i];
        ntt(a, true);
        a.resize(n + m - 1);
    }
    else {
        std::vector<int> ai(sz), bi(sz);
        for (int i = 0; i < n; i++) ai[i] = a[i].val;
        for (int i = 0; i < m; i++) bi[i] = b[i].val;
        auto ntt0 = nttconv_<nttprimes[0]>(ai, bi);
        auto ntt1 = nttconv_<nttprimes[1]>(ai, bi);
        auto ntt2 = nttconv_<nttprimes[2]>(ai, bi);
        a.resize(n + m - 1);
        for (int i = 0; i < n + m - 1; i++) {
            a[i] = garner_ntt_(ntt0[i].val, ntt1[i].val, ntt2[i].val, mod);
        }
    }
    return a;
}

// Calculate [x^N](num(x) / den(x))
// Coplexity: O(LlgLlgN) ( L = size(num) + size(den) )
template <typename Tp>
Tp coefficient_of_rational_function(long long N, std::vector<Tp> num, std::vector<Tp> den)
{
    assert(N >= 0);
    while (den.size() and den.back() == 0) den.pop_back();
    assert(den.size());
    int h = 0;
    while (den[h] == 0) h++;
    N += h;
    den.erase(den.begin(), den.begin() + h);

    if (den.size() == 1)
    {
        assert(N < int(num.size()));
        return num[N] / den[0];
    }

    while (N)
    {
        std::vector<Tp> g = den;
        for (size_t i = 1; i < g.size(); i += 2)
        {
            g[i] = -g[i];
        }
        auto conv_num_g = nttconv(num, g);
        num.resize((conv_num_g.size() + 1 - (N & 1)) / 2);
        for (size_t i = 0; i < num.size(); i++)
        {
            num[i] = conv_num_g[i * 2 + (N & 1)];
        }
        auto conv_den_g = nttconv(den, g);
        for (size_t i = 0; i < den.size(); i++)
        {
            den[i] = conv_den_g[i * 2];
        }
        N >>= 1;
    }
    return num[0] / den[0];
}

int main()
{
    lint N, M;
    cin >> N >> M;
    vector<mint> A(N + 1);
    FOR(i, 2, N + 1) cin >> A[i];
    vector<lint> nd = sieve.Divisors(N);
    mint ret = 0;

    auto add = [&](int x, int y) -> void {
        if (y == N or x >= y or x == 1) return;
        // 1 -> x -> y -> N
        mint a = -A[x] + 1, b = -A[y] + 1, c = -A[N] + 1;
        vector<mint> den { 1, a + b + c, a * b + b * c + c * a, a * b * c };
        mint tmp = coefficient_of_rational_function<mint>(M - 3, {1}, den);
        ret += tmp;
    };

    for (auto x : nd) for (auto y : nd) if (y > x and y % x == 0)
    {
        add(x, y);
    }

    cout << ret << '\n';

    int Q;
    cin >> Q;
    vector<set<int>> prv(N + 1), nxt(N + 1);
    // for (auto x : nd) for (auto y : nd) if (y > x and y % x == 0) prv[y].insert(x), nxt[x].insert(y);

    while (Q--) {
        int x, y;
        cin >> x >> y;
        prv[y].insert(x), nxt[x].insert(y);
        if (y == N) {
            for (auto xx : prv[x]) {
                add(xx, x);
            }
            for (auto xx : sieve.Divisors(x)) {
                add(xx, x);
            }
        } else {
            if (prv[N].count(y) or N % y == 0) {
                add(x, y);
            }
        }
        cout << ret << '\n';
    }
}
0