#655085 (C++17) No.1504 ヌメロニム

提出ソース

結果

問題	No.1504 ヌメロニム
ユーザー	hitonanode
提出日時	2021-05-07 21:51:43
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	351 ms / 2,000 ms
コード長	22,076 bytes
コンパイル時間	3,459 ms
コンパイル使用メモリ	184,048 KB
実行使用メモリ	63,924 KB
最終ジャッジ日時	2024-09-15 09:44:05
合計ジャッジ時間	12,768 ms
ジャッジサーバーID （参考情報）	judge2 / judge3

このコードへのチャレンジ
（要ログイン）

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	2 ms 5,376 KB
testcase_02	AC	2 ms 5,376 KB
testcase_03	AC	18 ms 13,620 KB
testcase_04	AC	3 ms 5,376 KB
testcase_05	AC	4 ms 5,376 KB
testcase_06	AC	2 ms 5,376 KB
testcase_07	AC	4 ms 5,376 KB
testcase_08	AC	2 ms 5,376 KB
testcase_09	AC	2 ms 5,376 KB
testcase_10	AC	2 ms 5,376 KB
testcase_11	AC	2 ms 5,376 KB
testcase_12	AC	2 ms 5,376 KB
testcase_13	AC	2 ms 5,376 KB
testcase_14	AC	2 ms 5,376 KB
testcase_15	AC	18 ms 13,640 KB
testcase_16	AC	18 ms 13,744 KB
testcase_17	AC	18 ms 13,636 KB
testcase_18	AC	18 ms 13,872 KB
testcase_19	AC	2 ms 5,376 KB
testcase_20	AC	55 ms 44,644 KB
testcase_21	AC	54 ms 44,492 KB
testcase_22	AC	55 ms 44,480 KB
testcase_23	AC	18 ms 13,624 KB
testcase_24	AC	322 ms 63,452 KB
testcase_25	AC	204 ms 59,576 KB
testcase_26	AC	351 ms 63,784 KB
testcase_27	AC	212 ms 60,484 KB
testcase_28	AC	214 ms 60,572 KB
testcase_29	AC	326 ms 63,572 KB
testcase_30	AC	338 ms 63,692 KB
testcase_31	AC	204 ms 59,472 KB
testcase_32	AC	216 ms 60,360 KB
testcase_33	AC	322 ms 63,612 KB
testcase_34	AC	89 ms 48,116 KB
testcase_35	AC	85 ms 47,364 KB
testcase_36	AC	189 ms 56,668 KB
testcase_37	AC	70 ms 46,016 KB
testcase_38	AC	331 ms 63,672 KB
testcase_39	AC	333 ms 63,676 KB
testcase_40	AC	328 ms 63,796 KB
testcase_41	AC	327 ms 63,924 KB
testcase_42	AC	328 ms 63,672 KB
testcase_43	AC	331 ms 63,800 KB
testcase_44	AC	329 ms 63,668 KB
testcase_45	AC	329 ms 63,796 KB
testcase_46	AC	329 ms 63,800 KB
testcase_47	AC	332 ms 63,804 KB
testcase_48	AC	206 ms 60,484 KB
testcase_49	AC	202 ms 58,776 KB
testcase_50	AC	54 ms 44,628 KB
testcase_51	AC	53 ms 44,476 KB
testcase_52	AC	18 ms 13,768 KB
testcase_53	AC	53 ms 44,364 KB
testcase_54	AC	18 ms 13,760 KB
testcase_55	AC	86 ms 47,320 KB
testcase_56	AC	18 ms 13,876 KB
testcase_57	AC	2 ms 5,376 KB
testcase_58	AC	17 ms 13,872 KB
testcase_59	AC	18 ms 13,752 KB
testcase_60	AC	18 ms 13,752 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

raw source code

#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 <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) { 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; }
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::lower_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) { 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
#else
#define dbg(x) (x)
#endif

template <int mod> struct ModInt {
#if __cplusplus >= 201402L
#define MDCONST constexpr
#else
#define MDCONST
#endif
    using lint = long long;
    MDCONST 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).pow((mod - 1) / i) == 1) {
                            ok = false;
                            break;
                        }
                    if (ok) return g;
                }
                return -1;
            }();
        }
        return primitive_root;
    }
    int val;
    MDCONST ModInt() : val(0) {}
    MDCONST ModInt &_setval(lint v) { return val = (v >= mod ? v - mod : v), *this; }
    MDCONST ModInt(lint v) { _setval(v % mod + mod); }
    MDCONST explicit operator bool() const { return val != 0; }
    MDCONST ModInt operator+(const ModInt &x) const { return ModInt()._setval((lint)val + x.val); }
    MDCONST ModInt operator-(const ModInt &x) const { return ModInt()._setval((lint)val - x.val + mod); }
    MDCONST ModInt operator*(const ModInt &x) const { return ModInt()._setval((lint)val * x.val % mod); }
    MDCONST ModInt operator/(const ModInt &x) const { return ModInt()._setval((lint)val * x.inv() % mod); }
    MDCONST ModInt operator-() const { return ModInt()._setval(mod - val); }
    MDCONST ModInt &operator+=(const ModInt &x) { return *this = *this + x; }
    MDCONST ModInt &operator-=(const ModInt &x) { return *this = *this - x; }
    MDCONST ModInt &operator*=(const ModInt &x) { return *this = *this * x; }
    MDCONST ModInt &operator/=(const ModInt &x) { return *this = *this / x; }
    friend MDCONST ModInt operator+(lint a, const ModInt &x) { return ModInt()._setval(a % mod + x.val); }
    friend MDCONST ModInt operator-(lint a, const ModInt &x) { return ModInt()._setval(a % mod - x.val + mod); }
    friend MDCONST ModInt operator*(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.val % mod); }
    friend MDCONST ModInt operator/(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.inv() % mod); }
    MDCONST bool operator==(const ModInt &x) const { return val == x.val; }
    MDCONST bool operator!=(const ModInt &x) const { return val != x.val; }
    MDCONST 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;
        return is >> t, x = ModInt(t), is;
    }
    MDCONST friend std::ostream &operator<<(std::ostream &os, const ModInt &x) { return os << x.val; }
    MDCONST ModInt pow(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;
    }

    static std::vector<long long> facs, invs;
    MDCONST static void _precalculation(int N) {
        int l0 = facs.size();
        if (N <= l0) return;
        facs.resize(N), invs.resize(N);
        for (int i = l0; i < N; i++) facs[i] = facs[i - 1] * i % mod;
        long long facinv = ModInt(facs.back()).pow(mod - 2).val;
        for (int i = N - 1; i >= l0; i--) {
            invs[i] = facinv * facs[i - 1] % mod;
            facinv = facinv * i % mod;
        }
    }
    MDCONST lint inv() const {
        if (this->val < std::min(mod >> 1, 1 << 21)) {
            while (this->val >= int(facs.size())) _precalculation(facs.size() * 2);
            return invs[this->val];
        } else {
            return this->pow(mod - 2).val;
        }
    }
    MDCONST ModInt fac() const {
        while (this->val >= int(facs.size())) _precalculation(facs.size() * 2);
        return facs[this->val];
    }

    MDCONST ModInt doublefac() const {
        lint k = (this->val + 1) / 2;
        return (this->val & 1) ? ModInt(k * 2).fac() / (ModInt(2).pow(k) * ModInt(k).fac())
                               : ModInt(k).fac() * ModInt(2).pow(k);
    }
    MDCONST ModInt nCr(const ModInt &r) const {
        return (this->val < r.val) ? 0 : this->fac() / ((*this - r).fac() * r.fac());
    }

    ModInt sqrt() const {
        if (val == 0) return 0;
        if (mod == 2) return val;
        if (pow((mod - 1) / 2) != 1) return 0;
        ModInt b = 1;
        while (b.pow((mod - 1) / 2) == 1) b += 1;
        int e = 0, m = mod - 1;
        while (m % 2 == 0) m >>= 1, e++;
        ModInt x = pow((m - 1) / 2), y = (*this) * x * x;
        x *= (*this);
        ModInt z = b.pow(m);
        while (y != 1) {
            int j = 0;
            ModInt t = y;
            while (t != 1) j++, t *= t;
            z = z.pow(1LL << (e - j - 1));
            x *= z, z *= z, y *= z;
            e = j;
        }
        return ModInt(std::min(x.val, mod - x.val));
    }
};
template <int mod> std::vector<long long> ModInt<mod>::facs = {1};
template <int mod> std::vector<long long> ModInt<mod>::invs = {0};
using mint = ModInt<998244353>;

// 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.pow((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;
}

// Formal Power Series (形式的冪級数) based on ModInt<mod> / ModIntRuntime
// Reference: https://ei1333.github.io/luzhiled/snippets/math/formal-power-series.html
template <typename T> struct FormalPowerSeries : vector<T> {
    using vector<T>::vector;
    using P = FormalPowerSeries;

    void shrink() {
        while (this->size() and this->back() == T(0)) this->pop_back();
    }

    P operator+(const P &r) const { return P(*this) += r; }
    P operator+(const T &v) const { return P(*this) += v; }
    P operator-(const P &r) const { return P(*this) -= r; }
    P operator-(const T &v) const { return P(*this) -= v; }
    P operator*(const P &r) const { return P(*this) *= r; }
    P operator*(const T &v) const { return P(*this) *= v; }
    P operator/(const P &r) const { return P(*this) /= r; }
    P operator/(const T &v) const { return P(*this) /= v; }
    P operator%(const P &r) const { return P(*this) %= r; }

    P &operator+=(const P &r) {
        if (r.size() > this->size()) this->resize(r.size());
        for (int i = 0; i < (int)r.size(); i++) (*this)[i] += r[i];
        shrink();
        return *this;
    }
    P &operator+=(const T &v) {
        if (this->empty()) this->resize(1);
        (*this)[0] += v;
        shrink();
        return *this;
    }
    P &operator-=(const P &r) {
        if (r.size() > this->size()) this->resize(r.size());
        for (int i = 0; i < (int)r.size(); i++) (*this)[i] -= r[i];
        shrink();
        return *this;
    }
    P &operator-=(const T &v) {
        if (this->empty()) this->resize(1);
        (*this)[0] -= v;
        shrink();
        return *this;
    }
    P &operator*=(const T &v) {
        for (auto &x : (*this)) x *= v;
        shrink();
        return *this;
    }
    P &operator*=(const P &r) {
        if (this->empty() || r.empty())
            this->clear();
        else {
            auto ret = nttconv(*this, r);
            *this = P(ret.begin(), ret.end());
        }
        return *this;
    }
    P &operator%=(const P &r) {
        *this -= *this / r * r;
        shrink();
        return *this;
    }
    P operator-() const {
        P ret = *this;
        for (auto &v : ret) v = -v;
        return ret;
    }
    P &operator/=(const T &v) {
        assert(v != T(0));
        for (auto &x : (*this)) x /= v;
        return *this;
    }
    P &operator/=(const P &r) {
        if (this->size() < r.size()) {
            this->clear();
            return *this;
        }
        int n = (int)this->size() - r.size() + 1;
        return *this = (reversed().pre(n) * r.reversed().inv(n)).pre(n).reversed(n);
    }
    P pre(int sz) const {
        P ret(this->begin(), this->begin() + min((int)this->size(), sz));
        ret.shrink();
        return ret;
    }
    P operator>>(int sz) const {
        if ((int)this->size() <= sz) return {};
        return P(this->begin() + sz, this->end());
    }
    P operator<<(int sz) const {
        if (this->empty()) return {};
        P ret(*this);
        ret.insert(ret.begin(), sz, T(0));
        return ret;
    }

    P reversed(int deg = -1) const {
        assert(deg >= -1);
        P ret(*this);
        if (deg != -1) ret.resize(deg, T(0));
        reverse(ret.begin(), ret.end());
        ret.shrink();
        return ret;
    }

    P differential() const { // formal derivative (differential) of f.p.s.
        const int n = (int)this->size();
        P ret(max(0, n - 1));
        for (int i = 1; i < n; i++) ret[i - 1] = (*this)[i] * T(i);
        return ret;
    }

    P integral() const {
        const int n = (int)this->size();
        P ret(n + 1);
        ret[0] = T(0);
        for (int i = 0; i < n; i++) ret[i + 1] = (*this)[i] / T(i + 1);
        return ret;
    }

    P inv(int deg) const {
        assert(deg >= -1);
        assert(this->size() and ((*this)[0]) != T(0)); // Requirement: F(0) != 0
        const int n = this->size();
        if (deg == -1) deg = n;
        P ret({T(1) / (*this)[0]});
        for (int i = 1; i < deg; i <<= 1) { ret = (ret + ret - ret * ret * pre(i << 1)).pre(i << 1); }
        ret = ret.pre(deg);
        ret.shrink();
        return ret;
    }

    P log(int deg = -1) const {
        assert(deg >= -1);
        assert(this->size() and ((*this)[0]) == T(1)); // Requirement: F(0) = 1
        const int n = (int)this->size();
        if (deg == 0) return {};
        if (deg == -1) deg = n;
        return (this->differential() * this->inv(deg)).pre(deg - 1).integral();
    }

    P sqrt(int deg = -1) const {
        assert(deg >= -1);
        const int n = (int)this->size();
        if (deg == -1) deg = n;
        if (this->empty()) return {};
        if ((*this)[0] == T(0)) {
            for (int i = 1; i < n; i++)
                if ((*this)[i] != T(0)) {
                    if ((i & 1) or deg - i / 2 <= 0) return {};
                    return (*this >> i).sqrt(deg - i / 2) << (i / 2);
                }
            return {};
        }
        T sqrtf0 = (*this)[0].sqrt();
        if (sqrtf0 == T(0)) return {};

        P y = (*this) / (*this)[0], ret({T(1)});
        T inv2 = T(1) / T(2);
        for (int i = 1; i < deg; i <<= 1) { ret = (ret + y.pre(i << 1) * ret.inv(i << 1)) * inv2; }
        return ret.pre(deg) * sqrtf0;
    }

    P exp(int deg = -1) const {
        assert(deg >= -1);
        assert(this->empty() or ((*this)[0]) == T(0)); // Requirement: F(0) = 0
        const int n = (int)this->size();
        if (deg == -1) deg = n;
        P ret({T(1)});
        for (int i = 1; i < deg; i <<= 1) { ret = (ret * (pre(i << 1) + T(1) - ret.log(i << 1))).pre(i << 1); }
        return ret.pre(deg);
    }

    P pow(long long k, int deg = -1) const {
        assert(deg >= -1);
        const int n = (int)this->size();
        if (deg == -1) deg = n;
        for (int i = 0; i < n; i++) {
            if ((*this)[i] != T(0)) {
                T rev = T(1) / (*this)[i];
                P C = (*this) * rev, D(n - i);
                for (int j = i; j < n; j++) D[j - i] = C.coeff(j);
                D = (D.log(deg) * T(k)).exp(deg) * (*this)[i].pow(k);
                if (k * (i > 0) > deg or k * i > deg) return {};
                P E(deg);
                long long S = i * k;
                for (int j = 0; j + S < deg and j < (int)D.size(); j++) E[j + S] = D[j];
                E.shrink();
                return E;
            }
        }
        return *this;
    }

    // Calculate f(X + c) from f(X), O(NlogN)
    P shift(T c) const {
        const int n = (int)this->size();
        P ret = *this;
        for (int i = 0; i < n; i++) { ret[i] *= T(i).fac(); }
        reverse(ret.begin(), ret.end());
        P exp_cx(n, 1);
        for (int i = 1; i < n; i++) { exp_cx[i] = exp_cx[i - 1] * c / i; }
        ret = (ret * exp_cx), ret.resize(n);
        reverse(ret.begin(), ret.end());
        for (int i = 0; i < n; i++) { ret[i] /= T(i).fac(); }
        return ret;
    }

    T coeff(int i) const {
        if ((int)this->size() <= i or i < 0) return T(0);
        return (*this)[i];
    }

    T eval(T x) const {
        T ret = 0, w = 1;
        for (auto &v : *this) ret += w * v, w *= x;
        return ret;
    }
};

using fps = FormalPowerSeries<mint>;

int main() {
    int N;
    string S;
    cin >> N >> S;
    fps vi(N), vn(N);
    REP(i, N) (S[i] == 'i' ? vi[i] : vn[i]) = 1;
    reverse(ALL(vi));
    auto v = ((vi * vn) >> N).shift(1);
    int ret = 0;
    for (auto x : v) ret ^= x.val;
    cout << ret << '\n';
}

yukicoder

結果

テストケース

ソースコード