結果

問題 No.1783 Remix Sum
ユーザー 👑 hitonanodehitonanode
提出日時 2021-12-12 04:50:41
言語 C++23
(gcc 12.3.0 + boost 1.83.0)
結果
TLE  
(最新)
AC  
(最初)
実行時間 -
コード長 16,333 bytes
コンパイル時間 6,326 ms
コンパイル使用メモリ 256,364 KB
実行使用メモリ 21,692 KB
最終ジャッジ日時 2023-09-27 19:25:25
合計ジャッジ時間 47,158 ms
ジャッジサーバーID
（参考情報） 		judge12 / judge14
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 1 ms
4,352 KB
testcase_01 AC 2 ms
4,356 KB
testcase_02 AC 2 ms
4,384 KB
testcase_03 AC 2 ms
4,356 KB
testcase_04 AC 87 ms
4,356 KB
testcase_05 AC 87 ms
4,352 KB
testcase_06 AC 138 ms
4,356 KB
testcase_07 AC 453 ms
5,400 KB
testcase_08 AC 151 ms
4,356 KB
testcase_09 AC 151 ms
4,352 KB
testcase_10 AC 87 ms
4,356 KB
testcase_11 AC 87 ms
4,356 KB
testcase_12 AC 555 ms
5,128 KB
testcase_13 AC 250 ms
5,088 KB
testcase_14 AC 130 ms
4,356 KB
testcase_15 AC 385 ms
17,180 KB
testcase_16 AC 462 ms
5,168 KB
testcase_17 AC 565 ms
5,296 KB
testcase_18 AC 86 ms
4,352 KB
testcase_19 AC 178 ms
4,352 KB
testcase_20 AC 198 ms
4,352 KB
testcase_21 AC 176 ms
4,352 KB
testcase_22 AC 179 ms
4,356 KB
testcase_23 AC 235 ms
4,356 KB
testcase_24 AC 122 ms
4,352 KB
testcase_25 AC 139 ms
4,352 KB
testcase_26 AC 603 ms
5,052 KB
testcase_27 AC 138 ms
4,356 KB
testcase_28 AC 107 ms
4,352 KB
testcase_29 AC 209 ms
4,352 KB
testcase_30 AC 197 ms
4,356 KB
testcase_31 AC 176 ms
4,352 KB
testcase_32 AC 676 ms
17,404 KB
testcase_33 AC 198 ms
4,356 KB
testcase_34 AC 128 ms
4,352 KB
testcase_35 AC 264 ms
5,132 KB
testcase_36 AC 288 ms
17,180 KB
testcase_37 AC 289 ms
17,152 KB
testcase_38 AC 263 ms
5,236 KB
testcase_39 AC 127 ms
4,356 KB
testcase_40 AC 99 ms
4,352 KB
testcase_41 AC 128 ms
4,356 KB
testcase_42 AC 127 ms
4,360 KB
testcase_43 AC 264 ms
5,172 KB
testcase_44 AC 135 ms
4,356 KB
testcase_45 AC 1,234 ms
4,356 KB
testcase_46 AC 2,174 ms
4,352 KB
testcase_47 AC 3,540 ms
4,352 KB
testcase_48 AC 9,562 ms
5,124 KB
testcase_49 TLE -
testcase_50 -- -
testcase_51 -- -
testcase_52 -- -
testcase_53 -- -
testcase_54 -- -
testcase_55 -- -
testcase_56 -- -
testcase_57 -- -
testcase_58 -- -
testcase_59 -- -
testcase_60 -- -
testcase_61 -- -
testcase_62 -- -
testcase_63 -- -
testcase_64 -- -
testcase_65 -- -
testcase_66 -- -
testcase_67 -- -
testcase_68 -- -
testcase_69 -- -
testcase_70 -- -
testcase_71 -- -
testcase_72 -- -
testcase_73 -- -
testcase_74 -- -
testcase_75 -- -
testcase_76 -- -
testcase_77 -- -
testcase_78 -- -
testcase_79 -- -
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 # 

// #pragma GCC optimize("O3,unroll-loops")
#pragma GCC optimize("Ofast")
#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
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) { return m < q ? (m = q, true) : false; }
template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
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> sort_unique(vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <typename T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }
template <typename T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }
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; }
template <typename T, size_t sz> ostream &operator<<(ostream &os, const array<T, sz> &arr) { os << '['; for (auto v : arr) 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) { os << '('; 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
const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";
#define dbg(x) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl
#define dbgif(cond, x) ((cond) ? cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl : cerr)
#else
#define dbg(x) (x)
#define dbgif(cond, x) 0
#endif

template <typename T> T rd_integer() {
    T ret = 0;
    bool minus = false;

    char c = getchar_unlocked();
    while (!isdigit(c)) minus |= (c == '-'), c = getchar_unlocked();
    while (isdigit(c)) ret = (ret << 1) + (ret << 3) + (c ^ 48), c = getchar_unlocked();

    return minus ? -ret : ret;
}
int rdi() { return rd_integer<int>(); }
long long rdll() { return rd_integer<long long>(); }

template <typename T> void wt_integer(T x, char delim) {
    if (x == 0) {
        putchar('0'), putchar(delim);
        return;
    }
    if (x < 0) putchar('-'), x = -x;
    static char cache[20];
    char *head = cache;
    while (x) *head = '0' + x % 10, head++, x /= 10;
    while (head != cache) putchar(*(--head));
    putchar(delim);
}


constexpr int md = (115 << 20) + 1;

#include <atcoder/modint>
using mint = atcoder::static_modint<md>;
#include <atcoder/convolution>

// Multivariate convolution (Linear, overflow cutoff)
// Complexity: (kN \log N + k^2 N)$
// Note that the vectors store the infomation in **column-major order**
// Implementation idea: https://rushcheyo.blog.uoj.ac/blog/6547
// Details of my implementation: https://hitonanode.github.io/cplib-cpp/convolution/multivar_ntt.hpp
template <typename MODINT> struct multivar_ntt {
    int K, N, fftlen;
    std::vector<int> dim;
    std::vector<char> chi;
    MODINT invfftlen;
    vector<MODINT> g;
    std::vector<std::vector<MODINT>> gex, hex;
    vector<vector<int>> chi2i;

private:
    void _initialize(const std::vector<int> &dim_) {
        dim = dim_;
        K = dim_.size();
        N = std::accumulate(dim_.begin(), dim_.end(), 1, [&](int l, int r) { return l * r; });
        fftlen = 1;
        while (fftlen < N * 2) fftlen <<= 1;
        invfftlen = MODINT(fftlen).inv();

        chi.resize(fftlen);
        int t = 1;
        for (auto d : dim_) {
            t *= d;
            for (int s = t; s < fftlen; s += t) chi[s] += 1;
        }
        for (int i = 0; i + 1 < fftlen; i++) {
            chi[i + 1] += chi[i];
            if (chi[i + 1] >= K) chi[i + 1] -= K;
        }
        chi2i.assign(K, {});
        if (K) {
            for (int i = 0; i < N; ++i) chi2i[chi[i]].push_back(i);
        }
    }

public:
    void operator()(std::vector<MODINT> &f) {
        assert(int(f.size()) == N);
        assert(int(g.size()) == N);
        if (dim.empty()) {
            f[0] *= g[0];
            return;
        }
        hex.assign(K, std::vector<MODINT>(fftlen));

        vector<MODINT> fexdf(fftlen);
        for (int df = 0; df < K; ++df) {
            fexdf.assign(fftlen, 0);
            for (auto i : chi2i[df]) {
                fexdf[i] = f[i];
            }
            atcoder::internal::butterfly(fexdf);
            for (int dg = 0; dg < K; dg++) {
                int dh = (df + dg < K) ? df + dg : df + dg - K;
                for (int i = 0; i < fftlen; i++) hex[dh][i] += fexdf[i] * gex[dg][i];
            }
        }
        for (auto &vec : hex) atcoder::internal::butterfly_inv(vec);
        for (int i = 0; i < N; i++) f[i] = hex[chi[i]][i] * invfftlen;
    }

    multivar_ntt(const std::vector<int> &dim_) { _initialize(dim_); }
    void set_g(const vector<MODINT> &g_) {
        g = g_;
        gex.assign(K, vector<MODINT>(fftlen));
        if (dim.empty()) return;
        for (int i = 0; i < N; i++) gex[chi[i]][i] = g[i];
        for (auto &vec : gex) atcoder::internal::butterfly(vec);
    }
    void double_g() {
        if (!K) {
            g[0] *= g[0];
            return;
        }
        vector<MODINT> ftmp(K), gtmp(K * 2);
        for (int i = 0; i < fftlen; ++i) {
            gtmp.assign(K * 2, 0);
            for (int k = 0; k < K; ++k) ftmp[k] = gex[k][i], gtmp[k * 2] = ftmp[k] * ftmp[k];
            for (int k = 0; k < K; ++k) {
                for (int l = 0; l < k; ++l) gtmp[k + l] += ftmp[k] * ftmp[l] * 2;
            }
            for (int k = 0; k < K; ++k) gex[k][i] = gtmp[k] + gtmp[k + K];
        }
        for (auto &vec : gex) atcoder::internal::butterfly_inv(vec);
        for (int i = 0; i < N; ++i) g[i] = gex[chi[i]][i] * invfftlen;
        gex.assign(K, vector<MODINT>(fftlen));
        for (int i = 0; i < N; i++) gex[chi[i]][i] = g[i];
        for (auto &vec : gex) atcoder::internal::butterfly(vec);
    }
};

void ntt(vector<mint> &vec, bool tf) {
    if (tf) {
        atcoder::internal::butterfly_inv(vec);
        mint szinv = mint(vec.size()).inv();
        for (auto &x : vec) x *= szinv;
    } else {
        atcoder::internal::butterfly(vec);
    }
}

template <typename ModInt> std::vector<ModInt> inv_of_poly_mod_monomial(const std::vector<ModInt> &f, int l) {
    assert(l > 0);
    if (f.empty()) return {};
    const ModInt ret0 = f[0].inv();
    if (ret0 * f[0] != ModInt(1)) return {};
    std::vector<ModInt> ret{ret0};
    unsigned sz = 1;
    while (ret.size() < l) {
        std::vector<ModInt> h0(sz * 2), h1(sz * 2), a(sz * 2);
        std::copy(ret.begin(), ret.end(), a.begin());
        std::copy(f.begin(), f.begin() + std::min<unsigned>(sz, f.size()), h0.begin());
        if (int(f.size()) >= sz) std::copy(f.begin() + sz, f.begin() + std::min<unsigned>(sz * 2, f.size()), h1.begin());
        ntt(a, false);
        ntt(h0, false);
        ntt(h1, false);
        for (unsigned i = 0; i < sz * 2; i++) h0[i] *= a[i];
        for (unsigned i = 0; i < sz * 2; i++) h1[i] *= a[i];
        ntt(h0, true);
        ntt(h1, true);
        for (unsigned i = 0; i < sz; i++) h1[i] += h0[i + sz];
        std::fill(h1.begin() + sz, h1.end(), 0);
        ntt(h1, false);
        for (unsigned i = 0; i < sz * 2; i++) h1[i] *= a[i];
        ntt(h1, true);
        ret.resize(std::min<unsigned>(sz * 2, l));
        for (unsigned i = sz; i < ret.size(); i++) ret[i] = -h1[i - sz];
        sz *= 2;
    }
    return ret;
}

// https://uoj.ac/submission/460059
using fps = vector<mint>;
fps multi_inv(const fps &f, const vector<int> &base) {
    assert(!f.empty() && f[0] != 0);

    int n = f.size(), s = base.size(), W = 1;
    while (W < 2 * n) W *= 2;

    vector<int> chi(W);
    for (int i = 0; i < W; i++) {
        int x = i;
        for (int j = 0; j < s - 1; j++) chi[i] += (x /= base[j]);
        chi[i] %= s;
    }

    auto hadamard_prod = [&s](vector<fps> &F, vector<fps> &G, vector<fps> &H) {
        fps a(s);
        for (int k = 0; k < (int)F[0].size(); k++) {
            fill(begin(a), end(a), typename fps::value_type());
            for (int i = 0; i < s; i++)
                for (int j = 0; j < s; j++) { a[i + j - (i + j >= s ? s : 0)] += F[i][k] * G[j][k]; }
            for (int i = 0; i < s; i++) H[i][k] = a[i];
        }
    };

    fps g(W);
    g[0] = f[0].inv();
    for (int d = 1; d < n; d *= 2) {
        vector<fps> F(s, fps(2 * d)), G(s, fps(2 * d)), H(s, fps(2 * d));
        for (int j = 0; j < min((int)f.size(), 2 * d); j++) F[chi[j]][j] = f[j];
        for (int j = 0; j < d; j++) G[chi[j]][j] = g[j];
        for (auto &x : F) ntt(x, false);
        for (auto &x : G) ntt(x, false);
        hadamard_prod(F, G, H);
        for (auto &x : H) ntt(x, true);
        for (auto &x : F) fill(begin(x), end(x), typename fps::value_type());
        for (int j = d; j < 2 * d; j++) F[chi[j]][j] = H[chi[j]][j];
        for (auto &x : F) ntt(x, false);
        hadamard_prod(F, G, H);
        for (auto &x : H) ntt(x, true);
        for (int j = d; j < 2 * d; j++) g[j] = -H[chi[j]][j];
    }
    return {begin(g), begin(g) + n};
}

int main() {
    auto START = std::chrono::system_clock::now();
    
    constexpr int E = 10;
    const mint r10 = 9142366;
    int N = rdi(), K = rdi();
    lint M = rdll();
    int T = rdi();
    // M %= mint::mod() - 1;
    int K10 = 1;
    REP(t, K) K10 *= 10;

    vector<int> diminfo(T, E);  // T 桁切捨，K - T 桁周期
    multivar_ntt<mint> mntt(diminfo);


    vector nttmat(E, vector<mint>(E));
    REP(i, nttmat.size()) REP(j, nttmat[i].size()) nttmat[i][j] = r10.pow(i * j);
    auto inttmat = nttmat;
    for (auto &vec : inttmat) for (auto &x : vec) x = x.inv() / mint(10);

    auto ntt10 = [&](const array<mint, 10> &v) {
        array<mint, 10> ret;
        ret.fill(0);
        REP(i, E) REP(j, E) ret[i] += nttmat[i][j] * v[j];
        return ret;
    };

    auto intt10 = [&](const array<mint, 10> &v) {
        array<mint, 10> ret;
        ret.fill(0);
        REP(i, E) REP(j, E) ret[i] += inttmat[i][j] * v[j];
        return ret;
    };

    auto circular_ntt = [&](vector<mint> &f) {
        for (int di = mntt.N; di < K10; di *= 10) {
            for (int l = 0; l < K10; l += di * 10) {
                for (int i = l; i < l + di; ++i) {
                    // [i, i + di, i + 2di, ..., i + 9di] を NTT
                    auto impose_ntt = [&](vector<mint> &v) {
                        static array<mint, 10> ntttmp;
                        ntttmp.fill(0);
                        REP(k, E) ntttmp[k] = v[i + k * di];
                        ntttmp = ntt10(ntttmp);
                        REP(k, E) v[i + k * di] = ntttmp[k];
                    };
                    impose_ntt(f);
                }
            }
        }
    };
    auto circular_intt = [&](vector<mint> &g) {
        for (int di = mntt.N; di < K10; di *= 10) {
            for (int l = 0; l < K10; l += di * 10) {
                for (int i = l; i < l + di; ++i) {
                    // [i, i + di, i + 2di, ..., i + 9di] を NTT
                    auto impose_intt = [&](vector<mint> &v) {
                        static array<mint, 10> ntttmp;
                        REP(k, E) ntttmp[k] = v[i + k * di];
                        ntttmp = intt10(ntttmp);
                        REP(k, E) v[i + k * di] = ntttmp[k];
                    };
                    impose_intt(g);
                }
            }
        }
    };

    vector<mint> dp(K10), trans(K10);
    dp[0] = 1;
    while (N--) trans[rdi()] += 1;

    circular_ntt(dp);
    circular_ntt(trans);

    // 寝たい
    for (int l = 0; l < K10; l += mntt.N) {
        vector<mint> fsub(dp.begin() + l, dp.begin() + l + mntt.N);
        vector<mint> gsub(trans.begin() + l, trans.begin() + l + mntt.N);
        lint p = M;
        if (gsub[0] == 0) chmin(p, 100000LL);
        else if (T > 0 and __builtin_popcountll(p) > __builtin_popcountll(p + 1) + 15) {
            // すみません...
            dbg("red");
            p++;
            auto ginv = multi_inv(gsub, mntt.dim);
            mntt.set_g(ginv);
            mntt(fsub);
        }
        // Multivar pow なにもわからない......
        mntt.set_g(gsub);
        while (p) {
            if (p & 1) mntt(fsub);
            p /= 2;
            if (!p) break;
            mntt.double_g();
        }
        REP(i, fsub.size()) dp[i + l] = fsub[i];
    }

    circular_intt(dp);
// #ifndef HITONANODE_LOCAL
    for (auto x : dp) wt_integer(x.val(), '\n');
// #endif
    int64_t spent_ms = std::chrono::duration_cast<std::chrono::milliseconds>(std::chrono::system_clock::now() - START).count();
    dbg(spent_ms);
}
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