結果
問題 | No.1621 Sequence Inversions |
ユーザー | 👑 hos.lyric |
提出日時 | 2021-07-22 21:25:49 |
言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 217 ms / 3,000 ms |
コード長 | 35,777 bytes |
コンパイル時間 | 1,661 ms |
コンパイル使用メモリ | 125,536 KB |
実行使用メモリ | 22,548 KB |
最終ジャッジ日時 | 2024-07-17 16:17:12 |
合計ジャッジ時間 | 4,898 ms |
ジャッジサーバーID (参考情報) |
judge3 / judge2 |
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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 | 23 ms
20,484 KB |
testcase_01 | AC | 24 ms
18,340 KB |
testcase_02 | AC | 25 ms
20,640 KB |
testcase_03 | AC | 23 ms
18,028 KB |
testcase_04 | AC | 34 ms
19,064 KB |
testcase_05 | AC | 23 ms
18,828 KB |
testcase_06 | AC | 24 ms
20,672 KB |
testcase_07 | AC | 25 ms
20,336 KB |
testcase_08 | AC | 41 ms
21,392 KB |
testcase_09 | AC | 39 ms
21,744 KB |
testcase_10 | AC | 38 ms
20,996 KB |
testcase_11 | AC | 43 ms
21,512 KB |
testcase_12 | AC | 55 ms
21,388 KB |
testcase_13 | AC | 72 ms
20,688 KB |
testcase_14 | AC | 126 ms
20,928 KB |
testcase_15 | AC | 214 ms
21,440 KB |
testcase_16 | AC | 196 ms
21,680 KB |
testcase_17 | AC | 212 ms
21,072 KB |
testcase_18 | AC | 111 ms
21,112 KB |
testcase_19 | AC | 26 ms
20,556 KB |
testcase_20 | AC | 84 ms
21,128 KB |
testcase_21 | AC | 216 ms
22,548 KB |
testcase_22 | AC | 216 ms
22,012 KB |
testcase_23 | AC | 217 ms
21,020 KB |
testcase_24 | AC | 24 ms
20,304 KB |
testcase_25 | AC | 23 ms
20,228 KB |
testcase_26 | AC | 24 ms
18,412 KB |
testcase_27 | AC | 26 ms
21,300 KB |
testcase_28 | AC | 23 ms
20,460 KB |
ソースコード
#include <cassert>#include <cmath>#include <cstdint>#include <cstdio>#include <cstdlib>#include <cstring>#include <algorithm>#include <bitset>#include <complex>#include <deque>#include <functional>#include <iostream>#include <map>#include <numeric>#include <queue>#include <set>#include <sstream>#include <string>#include <unordered_map>#include <unordered_set>#include <utility>#include <vector>using namespace std;using Int = long long;template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }////////////////////////////////////////////////////////////////////////////////template <unsigned M_> struct ModInt {static constexpr unsigned M = M_;unsigned x;constexpr ModInt() : x(0U) {}constexpr ModInt(unsigned x_) : x(x_ % M) {}constexpr ModInt(unsigned long long x_) : x(x_ % M) {}constexpr ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}constexpr ModInt(long long x_) : x(((x_ %= static_cast<long long>(M)) < 0) ? (x_ + static_cast<long long>(M)) : x_) {}ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; }ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; }ModInt &operator*=(const ModInt &a) { x = (static_cast<unsigned long long>(x) * a.x) % M; return *this; }ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); }ModInt pow(long long e) const {if (e < 0) return inv().pow(-e);ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b;}ModInt inv() const {unsigned a = M, b = x; int y = 0, z = 1;for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast<int>(q) * z; y = z; z = w; }assert(a == 1U); return ModInt(y);}ModInt operator+() const { return *this; }ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; }ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); }ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); }ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); }ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); }template <class T> friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); }template <class T> friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); }template <class T> friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); }template <class T> friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); }explicit operator bool() const { return x; }bool operator==(const ModInt &a) const { return (x == a.x); }bool operator!=(const ModInt &a) const { return (x != a.x); }friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; }};////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////constexpr unsigned MO = 998244353U;constexpr unsigned MO2 = 2U * MO;constexpr int FFT_MAX = 23;using Mint = ModInt<MO>;constexpr Mint FFT_ROOTS[FFT_MAX + 1] = {1U, 998244352U, 911660635U, 372528824U, 929031873U, 452798380U, 922799308U, 781712469U, 476477967U,166035806U, 258648936U, 584193783U, 63912897U, 350007156U, 666702199U, 968855178U, 629671588U, 24514907U, 996173970U, 363395222U, 565042129U,733596141U, 267099868U, 15311432U};constexpr Mint INV_FFT_ROOTS[FFT_MAX + 1] = {1U, 998244352U, 86583718U, 509520358U, 337190230U, 87557064U, 609441965U, 135236158U, 304459705U,685443576U, 381598368U, 335559352U, 129292727U, 358024708U, 814576206U, 708402881U, 283043518U, 3707709U, 121392023U, 704923114U, 950391366U,428961804U, 382752275U, 469870224U};constexpr Mint FFT_RATIOS[FFT_MAX] = {911660635U, 509520358U, 369330050U, 332049552U, 983190778U, 123842337U, 238493703U, 975955924U, 603855026U,856644456U, 131300601U, 842657263U, 730768835U, 942482514U, 806263778U, 151565301U, 510815449U, 503497456U, 743006876U, 741047443U, 56250497U,867605899U};constexpr Mint INV_FFT_RATIOS[FFT_MAX] = {86583718U, 372528824U, 373294451U, 645684063U, 112220581U, 692852209U, 155456985U, 797128860U, 90816748U,860285882U, 927414960U, 354738543U, 109331171U, 293255632U, 535113200U, 308540755U, 121186627U, 608385704U, 438932459U, 359477183U, 824071951U,103369235U};// as[rev(i)] <- \sum_j \zeta^(ij) as[j]void fft(Mint *as, int n) {assert(!(n & (n - 1))); assert(1 <= n); assert(n <= 1 << FFT_MAX);int m = n;if (m >>= 1) {for (int i = 0; i < m; ++i) {const unsigned x = as[i + m].x; // < MOas[i + m].x = as[i].x + MO - x; // < 2 MOas[i].x += x; // < 2 MO}}if (m >>= 1) {Mint prod = 1U;for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {for (int i = i0; i < i0 + m; ++i) {const unsigned x = (prod * as[i + m]).x; // < MOas[i + m].x = as[i].x + MO - x; // < 3 MOas[i].x += x; // < 3 MO}prod *= FFT_RATIOS[__builtin_ctz(++h)];}}for (; m; ) {if (m >>= 1) {Mint prod = 1U;for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {for (int i = i0; i < i0 + m; ++i) {const unsigned x = (prod * as[i + m]).x; // < MOas[i + m].x = as[i].x + MO - x; // < 4 MOas[i].x += x; // < 4 MO}prod *= FFT_RATIOS[__builtin_ctz(++h)];}}if (m >>= 1) {Mint prod = 1U;for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {for (int i = i0; i < i0 + m; ++i) {const unsigned x = (prod * as[i + m]).x; // < MOas[i].x = (as[i].x >= MO2) ? (as[i].x - MO2) : as[i].x; // < 2 MOas[i + m].x = as[i].x + MO - x; // < 3 MOas[i].x += x; // < 3 MO}prod *= FFT_RATIOS[__builtin_ctz(++h)];}}}for (int i = 0; i < n; ++i) {as[i].x = (as[i].x >= MO2) ? (as[i].x - MO2) : as[i].x; // < 2 MOas[i].x = (as[i].x >= MO) ? (as[i].x - MO) : as[i].x; // < MO}}// as[i] <- (1/n) \sum_j \zeta^(-ij) as[rev(j)]void invFft(Mint *as, int n) {assert(!(n & (n - 1))); assert(1 <= n); assert(n <= 1 << FFT_MAX);int m = 1;if (m < n >> 1) {Mint prod = 1U;for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {for (int i = i0; i < i0 + m; ++i) {const unsigned long long y = as[i].x + MO - as[i + m].x; // < 2 MOas[i].x += as[i + m].x; // < 2 MOas[i + m].x = (prod.x * y) % MO; // < MO}prod *= INV_FFT_RATIOS[__builtin_ctz(++h)];}m <<= 1;}for (; m < n >> 1; m <<= 1) {Mint prod = 1U;for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {for (int i = i0; i < i0 + (m >> 1); ++i) {const unsigned long long y = as[i].x + MO2 - as[i + m].x; // < 4 MOas[i].x += as[i + m].x; // < 4 MOas[i].x = (as[i].x >= MO2) ? (as[i].x - MO2) : as[i].x; // < 2 MOas[i + m].x = (prod.x * y) % MO; // < MO}for (int i = i0 + (m >> 1); i < i0 + m; ++i) {const unsigned long long y = as[i].x + MO - as[i + m].x; // < 2 MOas[i].x += as[i + m].x; // < 2 MOas[i + m].x = (prod.x * y) % MO; // < MO}prod *= INV_FFT_RATIOS[__builtin_ctz(++h)];}}if (m < n) {for (int i = 0; i < m; ++i) {const unsigned y = as[i].x + MO2 - as[i + m].x; // < 4 MOas[i].x += as[i + m].x; // < 4 MOas[i + m].x = y; // < 4 MO}}const Mint invN = Mint(n).inv();for (int i = 0; i < n; ++i) {as[i] *= invN;}}void fft(vector<Mint> &as) {fft(as.data(), as.size());}void invFft(vector<Mint> &as) {invFft(as.data(), as.size());}vector<Mint> convolve(vector<Mint> as, vector<Mint> bs) {if (as.empty() || bs.empty()) return {};const int len = as.size() + bs.size() - 1;int n = 1;as.resize(n); fft(as);for (; n < len; n <<= 1) {}bs.resize(n); fft(bs);for (int i = 0; i < n; ++i) as[i] *= bs[i];invFft(as);as.resize(len);return as;}vector<Mint> square(vector<Mint> as) {if (as.empty()) return {};const int len = as.size() + as.size() - 1;int n = 1;for (; n < len; n <<= 1) {}as.resize(n); fft(as);for (int i = 0; i < n; ++i) as[i] *= as[i];invFft(as);as.resize(len);return as;}////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////// inv: log, exp, powconstexpr int LIM_INV = 1 << 20; // @Mint inv[LIM_INV], fac[LIM_INV], invFac[LIM_INV];struct ModIntPreparator {ModIntPreparator() {inv[1] = 1;for (int i = 2; i < LIM_INV; ++i) inv[i] = -((Mint::M / i) * inv[Mint::M % i]);fac[0] = 1;for (int i = 1; i < LIM_INV; ++i) fac[i] = fac[i - 1] * i;invFac[0] = 1;for (int i = 1; i < LIM_INV; ++i) invFac[i] = invFac[i - 1] * inv[i];}} preparator;// polyWork0: *, inv, div, divAt, log, exp, pow, sqrt// polyWork1: inv, div, divAt, log, exp, pow, sqrt// polyWork2: divAt, exp, pow, sqrt// polyWork3: exp, pow, sqrtstatic constexpr int LIM_POLY = 1 << 20; // @static_assert(LIM_POLY <= 1 << FFT_MAX, "Poly: LIM_POLY <= 1 << FFT_MAX must hold.");static Mint polyWork0[LIM_POLY], polyWork1[LIM_POLY], polyWork2[LIM_POLY], polyWork3[LIM_POLY];struct Poly : public vector<Mint> {Poly() {}explicit Poly(int n) : vector<Mint>(n) {}Poly(const vector<Mint> &vec) : vector<Mint>(vec) {}Poly(std::initializer_list<Mint> il) : vector<Mint>(il) {}int size() const { return vector<Mint>::size(); }Mint at(long long k) const { return (0 <= k && k < size()) ? (*this)[k] : 0U; }int ord() const { for (int i = 0; i < size(); ++i) if ((*this)[i]) return i; return -1; }int deg() const { for (int i = size(); --i >= 0; ) if ((*this)[i]) return i; return -1; }Poly mod(int n) const { return Poly(vector<Mint>(data(), data() + min(n, size()))); }friend std::ostream &operator<<(std::ostream &os, const Poly &fs) {os << "[";for (int i = 0; i < fs.size(); ++i) { if (i > 0) os << ", "; os << fs[i]; }return os << "]";}Poly &operator+=(const Poly &fs) {if (size() < fs.size()) resize(fs.size());for (int i = 0; i < fs.size(); ++i) (*this)[i] += fs[i];return *this;}Poly &operator-=(const Poly &fs) {if (size() < fs.size()) resize(fs.size());for (int i = 0; i < fs.size(); ++i) (*this)[i] -= fs[i];return *this;}// 3 E(|t| + |f|)Poly &operator*=(const Poly &fs) {if (empty() || fs.empty()) return *this = {};const int nt = size(), nf = fs.size();int n = 1;for (; n < nt + nf - 1; n <<= 1) {}assert(n <= LIM_POLY);resize(n);fft(data(), n); // 1 E(n)memcpy(polyWork0, fs.data(), nf * sizeof(Mint));memset(polyWork0 + nf, 0, (n - nf) * sizeof(Mint));fft(polyWork0, n); // 1 E(n)for (int i = 0; i < n; ++i) (*this)[i] *= polyWork0[i];invFft(data(), n); // 1 E(n)resize(nt + nf - 1);return *this;}// 13 E(deg(t) - deg(f) + 1)// rev(t) = rev(f) rev(q) + x^(deg(t)-deg(f)+1) rev(r)Poly &operator/=(const Poly &fs) {const int m = deg(), n = fs.deg();assert(n != -1);if (m < n) return *this = {};Poly tsRev(m - n + 1), fsRev(min(m - n, n) + 1);for (int i = 0; i <= m - n; ++i) tsRev[i] = (*this)[m - i];for (int i = 0, i0 = min(m - n, n); i <= i0; ++i) fsRev[i] = fs[n - i];const Poly qsRev = tsRev.div(fsRev, m - n + 1); // 13 E(m - n + 1)resize(m - n + 1);for (int i = 0; i <= m - n; ++i) (*this)[i] = qsRev[m - n - i];return *this;}// 13 E(deg(t) - deg(f) + 1) + 3 E(|t|)Poly &operator%=(const Poly &fs) {const Poly qs = *this / fs; // 13 E(deg(t) - deg(f) + 1)*this -= fs * qs; // 3 E(|t|)resize(deg() + 1);return *this;}Poly &operator*=(const Mint &a) {for (int i = 0; i < size(); ++i) (*this)[i] *= a;return *this;}Poly &operator/=(const Mint &a) {const Mint b = a.inv();for (int i = 0; i < size(); ++i) (*this)[i] *= b;return *this;}Poly operator+() const { return *this; }Poly operator-() const {Poly fs(size());for (int i = 0; i < size(); ++i) fs[i] = -(*this)[i];return fs;}Poly operator+(const Poly &fs) const { return (Poly(*this) += fs); }Poly operator-(const Poly &fs) const { return (Poly(*this) -= fs); }Poly operator*(const Poly &fs) const { return (Poly(*this) *= fs); }Poly operator/(const Poly &fs) const { return (Poly(*this) /= fs); }Poly operator%(const Poly &fs) const { return (Poly(*this) %= fs); }Poly operator*(const Mint &a) const { return (Poly(*this) *= a); }Poly operator/(const Mint &a) const { return (Poly(*this) /= a); }friend Poly operator*(const Mint &a, const Poly &fs) { return fs * a; }// 10 E(n)// f <- f - (t f - 1) fPoly inv(int n) const {assert(!empty()); assert((*this)[0]); assert(1 <= n);assert(n == 1 || 1 << (32 - __builtin_clz(n - 1)) <= LIM_POLY);Poly fs(n);fs[0] = (*this)[0].inv();for (int m = 1; m < n; m <<= 1) {memcpy(polyWork0, data(), min(m << 1, size()) * sizeof(Mint));memset(polyWork0 + min(m << 1, size()), 0, ((m << 1) - min(m << 1, size())) * sizeof(Mint));fft(polyWork0, m << 1); // 2 E(n)memcpy(polyWork1, fs.data(), min(m << 1, n) * sizeof(Mint));memset(polyWork1 + min(m << 1, n), 0, ((m << 1) - min(m << 1, n)) * sizeof(Mint));fft(polyWork1, m << 1); // 2 E(n)for (int i = 0; i < m << 1; ++i) polyWork0[i] *= polyWork1[i];invFft(polyWork0, m << 1); // 2 E(n)memset(polyWork0, 0, m * sizeof(Mint));fft(polyWork0, m << 1); // 2 E(n)for (int i = 0; i < m << 1; ++i) polyWork0[i] *= polyWork1[i];invFft(polyWork0, m << 1); // 2 E(n)for (int i = m, i0 = min(m << 1, n); i < i0; ++i) fs[i] = -polyWork0[i];}return fs;}// 9 E(n)// Need (4 m)-th roots of unity to lift from (mod x^m) to (mod x^(2m)).// f <- f - (t f - 1) f// (t f^2) mod ((x^(2m) - 1) (x^m - 1^(1/4)))/*Poly inv(int n) const {assert(!empty()); assert((*this)[0]); assert(1 <= n);assert(n == 1 || 3 << (31 - __builtin_clz(n - 1)) <= LIM_POLY);assert(n <= 1 << (FFT_MAX - 1));Poly fs(n);fs[0] = (*this)[0].inv();for (int h = 2, m = 1; m < n; ++h, m <<= 1) {const Mint a = FFT_ROOTS[h], b = INV_FFT_ROOTS[h];memcpy(polyWork0, data(), min(m << 1, size()) * sizeof(Mint));memset(polyWork0 + min(m << 1, size()), 0, ((m << 1) - min(m << 1, size())) * sizeof(Mint));{Mint aa = 1;for (int i = 0; i < m; ++i) { polyWork0[(m << 1) + i] = aa * polyWork0[i]; aa *= a; }for (int i = 0; i < m; ++i) { polyWork0[(m << 1) + i] += aa * polyWork0[m + i]; aa *= a; }}fft(polyWork0, m << 1); // 2 E(n)fft(polyWork0 + (m << 1), m); // 1 E(n)memcpy(polyWork1, fs.data(), min(m << 1, n) * sizeof(Mint));memset(polyWork1 + min(m << 1, n), 0, ((m << 1) - min(m << 1, n)) * sizeof(Mint));{Mint aa = 1;for (int i = 0; i < m; ++i) { polyWork1[(m << 1) + i] = aa * polyWork1[i]; aa *= a; }for (int i = 0; i < m; ++i) { polyWork1[(m << 1) + i] += aa * polyWork1[m + i]; aa *= a; }}fft(polyWork1, m << 1); // 2 E(n)fft(polyWork1 + (m << 1), m); // 1 E(n)for (int i = 0; i < (m << 1) + m; ++i) polyWork0[i] *= polyWork1[i] * polyWork1[i];invFft(polyWork0, m << 1); // 2 E(n)invFft(polyWork0 + (m << 1), m); // 1 E(n)// 2 f0 + (-f2), (-f1) + (-f3), 1^(1/4) (-f1) - (-f2) - 1^(1/4) (-f3){Mint bb = 1;for (int i = 0, i0 = min(m, n - m); i < i0; ++i) {unsigned x = polyWork0[i].x + (bb * polyWork0[(m << 1) + i]).x + MO2 - (fs[i].x << 1); // < 4 MOfs[m + i] = Mint(static_cast<unsigned long long>(FFT_ROOTS[2].x) * x) - polyWork0[m + i];fs[m + i].x = ((fs[m + i].x & 1) ? (fs[m + i].x + MO) : fs[m + i].x) >> 1;bb *= b;}}}return fs;}*/// 13 E(n)// g = (1 / f) mod x^m// h <- h - (f h - t) gPoly div(const Poly &fs, int n) const {assert(!fs.empty()); assert(fs[0]); assert(1 <= n);if (n == 1) return {at(0) / fs[0]};// m < n <= 2 mconst int m = 1 << (31 - __builtin_clz(n - 1));assert(m << 1 <= LIM_POLY);Poly gs = fs.inv(m); // 5 E(n)gs.resize(m << 1);fft(gs.data(), m << 1); // 1 E(n)memcpy(polyWork0, data(), min(m, size()) * sizeof(Mint));memset(polyWork0 + min(m, size()), 0, ((m << 1) - min(m, size())) * sizeof(Mint));fft(polyWork0, m << 1); // 1 E(n)for (int i = 0; i < m << 1; ++i) polyWork0[i] *= gs[i];invFft(polyWork0, m << 1); // 1 E(n)Poly hs(n);memcpy(hs.data(), polyWork0, m * sizeof(Mint));memset(polyWork0 + m, 0, m * sizeof(Mint));fft(polyWork0, m << 1); // 1 E(n)memcpy(polyWork1, fs.data(), min(m << 1, fs.size()) * sizeof(Mint));memset(polyWork1 + min(m << 1, fs.size()), 0, ((m << 1) - min(m << 1, fs.size())) * sizeof(Mint));fft(polyWork1, m << 1); // 1 E(n)for (int i = 0; i < m << 1; ++i) polyWork0[i] *= polyWork1[i];invFft(polyWork0, m << 1); // 1 E(n)memset(polyWork0, 0, m * sizeof(Mint));for (int i = m, i0 = min(m << 1, size()); i < i0; ++i) polyWork0[i] -= (*this)[i];fft(polyWork0, m << 1); // 1 E(n)for (int i = 0; i < m << 1; ++i) polyWork0[i] *= gs[i];invFft(polyWork0, m << 1); // 1 E(n)for (int i = m; i < n; ++i) hs[i] = -polyWork0[i];return hs;}// (4 (floor(log_2 k) - ceil(log_2 |fs|)) + 16) E(|fs|)// [x^k] (t(x) / f(x)) = [x^k] ((t(x) f(-x)) / (f(x) f(-x))// polyWork0: half of (2 m)-th roots of unity, inversed, bit-reversedMint divAt(const Poly &fs, long long k) const {assert(k >= 0);if (size() >= fs.size()) {// TODO: operator%assert(false);}int h = 0, m = 1;for (; m < fs.size(); ++h, m <<= 1) {}if (k < m) {const Poly gs = fs.inv(k + 1); // 10 E(|fs|)Mint sum;for (int i = 0, i0 = min<int>(k + 1, size()); i < i0; ++i) sum += (*this)[i] * gs[k - i];return sum;}assert(m << 1 <= LIM_POLY);polyWork0[0] = Mint(2U).inv();for (int hh = 0; hh < h; ++hh) for (int i = 0; i < 1 << hh; ++i) polyWork0[1 << hh | i] = polyWork0[i] * INV_FFT_ROOTS[hh + 2];const Mint a = FFT_ROOTS[h + 1];memcpy(polyWork2, data(), size() * sizeof(Mint));memset(polyWork2 + size(), 0, ((m << 1) - size()) * sizeof(Mint));fft(polyWork2, m << 1); // 2 E(|fs|)memcpy(polyWork1, fs.data(), fs.size() * sizeof(Mint));memset(polyWork1 + fs.size(), 0, ((m << 1) - fs.size()) * sizeof(Mint));fft(polyWork1, m << 1); // 2 E(|fs|)for (; ; ) {if (k & 1) {for (int i = 0; i < m; ++i) polyWork2[i] = polyWork0[i] * (polyWork2[i << 1 | 0] * polyWork1[i << 1 | 1] - polyWork2[i << 1 | 1] *polyWork1[i << 1 | 0]);} else {for (int i = 0; i < m; ++i) {polyWork2[i] = polyWork2[i << 1 | 0] * polyWork1[i << 1 | 1] + polyWork2[i << 1 | 1] * polyWork1[i << 1 | 0];polyWork2[i].x = ((polyWork2[i].x & 1) ? (polyWork2[i].x + MO) : polyWork2[i].x) >> 1;}}for (int i = 0; i < m; ++i) polyWork1[i] = polyWork1[i << 1 | 0] * polyWork1[i << 1 | 1];if ((k >>= 1) < m) {invFft(polyWork2, m); // 1 E(|fs|)invFft(polyWork1, m); // 1 E(|fs|)// Poly::inv does not use polyWork2const Poly gs = Poly(vector<Mint>(polyWork1, polyWork1 + k + 1)).inv(k + 1); // 10 E(|fs|)Mint sum;for (int i = 0; i <= k; ++i) sum += polyWork2[i] * gs[k - i];return sum;}memcpy(polyWork2 + m, polyWork2, m * sizeof(Mint));invFft(polyWork2 + m, m); // (floor(log_2 k) - ceil(log_2 |fs|)) E(|fs|)memcpy(polyWork1 + m, polyWork1, m * sizeof(Mint));invFft(polyWork1 + m, m); // (floor(log_2 k) - ceil(log_2 |fs|)) E(|fs|)Mint aa = 1;for (int i = m; i < m << 1; ++i) { polyWork2[i] *= aa; polyWork1[i] *= aa; aa *= a; }fft(polyWork2 + m, m); // (floor(log_2 k) - ceil(log_2 |fs|)) E(|fs|)fft(polyWork1 + m, m); // (floor(log_2 k) - ceil(log_2 |fs|)) E(|fs|)}}// 13 E(n)// D log(t) = (D t) / tPoly log(int n) const {assert(!empty()); assert((*this)[0].x == 1U); assert(n <= LIM_INV);Poly fs = mod(n);for (int i = 0; i < fs.size(); ++i) fs[i] *= i;fs = fs.div(*this, n);for (int i = 1; i < n; ++i) fs[i] *= ::inv[i];return fs;}// (16 + 1/2) E(n)// f = exp(t) mod x^m ==> (D f) / f == D t (mod x^m)// g = (1 / exp(t)) mod x^m// f <- f - (log f - t) / (1 / f)// = f - (I ((D f) / f) - t) f// == f - (I ((D f) / f + (f g - 1) ((D f) / f - D (t mod x^m))) - t) f (mod x^(2m))// = f - (I (g (D f - f D (t mod x^m)) + D (t mod x^m)) - t) f// g <- g - (f g - 1) g// polyWork1: DFT(f, 2 m), polyWork2: g, polyWork3: DFT(g, 2 m)Poly exp(int n) const {assert(!empty()); assert(!(*this)[0]); assert(1 <= n);assert(n == 1 || 1 << (32 - __builtin_clz(n - 1)) <= min(LIM_INV, LIM_POLY));if (n == 1) return {1U};if (n == 2) return {1U, at(1)};Poly fs(n);fs[0].x = polyWork1[0].x = polyWork1[1].x = polyWork2[0].x = 1U;int m;for (m = 1; m << 1 < n; m <<= 1) {for (int i = 0, i0 = min(m, size()); i < i0; ++i) polyWork0[i] = i * (*this)[i];memset(polyWork0 + min(m, size()), 0, (m - min(m, size())) * sizeof(Mint));fft(polyWork0, m); // (1/2) E(n)for (int i = 0; i < m; ++i) polyWork0[i] *= polyWork1[i];invFft(polyWork0, m); // (1/2) E(n)for (int i = 0; i < m; ++i) polyWork0[i] -= i * fs[i];memset(polyWork0 + m, 0, m * sizeof(Mint));fft(polyWork0, m << 1); // 1 E(n)memcpy(polyWork3, polyWork2, m * sizeof(Mint));memset(polyWork3 + m, 0, m * sizeof(Mint));fft(polyWork3, m << 1); // 1 E(n)for (int i = 0; i < m << 1; ++i) polyWork0[i] *= polyWork3[i];invFft(polyWork0, m << 1); // 1 E(n)for (int i = 0; i < m; ++i) polyWork0[i] *= ::inv[m + i];for (int i = 0, i0 = min(m, size() - m); i < i0; ++i) polyWork0[i] += (*this)[m + i];memset(polyWork0 + m, 0, m * sizeof(Mint));fft(polyWork0, m << 1); // 1 E(n)for (int i = 0; i < m << 1; ++i) polyWork0[i] *= polyWork1[i];invFft(polyWork0, m << 1); // 1 E(n)memcpy(fs.data() + m, polyWork0, m * sizeof(Mint));memcpy(polyWork1, fs.data(), (m << 1) * sizeof(Mint));memset(polyWork1 + (m << 1), 0, (m << 1) * sizeof(Mint));fft(polyWork1, m << 2); // 2 E(n)for (int i = 0; i < m << 1; ++i) polyWork0[i] = polyWork1[i] * polyWork3[i];invFft(polyWork0, m << 1); // 1 E(n)memset(polyWork0, 0, m * sizeof(Mint));fft(polyWork0, m << 1); // 1 E(n)for (int i = 0; i < m << 1; ++i) polyWork0[i] *= polyWork3[i];invFft(polyWork0, m << 1); // 1 E(n)for (int i = m; i < m << 1; ++i) polyWork2[i] = -polyWork0[i];}for (int i = 0, i0 = min(m, size()); i < i0; ++i) polyWork0[i] = i * (*this)[i];memset(polyWork0 + min(m, size()), 0, (m - min(m, size())) * sizeof(Mint));fft(polyWork0, m); // (1/2) E(n)for (int i = 0; i < m; ++i) polyWork0[i] *= polyWork1[i];invFft(polyWork0, m); // (1/2) E(n)for (int i = 0; i < m; ++i) polyWork0[i] -= i * fs[i];memcpy(polyWork0 + m, polyWork0 + (m >> 1), (m >> 1) * sizeof(Mint));memset(polyWork0 + (m >> 1), 0, (m >> 1) * sizeof(Mint));memset(polyWork0 + m + (m >> 1), 0, (m >> 1) * sizeof(Mint));fft(polyWork0, m); // (1/2) E(n)fft(polyWork0 + m, m); // (1/2) E(n)memcpy(polyWork3 + m, polyWork2 + (m >> 1), (m >> 1) * sizeof(Mint));memset(polyWork3 + m + (m >> 1), 0, (m >> 1) * sizeof(Mint));fft(polyWork3 + m, m); // (1/2) E(n)for (int i = 0; i < m; ++i) polyWork0[m + i] = polyWork0[i] * polyWork3[m + i] + polyWork0[m + i] * polyWork3[i];for (int i = 0; i < m; ++i) polyWork0[i] *= polyWork3[i];invFft(polyWork0, m); // (1/2) E(n)invFft(polyWork0 + m, m); // (1/2) E(n)for (int i = 0; i < m >> 1; ++i) polyWork0[(m >> 1) + i] += polyWork0[m + i];for (int i = 0; i < m; ++i) polyWork0[i] *= ::inv[m + i];for (int i = 0, i0 = min(m, size() - m); i < i0; ++i) polyWork0[i] += (*this)[m + i];memset(polyWork0 + m, 0, m * sizeof(Mint));fft(polyWork0, m << 1); // 1 E(n)for (int i = 0; i < m << 1; ++i) polyWork0[i] *= polyWork1[i];invFft(polyWork0, m << 1); // 1 E(n)memcpy(fs.data() + m, polyWork0, (n - m) * sizeof(Mint));return fs;}// (29 + 1/2) E(n)// g <- g - (log g - a log t) gPoly pow(Mint a, int n) const {assert(!empty()); assert((*this)[0].x == 1U); assert(1 <= n);return (a * log(n)).exp(n); // 13 E(n) + (16 + 1/2) E(n)}// (29 + 1/2) E(n - a ord(t))Poly pow(long long a, int n) const {assert(a >= 0); assert(1 <= n);if (a == 0) { Poly gs(n); gs[0].x = 1U; return gs; }const int o = ord();if (o == -1 || o > (n - 1) / a) return Poly(n);const Mint b = (*this)[o].inv(), c = (*this)[o].pow(a);const int ntt = min<int>(n - a * o, size() - o);Poly tts(ntt);for (int i = 0; i < ntt; ++i) tts[i] = b * (*this)[o + i];tts = tts.pow(Mint(a), n - a * o); // (29 + 1/2) E(n - a ord(t))Poly gs(n);for (int i = 0; i < n - a * o; ++i) gs[a * o + i] = c * tts[i];return gs;}// (10 + 1/2) E(n)// f = t^(1/2) mod x^m, g = 1 / t^(1/2) mod x^m// f <- f - (f^2 - h) g / 2// g <- g - (f g - 1) g// polyWork1: DFT(f, m), polyWork2: g, polyWork3: DFT(g, 2 m)Poly sqrt(int n) const {assert(!empty()); assert((*this)[0].x == 1U); assert(1 <= n);assert(n == 1 || 1 << (32 - __builtin_clz(n - 1)) <= LIM_POLY);if (n == 1) return {1U};if (n == 2) return {1U, at(1) / 2};Poly fs(n);fs[0].x = polyWork1[0].x = polyWork2[0].x = 1U;int m;for (m = 1; m << 1 < n; m <<= 1) {for (int i = 0; i < m; ++i) polyWork1[i] *= polyWork1[i];invFft(polyWork1, m); // (1/2) E(n)for (int i = 0, i0 = min(m, size()); i < i0; ++i) polyWork1[i] -= (*this)[i];for (int i = 0, i0 = min(m, size() - m); i < i0; ++i) polyWork1[i] -= (*this)[m + i];memset(polyWork1 + m, 0, m * sizeof(Mint));fft(polyWork1, m << 1); // 1 E(n)memcpy(polyWork3, polyWork2, m * sizeof(Mint));memset(polyWork3 + m, 0, m * sizeof(Mint));fft(polyWork3, m << 1); // 1 E(n)for (int i = 0; i < m << 1; ++i) polyWork1[i] *= polyWork3[i];invFft(polyWork1, m << 1); // 1 E(n)for (int i = 0; i < m; ++i) { polyWork1[i] = -polyWork1[i]; fs[m + i].x = ((polyWork1[i].x & 1) ? (polyWork1[i].x + MO) : polyWork1[i].x) >> 1;}memcpy(polyWork1, fs.data(), (m << 1) * sizeof(Mint));fft(polyWork1, m << 1); // 1 E(n)for (int i = 0; i < m << 1; ++i) polyWork0[i] = polyWork1[i] * polyWork3[i];invFft(polyWork0, m << 1); // 1 E(n)memset(polyWork0, 0, m * sizeof(Mint));fft(polyWork0, m << 1); // 1 E(n)for (int i = 0; i < m << 1; ++i) polyWork0[i] *= polyWork3[i];invFft(polyWork0, m << 1); // 1 E(n)for (int i = m; i < m << 1; ++i) polyWork2[i] = -polyWork0[i];}for (int i = 0; i < m; ++i) polyWork1[i] *= polyWork1[i];invFft(polyWork1, m); // (1/2) E(n)for (int i = 0, i0 = min(m, size()); i < i0; ++i) polyWork1[i] -= (*this)[i];for (int i = 0, i0 = min(m, size() - m); i < i0; ++i) polyWork1[i] -= (*this)[m + i];memcpy(polyWork1 + m, polyWork1 + (m >> 1), (m >> 1) * sizeof(Mint));memset(polyWork1 + (m >> 1), 0, (m >> 1) * sizeof(Mint));memset(polyWork1 + m + (m >> 1), 0, (m >> 1) * sizeof(Mint));fft(polyWork1, m); // (1/2) E(n)fft(polyWork1 + m, m); // (1/2) E(n)memcpy(polyWork3 + m, polyWork2 + (m >> 1), (m >> 1) * sizeof(Mint));memset(polyWork3 + m + (m >> 1), 0, (m >> 1) * sizeof(Mint));fft(polyWork3 + m, m); // (1/2) E(n)// for (int i = 0; i < m << 1; ++i) polyWork1[i] *= polyWork3[i];for (int i = 0; i < m; ++i) polyWork1[m + i] = polyWork1[i] * polyWork3[m + i] + polyWork1[m + i] * polyWork3[i];for (int i = 0; i < m; ++i) polyWork1[i] *= polyWork3[i];invFft(polyWork1, m); // (1/2) E(n)invFft(polyWork1 + m, m); // (1/2) E(n)for (int i = 0; i < m >> 1; ++i) polyWork1[(m >> 1) + i] += polyWork1[m + i];for (int i = 0; i < n - m; ++i) { polyWork1[i] = -polyWork1[i]; fs[m + i].x = ((polyWork1[i].x & 1) ? (polyWork1[i].x + MO) : polyWork1[i].x) >>1; }return fs;}// (10 + 1/2) E(n)// modSqrt must return a quadratic residue if exists, or anything otherwise.// Return {} if *this does not have a square root.template <class F> Poly sqrt(int n, F modSqrt) const {assert(1 <= n);const int o = ord();if (o == -1) return Poly(n);if (o & 1) return {};const Mint c = modSqrt((*this)[o]);if (c * c != (*this)[o]) return {};if (o >> 1 >= n) return Poly(n);const Mint b = (*this)[o].inv();const int ntt = min(n - (o >> 1), size() - o);Poly tts(ntt);for (int i = 0; i < ntt; ++i) tts[i] = b * (*this)[o + i];tts = tts.sqrt(n - (o >> 1)); // (10 + 1/2) E(n)Poly gs(n);for (int i = 0; i < n - (o >> 1); ++i) gs[(o >> 1) + i] = c * tts[i];return gs;}};Mint linearRecurrenceAt(const vector<Mint> &as, const vector<Mint> &cs, long long k) {assert(!cs.empty()); assert(cs[0]);const int d = cs.size() - 1;assert(as.size() >= static_cast<size_t>(d));return (Poly(vector<Mint>(as.begin(), as.begin() + d)) * cs).mod(d).divAt(cs, k);}struct SubproductTree {int logN, n, nn;vector<Mint> xs;// [DFT_4((X-xs[0])(X-xs[1])(X-xs[2])(X-xs[3]))] [(X-xs[0])(X-xs[1])(X-xs[2])(X-xs[3])mod X^4]// [ DFT_4((X-xs[0])(X-xs[1])) ] [ DFT_4((X-xs[2])(X-xs[3])) ]// [ DFT_2(X-xs[0]) ] [ DFT_2(X-xs[1]) ] [ DFT_2(X-xs[2]) ] [ DFT_2(X-xs[3]) ]vector<Mint> buf;vector<Mint *> gss;// (1 - xs[0] X) ... (1 - xs[nn-1] X)Poly all;// (ceil(log_2 n) + O(1)) E(n)SubproductTree(const vector<Mint> &xs_) {n = xs_.size();for (logN = 0, nn = 1; nn < n; ++logN, nn <<= 1) {}xs.assign(nn, 0U);memcpy(xs.data(), xs_.data(), n * sizeof(Mint));buf.assign((logN + 1) * (nn << 1), 0U);gss.assign(nn << 1, nullptr);for (int h = 0; h <= logN; ++h) for (int u = 1 << h; u < 1 << (h + 1); ++u) {gss[u] = buf.data() + (h * (nn << 1) + ((u - (1 << h)) << (logN - h + 1)));}for (int i = 0; i < nn; ++i) {gss[nn + i][0] = -xs[i] + 1;gss[nn + i][1] = -xs[i] - 1;}if (nn == 1) gss[1][1] += 2;for (int h = logN; --h >= 0; ) {const int m = 1 << (logN - h);for (int u = 1 << (h + 1); --u >= 1 << h; ) {for (int i = 0; i < m; ++i) gss[u][i] = gss[u << 1][i] * gss[u << 1 | 1][i];memcpy(gss[u] + m, gss[u], m * sizeof(Mint));invFft(gss[u] + m, m); // ((1/2) ceil(log_2 n) + O(1)) E(n)if (h > 0) {gss[u][m] -= 2;const Mint a = FFT_ROOTS[logN - h + 1];Mint aa = 1;for (int i = m; i < m << 1; ++i) { gss[u][i] *= aa; aa *= a; };fft(gss[u] + m, m); // ((1/2) ceil(log_2 n) + O(1)) E(n)}}}all.resize(nn + 1);all[0] = 1;for (int i = 1; i < nn; ++i) all[i] = gss[1][nn + nn - i];all[nn] = gss[1][nn] - 1;}// ((3/2) ceil(log_2 n) + O(1)) E(n) + 10 E(|fs|) + 3 E(|fs| + 2^(ceil(log_2 n)))vector<Mint> multiEval(const Poly &fs) const {vector<Mint> work0(nn), work1(nn), work2(nn);{const int m = max(fs.size(), 1);auto invAll = all.inv(m); // 10 E(|fs|)std::reverse(invAll.begin(), invAll.end());int mm;for (mm = 1; mm < m - 1 + nn; mm <<= 1) {}invAll.resize(mm, 0U);fft(invAll); // E(|fs| + 2^(ceil(log_2 n)))vector<Mint> ffs(mm, 0U);memcpy(ffs.data(), fs.data(), fs.size() * sizeof(Mint));fft(ffs); // E(|fs| + 2^(ceil(log_2 n)))for (int i = 0; i < mm; ++i) ffs[i] *= invAll[i];invFft(ffs); // E(|fs| + 2^(ceil(log_2 n)))memcpy(((logN & 1) ? work1 : work0).data(), ffs.data() + m - 1, nn * sizeof(Mint));}for (int h = 0; h < logN; ++h) {const int m = 1 << (logN - h);for (int u = 1 << h; u < 1 << (h + 1); ++u) {Mint *hs = (((logN - h) & 1) ? work1 : work0).data() + ((u - (1 << h)) << (logN - h));Mint *hs0 = (((logN - h) & 1) ? work0 : work1).data() + ((u - (1 << h)) << (logN - h));Mint *hs1 = hs0 + (m >> 1);fft(hs, m); // ((1/2) ceil(log_2 n) + O(1)) E(n)for (int i = 0; i < m; ++i) work2[i] = gss[u << 1 | 1][i] * hs[i];invFft(work2.data(), m); // ((1/2) ceil(log_2 n) + O(1)) E(n)memcpy(hs0, work2.data() + (m >> 1), (m >> 1) * sizeof(Mint));for (int i = 0; i < m; ++i) work2[i] = gss[u << 1][i] * hs[i];invFft(work2.data(), m); // ((1/2) ceil(log_2 n) + O(1)) E(n)memcpy(hs1, work2.data() + (m >> 1), (m >> 1) * sizeof(Mint));}}work0.resize(n);return work0;}// ((5/2) ceil(log_2 n) + O(1)) E(n)Poly interpolate(const vector<Mint> &ys) const {assert(static_cast<int>(ys.size()) == n);Poly gs(n);for (int i = 0; i < n; ++i) gs[i] = (i + 1) * all[n - (i + 1)];const vector<Mint> denoms = multiEval(gs); // ((3/2) ceil(log_2 n) + O(1)) E(n)vector<Mint> work(nn << 1, 0U);for (int i = 0; i < n; ++i) {// xs[0], ..., xs[n - 1] are not distinctassert(denoms[i]);work[i << 1] = work[i << 1 | 1] = ys[i] / denoms[i];}for (int h = logN; --h >= 0; ) {const int m = 1 << (logN - h);for (int u = 1 << (h + 1); --u >= 1 << h; ) {Mint *hs = work.data() + ((u - (1 << h)) << (logN - h + 1));for (int i = 0; i < m; ++i) hs[i] = gss[u << 1 | 1][i] * hs[i] + gss[u << 1][i] * hs[m + i];if (h > 0) {memcpy(hs + m, hs, m * sizeof(Mint));invFft(hs + m, m); // ((1/2) ceil(log_2 n) + O(1)) E(n)const Mint a = FFT_ROOTS[logN - h + 1];Mint aa = 1;for (int i = m; i < m << 1; ++i) { hs[i] *= aa; aa *= a; };fft(hs + m, m); // ((1/2) ceil(log_2 n) + O(1)) E(n)}}}invFft(work.data(), nn); // E(n)return Poly(vector<Mint>(work.data() + nn - n, work.data() + nn));}};////////////////////////////////////////////////////////////////////////////////int N, K;vector<int> A;int main() {for (; ~scanf("%d%d", &N, &K); ) {A.resize(N);for (int i = 0; i < N; ++i) {scanf("%d", &A[i]);}vector<Poly> fac(N + 1);fac[0] = Poly{1};for (int i = 1; i <= N; ++i) {Poly tmp(i);for (int j = 0; j < i; ++j) {tmp[j] = 1;}fac[i] = fac[i - 1] * tmp;}Poly ans = fac[N];for (int i = 0, j; i < N; i = j) {for (j = i; j < N && A[i] == A[j]; ++j) {}ans /= fac[j - i];}// cerr<<"ans = "<<ans<<endl;printf("%u\n", ans.at(K).x);}return 0;}