結果
問題 | No.1985 [Cherry 4th Tune] Early Summer Rain |
ユーザー | hitonanode |
提出日時 | 2022-06-17 23:05:02 |
言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 1,354 ms / 7,000 ms |
コード長 | 35,571 bytes |
コンパイル時間 | 4,114 ms |
コンパイル使用メモリ | 229,920 KB |
実行使用メモリ | 30,028 KB |
最終ジャッジ日時 | 2024-10-09 09:29:29 |
合計ジャッジ時間 | 32,700 ms |
ジャッジサーバーID (参考情報) |
judge1 / judge4 |
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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
5,248 KB |
testcase_01 | AC | 2 ms
5,248 KB |
testcase_02 | AC | 2 ms
5,248 KB |
testcase_03 | AC | 2 ms
5,248 KB |
testcase_04 | AC | 5 ms
5,248 KB |
testcase_05 | AC | 2 ms
5,248 KB |
testcase_06 | AC | 9 ms
6,816 KB |
testcase_07 | AC | 9 ms
6,820 KB |
testcase_08 | AC | 9 ms
5,248 KB |
testcase_09 | AC | 5 ms
5,248 KB |
testcase_10 | AC | 5 ms
5,248 KB |
testcase_11 | AC | 9 ms
5,248 KB |
testcase_12 | AC | 4 ms
5,248 KB |
testcase_13 | AC | 4 ms
5,248 KB |
testcase_14 | AC | 138 ms
5,376 KB |
testcase_15 | AC | 122 ms
10,256 KB |
testcase_16 | AC | 296 ms
17,252 KB |
testcase_17 | AC | 300 ms
7,220 KB |
testcase_18 | AC | 633 ms
10,516 KB |
testcase_19 | AC | 585 ms
29,876 KB |
testcase_20 | AC | 276 ms
16,764 KB |
testcase_21 | AC | 583 ms
29,656 KB |
testcase_22 | AC | 300 ms
7,384 KB |
testcase_23 | AC | 67 ms
5,248 KB |
testcase_24 | AC | 789 ms
29,772 KB |
testcase_25 | AC | 794 ms
29,900 KB |
testcase_26 | AC | 790 ms
29,772 KB |
testcase_27 | AC | 784 ms
29,908 KB |
testcase_28 | AC | 1,349 ms
18,256 KB |
testcase_29 | AC | 787 ms
29,900 KB |
testcase_30 | AC | 1,353 ms
18,252 KB |
testcase_31 | AC | 1,351 ms
18,380 KB |
testcase_32 | AC | 1,351 ms
18,256 KB |
testcase_33 | AC | 790 ms
29,900 KB |
testcase_34 | AC | 787 ms
29,900 KB |
testcase_35 | AC | 1,354 ms
18,384 KB |
testcase_36 | AC | 785 ms
29,900 KB |
testcase_37 | AC | 787 ms
30,028 KB |
testcase_38 | AC | 1,353 ms
18,512 KB |
testcase_39 | AC | 2 ms
5,248 KB |
testcase_40 | AC | 1,215 ms
18,060 KB |
testcase_41 | AC | 645 ms
29,460 KB |
testcase_42 | AC | 1,280 ms
19,184 KB |
testcase_43 | AC | 748 ms
29,572 KB |
testcase_44 | AC | 946 ms
17,516 KB |
testcase_45 | AC | 686 ms
17,516 KB |
testcase_46 | AC | 1,216 ms
18,188 KB |
testcase_47 | AC | 640 ms
29,364 KB |
ソースコード
#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 >= 201703Ltemplate <typename... T> istream &operator>>(istream &is, tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); returnis; }template <typename... T> ostream &operator<<(ostream &os, const tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }#endiftemplate <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_LOCALconst 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) 0#define dbgif(cond, x) 0#endif#include <iostream>#include <set>#include <vector>template <int md> struct ModInt {#if __cplusplus >= 201402L#define MDCONST constexpr#else#define MDCONST#endifusing lint = long long;MDCONST static int mod() { return md; }static int get_primitive_root() {static int primitive_root = 0;if (!primitive_root) {primitive_root = [&]() {std::set<int> fac;int v = md - 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 < md; g++) {bool ok = true;for (auto i : fac)if (ModInt(g).pow((md - 1) / i) == 1) {ok = false;break;}if (ok) return g;}return -1;}();}return primitive_root;}int val_;int val() const noexcept { return val_; }MDCONST ModInt() : val_(0) {}MDCONST ModInt &_setval(lint v) { return val_ = (v >= md ? v - md : v), *this; }MDCONST ModInt(lint v) { _setval(v % md + md); }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_ + md);}MDCONST ModInt operator*(const ModInt &x) const {return ModInt()._setval((lint)val_ * x.val_ % md);}MDCONST ModInt operator/(const ModInt &x) const {return ModInt()._setval((lint)val_ * x.inv().val() % md);}MDCONST ModInt operator-() const { return ModInt()._setval(md - 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 % md + x.val_);}friend MDCONST ModInt operator-(lint a, const ModInt &x) {return ModInt()._setval(a % md - x.val_ + md);}friend MDCONST ModInt operator*(lint a, const ModInt &x) {return ModInt()._setval(a % md * x.val_ % md);}friend MDCONST ModInt operator/(lint a, const ModInt &x) {return ModInt()._setval(a % md * x.inv().val() % md);}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 {ModInt ans = 1, tmp = *this;while (n) {if (n & 1) ans *= tmp;tmp *= tmp, n >>= 1;}return ans;}static std::vector<ModInt> facs, facinvs, invs;MDCONST static void _precalculation(int N) {int l0 = facs.size();if (N > md) N = md;if (N <= l0) return;facs.resize(N), facinvs.resize(N), invs.resize(N);for (int i = l0; i < N; i++) facs[i] = facs[i - 1] * i;facinvs[N - 1] = facs.back().pow(md - 2);for (int i = N - 2; i >= l0; i--) facinvs[i] = facinvs[i + 1] * (i + 1);for (int i = N - 1; i >= l0; i--) invs[i] = facinvs[i] * facs[i - 1];}MDCONST ModInt inv() const {if (this->val_ < std::min(md >> 1, 1 << 21)) {while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2);return invs[this->val_];} else {return this->pow(md - 2);}}MDCONST ModInt fac() const {while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2);return facs[this->val_];}MDCONST ModInt facinv() const {while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2);return facinvs[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).facinv() * r.facinv();}MDCONST ModInt nPr(const ModInt &r) const {return (this->val_ < r.val_) ? 0 : this->fac() * (*this - r).facinv();}ModInt sqrt() const {if (val_ == 0) return 0;if (md == 2) return val_;if (pow((md - 1) / 2) != 1) return 0;ModInt b = 1;while (b.pow((md - 1) / 2) == 1) b += 1;int e = 0, m = md - 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_, md - x.val_));}};template <int md> std::vector<ModInt<md>> ModInt<md>::facs = {1};template <int md> std::vector<ModInt<md>> ModInt<md>::facinvs = {1};template <int md> std::vector<ModInt<md>> ModInt<md>::invs = {0};using mint = ModInt<998244353>;#include <algorithm>#include <array>#include <cassert>#include <tuple>#include <vector>// 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);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::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().val();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;elsentt(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().val();static const long long m01_inv_m2 = mint2(m01).inv().val();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) {if (a.empty() or b.empty()) return {};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::mod();if (skip_garner orstd::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;}template <typename MODINT>std::vector<MODINT> nttconv(const std::vector<MODINT> &a, const std::vector<MODINT> &b) {return nttconv<MODINT>(a, b, false);}#include <algorithm>#include <cassert>#include <vector>// 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.htmltemplate <typename T> struct FormalPowerSeries : std::vector<T> {using std::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() + std::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(std::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) != 0const 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) = 1const 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) = 0const 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();std::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);std::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;}};#include <algorithm>#include <cassert>#include <cmath>#include <iterator>#include <type_traits>#include <utility>#include <vector>namespace matrix_ {struct has_id_method_impl {template <class T_> static auto check(T_ *) -> decltype(T_::id(), std::true_type());template <class T_> static auto check(...) -> std::false_type;};template <class T_> struct has_id : decltype(has_id_method_impl::check<T_>(nullptr)) {};} // namespace matrix_template <typename T> struct matrix {int H, W;std::vector<T> elem;typename std::vector<T>::iterator operator[](int i) { return elem.begin() + i * W; }inline T &at(int i, int j) { return elem[i * W + j]; }inline T get(int i, int j) const { return elem[i * W + j]; }int height() const { return H; }int width() const { return W; }std::vector<std::vector<T>> vecvec() const {std::vector<std::vector<T>> ret(H);for (int i = 0; i < H; i++) {std::copy(elem.begin() + i * W, elem.begin() + (i + 1) * W, std::back_inserter(ret[i]));}return ret;}operator std::vector<std::vector<T>>() const { return vecvec(); }matrix() = default;matrix(int H, int W) : H(H), W(W), elem(H * W) {}matrix(const std::vector<std::vector<T>> &d) : H(d.size()), W(d.size() ? d[0].size() : 0) {for (auto &raw : d) std::copy(raw.begin(), raw.end(), std::back_inserter(elem));}template <typename T2, typename std::enable_if<matrix_::has_id<T2>::value>::type * = nullptr>static T2 _T_id() {return T2::id();}template <typename T2, typename std::enable_if<!matrix_::has_id<T2>::value>::type * = nullptr>static T2 _T_id() {return T2(1);}static matrix Identity(int N) {matrix ret(N, N);for (int i = 0; i < N; i++) ret.at(i, i) = _T_id<T>();return ret;}matrix operator-() const {matrix ret(H, W);for (int i = 0; i < H * W; i++) ret.elem[i] = -elem[i];return ret;}matrix operator*(const T &v) const {matrix ret = *this;for (auto &x : ret.elem) x *= v;return ret;}matrix operator/(const T &v) const {matrix ret = *this;const T vinv = _T_id<T>() / v;for (auto &x : ret.elem) x *= vinv;return ret;}matrix operator+(const matrix &r) const {matrix ret = *this;for (int i = 0; i < H * W; i++) ret.elem[i] += r.elem[i];return ret;}matrix operator-(const matrix &r) const {matrix ret = *this;for (int i = 0; i < H * W; i++) ret.elem[i] -= r.elem[i];return ret;}matrix operator*(const matrix &r) const {matrix ret(H, r.W);for (int i = 0; i < H; i++) {for (int k = 0; k < W; k++) {for (int j = 0; j < r.W; j++) ret.at(i, j) += this->get(i, k) * r.get(k, j);}}return ret;}matrix &operator*=(const T &v) { return *this = *this * v; }matrix &operator/=(const T &v) { return *this = *this / v; }matrix &operator+=(const matrix &r) { return *this = *this + r; }matrix &operator-=(const matrix &r) { return *this = *this - r; }matrix &operator*=(const matrix &r) { return *this = *this * r; }bool operator==(const matrix &r) const { return H == r.H and W == r.W and elem == r.elem; }bool operator!=(const matrix &r) const { return H != r.H or W != r.W or elem != r.elem; }bool operator<(const matrix &r) const { return elem < r.elem; }matrix pow(int64_t n) const {matrix ret = Identity(H);bool ret_is_id = true;if (n == 0) return ret;for (int i = 63 - __builtin_clzll(n); i >= 0; i--) {if (!ret_is_id) ret *= ret;if ((n >> i) & 1) ret *= (*this), ret_is_id = false;}return ret;}std::vector<T> pow_vec(int64_t n, std::vector<T> vec) const {matrix x = *this;while (n) {if (n & 1) vec = x * vec;x *= x;n >>= 1;}return vec;};matrix transpose() const {matrix ret(W, H);for (int i = 0; i < H; i++) {for (int j = 0; j < W; j++) ret.at(j, i) = this->get(i, j);}return ret;}// Gauss-Jordan elimination// - Require inverse for every non-zero element// - Complexity: O(H^2 W)template <typename T2, typename std::enable_if<std::is_floating_point<T2>::value>::type * = nullptr>static int choose_pivot(const matrix<T2> &mtr, int h, int c) noexcept {int piv = -1;for (int j = h; j < mtr.H; j++) {if (mtr.get(j, c) and (piv < 0 or std::abs(mtr.get(j, c)) > std::abs(mtr.get(piv, c))))piv = j;}return piv;}template <typename T2, typename std::enable_if<!std::is_floating_point<T2>::value>::type * = nullptr>static int choose_pivot(const matrix<T2> &mtr, int h, int c) noexcept {for (int j = h; j < mtr.H; j++) {if (mtr.get(j, c) != T2()) return j;}return -1;}matrix gauss_jordan() const {int c = 0;matrix mtr(*this);std::vector<int> ws;ws.reserve(W);for (int h = 0; h < H; h++) {if (c == W) break;int piv = choose_pivot(mtr, h, c);if (piv == -1) {c++;h--;continue;}if (h != piv) {for (int w = 0; w < W; w++) {std::swap(mtr[piv][w], mtr[h][w]);mtr.at(piv, w) *= -_T_id<T>(); // To preserve sign of determinant}}ws.clear();for (int w = c; w < W; w++) {if (mtr.at(h, w) != T()) ws.emplace_back(w);}const T hcinv = _T_id<T>() / mtr.at(h, c);for (int hh = 0; hh < H; hh++)if (hh != h) {const T coeff = mtr.at(hh, c) * hcinv;for (auto w : ws) mtr.at(hh, w) -= mtr.at(h, w) * coeff;mtr.at(hh, c) = T();}c++;}return mtr;}int rank_of_gauss_jordan() const {for (int i = H * W - 1; i >= 0; i--) {if (elem[i] != 0) return i / W + 1;}return 0;}int rank() const { return gauss_jordan().rank_of_gauss_jordan(); }T determinant_of_upper_triangle() const {T ret = _T_id<T>();for (int i = 0; i < H; i++) ret *= get(i, i);return ret;}int inverse() {assert(H == W);std::vector<std::vector<T>> ret = Identity(H), tmp = *this;int rank = 0;for (int i = 0; i < H; i++) {int ti = i;while (ti < H and tmp[ti][i] == 0) ti++;if (ti == H) {continue;} else {rank++;}ret[i].swap(ret[ti]), tmp[i].swap(tmp[ti]);T inv = _T_id<T>() / tmp[i][i];for (int j = 0; j < W; j++) ret[i][j] *= inv;for (int j = i + 1; j < W; j++) tmp[i][j] *= inv;for (int h = 0; h < H; h++) {if (i == h) continue;const T c = -tmp[h][i];for (int j = 0; j < W; j++) ret[h][j] += ret[i][j] * c;for (int j = i + 1; j < W; j++) tmp[h][j] += tmp[i][j] * c;}}*this = ret;return rank;}friend std::vector<T> operator*(const matrix &m, const std::vector<T> &v) {assert(m.W == int(v.size()));std::vector<T> ret(m.H);for (int i = 0; i < m.H; i++) {for (int j = 0; j < m.W; j++) ret[i] += m.get(i, j) * v[j];}return ret;}friend std::vector<T> operator*(const std::vector<T> &v, const matrix &m) {assert(int(v.size()) == m.H);std::vector<T> ret(m.W);for (int i = 0; i < m.H; i++) {for (int j = 0; j < m.W; j++) ret[j] += v[i] * m.get(i, j);}return ret;}std::vector<T> prod(const std::vector<T> &v) const { return (*this) * v; }std::vector<T> prod_left(const std::vector<T> &v) const { return v * (*this); }template <class OStream> friend OStream &operator<<(OStream &os, const matrix &x) {os << "[(" << x.H << " * " << x.W << " matrix)";os << "\n[column sums: ";for (int j = 0; j < x.W; j++) {T s = 0;for (int i = 0; i < x.H; i++) s += x.get(i, j);os << s << ",";}os << "]";for (int i = 0; i < x.H; i++) {os << "\n[";for (int j = 0; j < x.W; j++) os << x.get(i, j) << ",";os << "]";}os << "]\n";return os;}template <class IStream> friend IStream &operator>>(IStream &is, matrix &x) {for (auto &v : x.elem) is >> v;return is;}};#include <utility>#include <vector>// Solve Ax = b for T = ModInt<PRIME>// - retval: {one of the solution, {freedoms}} (if solution exists)// {{}, {}} (otherwise)// Complexity:// - Yield one of the possible solutions: O(H^2 W) (H: # of eqs., W: # of variables)// - Enumerate all of the bases: O(HW(H + W))template <typename T>std::pair<std::vector<T>, std::vector<std::vector<T>>>system_of_linear_equations(matrix<T> A, std::vector<T> b) {int H = A.height(), W = A.width();matrix<T> M(H, W + 1);for (int i = 0; i < H; i++) {for (int j = 0; j < W; j++) M[i][j] = A[i][j];M[i][W] = b[i];}M = M.gauss_jordan();std::vector<int> ss(W, -1);for (int i = 0; i < H; i++) {int j = 0;while (j <= W and M[i][j] == 0) j++;if (j == W) { // No solutionreturn {{}, {}};}if (j < W) ss[j] = i;}std::vector<T> x(W);std::vector<std::vector<T>> D;for (int j = 0; j < W; j++) {if (ss[j] == -1) {std::vector<T> d(W);d[j] = 1;for (int jj = 0; jj < j; jj++) {if (ss[jj] != -1) d[jj] = -M[ss[jj]][j] / M[ss[jj]][jj];}D.emplace_back(d);} elsex[j] = M[ss[j]][W] / M[ss[j]][j];}return std::make_pair(x, D);}using fps = FormalPowerSeries<mint>;int main() {int N, K;cin >> N >> K;vector<mint> E(N);cin >> E;dbg(E);// auto Einv = E.inv(N + 1);fps f(N + 1);REP(i, N) f[i + 1] = E[i];int cur = 0;while (E[cur] == 0) ++cur;fps fup(E.begin() + cur, E.end());dbg(fup);auto diff_of_log_f = f.differential() * fup.inv(N + 1);dbg(diff_of_log_f);diff_of_log_f.resize(cur + N + 1);diff_of_log_f.erase(diff_of_log_f.begin(), diff_of_log_f.begin() + cur);dbg(diff_of_log_f);fps g(N + 1);g[0] = 1;g -= f;g = g.inv(N + 1);dbg(f);dbg(g);fps ret(N + 1);const int D = 22;vector<mint> coe;if (K >= 0) {matrix<mint> mat(D, D);REP(e, D) mat[0][e] = 1;FOR(d, 1, D) REP(e, D) {mat[d][e] = mat[d - 1][e];if (e) mat[d][e] += mat[d][e - 1];}mat = mat.transpose();dbg(mat);vector<mint> vec(D);REP(d, D) vec[d] = mint(d + 1).pow(K);coe = system_of_linear_equations<mint>(mat, vec).first;dbg(coe);// coe} else {// exit(1);fps gd = g * f;// gd[0] = 0;dbg(gd);REP(_, -K) {// gd = (gd * diff_of_log_f).integral();gd = gd * diff_of_log_f;dbg(gd);gd.resize(N + 2);gd.erase(gd.begin());gd = gd.integral();gd.resize(N + 2);}FOR(i, 1, N + 1) cout << gd.coeff(i) << ' ';return 0;}// REP(d, D) REP(e, D) mat[d][e] =dbg(g);fps gpow = g;REP(d, D) {// dbg(f / g);ret += f * gpow * coe.at(d);gpow *= g;gpow.resize(N + 1);}// FOR(d, 1, N + 1) {// auto tmp = f.pow(d, N + 1);// if (K > 0) {// REP(_, K) tmp *= d;// }// if (K < 0) {// REP(_, -K) tmp /= d;// }// ret += tmp;// }FOR(i, 1, N + 1) cout << ret.coeff(i) << ' ';}