結果

問題 No.1460 Max of Min
ユーザー chocorusk
提出日時 2021-03-31 21:59:14
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 308 ms / 2,000 ms
コード長 25,552 bytes
コンパイル時間 1,704 ms
コンパイル使用メモリ 86,236 KB
最終ジャッジ日時 2025-01-20 03:28:54
ジャッジサーバーID
（参考情報） 		judge5 / judge5
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ファイルパターン 結果
sample AC * 3
other AC * 91
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ソースコード

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プレゼンテーションモードにする

#include <assert.h>
#include <string.h>
#include <initializer_list>
#include <ostream>
#ifndef LIBRA_ALGEBRA_FFT998244353_H_
#define LIBRA_ALGEBRA_FFT998244353_H_
#include <assert.h>
#include <string.h>
#include <vector>
#ifndef LIBRA_ALGEBRA_MODINT_H_
#define LIBRA_ALGEBRA_MODINT_H_
#include <assert.h>
#include <ostream>
template <unsigned M_> struct ModInt {
  static constexpr unsigned M = M_;
  unsigned x;
  constexpr ModInt() : x(0) {}
  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 = 1; 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 == 1); return ModInt(y);
  }
  ModInt operator+() const { return *this; }
  ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0; 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; }
};
#endif  // LIBRA_ALGEBRA_MODINT_H_
using std::vector;
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 - 1] = {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 - 1] = {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;  // < MO
      as[i + m].x = as[i].x + MO - x;  // < 2 MO
      as[i].x += x;  // < 2 MO
    }
  }
  if (m >>= 1) {
    Mint prod = 1;
    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;  // < MO
        as[i + m].x = as[i].x + MO - x;  // < 3 MO
        as[i].x += x;  // < 3 MO
      }
      prod *= FFT_RATIOS[__builtin_ctz(++h)];
    }
  }
  for (; m; ) {
    if (m >>= 1) {
      Mint prod = 1;
      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;  // < MO
          as[i + m].x = as[i].x + MO - x;  // < 4 MO
          as[i].x += x;  // < 4 MO
        }
        prod *= FFT_RATIOS[__builtin_ctz(++h)];
      }
    }
    if (m >>= 1) {
      Mint prod = 1;
      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;  // < MO
          as[i].x = (as[i].x >= MO2) ? (as[i].x - MO2) : as[i].x;  // < 2 MO
          as[i + m].x = as[i].x + MO - x;  // < 3 MO
          as[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 MO
    as[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 = 1;
    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 MO
        as[i].x += as[i + m].x;  // < 2 MO
        as[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 = 1;
    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 MO
        as[i].x += as[i + m].x;  // < 4 MO
        as[i].x = (as[i].x >= MO2) ? (as[i].x - MO2) : as[i].x;  // < 2 MO
        as[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 MO
        as[i].x += as[i + m].x;  // < 2 MO
        as[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 MO
      as[i].x += as[i + m].x;  // < 4 MO
      as[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;
  for (; n < len; n <<= 1) {}
  as.resize(n); fft(as);
  bs.resize(n); fft(bs);
  for (int i = 0; i < n; ++i) as[i] *= bs[i];
  invFft(as);
  as.resize(len);
  return as;
}
#endif  // LIBRA_ALGEBRA_FFT998244353_H_
using std::min;
using std::vector;
// inv: log, exp, pow
constexpr int LIM_INV = 1 << 20;  // @
Mint inv[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]);
  }
} preparator;
// polyWork0: operator*, inv, div, divAt, log, exp, pow
// polyWork1: inv, div, divAt, log, exp, pow
// polyWork2: divAt, exp, pow
// polyWork3: exp, pow
static constexpr int LIM_POLY = 1 << 20;  // @
static_assert(LIM_POLY <= 1 << FFT_MAX);
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; }
  Poly take(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;
  }
  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 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) f
  Poly 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 MO
          fs[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) g
  Poly div(const Poly &fs, int n) const {
    assert(!empty()); assert(!fs.empty()); assert(fs[0]); assert(1 <= n);
    if (n == 1) return {(*this)[0] / fs[0]};
    // m < n <= 2 m
    const 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-reversed
  Mint 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 polyWork2
        const 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) / t
  Poly log(int n) const {
    assert(!empty()); assert((*this)[0].x == 1U); assert(n <= LIM_INV);
    Poly fs = take(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, (1 < size()) ? (*this)[1] : 0U};
    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) g
  Poly pow(long long a, int n) const {
    assert(1 <= n);
    if (empty() || (*this)[0].x != 1U) {
      assert(a >= 0);
      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(a, n - a * o);
      Poly gs(n);
      for (int i = 0; i < n - a * o; ++i) gs[a * o + i] = c * tts[i];
      return gs;
    }
    assert(!empty()); assert((*this)[0].x == 1);
    return (a * log(n)).exp(n);  // 13 E(n) + (16 + 1/2) E(n)
  }
};
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).take(d).divAt(cs, k);
}
// -----------------------------------------------------------------------------
#include <stdio.h>
int readInt() {
  int c;
  for (; ; ) {
    c = getchar();
    if ('0' <= c && c <= '9') break;
    if (c == -1) throw -1;
    if (c == '-') return -readInt();
  }
  int x = c - '0';
  for (; ; ) {
    c = getchar();
    if (!('0' <= c && c <= '9')) return x;
    x = x * 10 + (c - '0');
  }
}
long long readLong() {
  int c;
  for (; ; ) {
    c = getchar();
    if ('0' <= c && c <= '9') break;
    if (c == -1) throw -1;
    if (c == '-') return -readLong();
  }
  long long x = c - '0';
  for (; ; ) {
    c = getchar();
    if (!('0' <= c && c <= '9')) return x;
    x = x * 10 + (c - '0');
  }
}
char writeIntBuffer[10];
void writeInt(int x) {
  if (x < 0) {
    putchar('-');
    x = -x;
  }
  int i = 0;
  do {
    writeIntBuffer[i++] = '0' + (x % 10);
    x /= 10;
  } while (x != 0);
  for (; i > 0; ) {
    putchar(writeIntBuffer[--i]);
  }
}
#include <iostream>
using namespace std;
// https://judge.yosupo.jp/problem/kth_term_of_linearly_recurrent_sequence
int main() {
    using ll=long long;
    int k; ll n;
    cin>>k>>n;
    ll a[1010], b[1010];
    for(int i=0; i<k; i++) cin>>a[i];
    for(int i=0; i<k; i++) cin>>b[i];
    ll l=-2e18, r=2e18;
    while(r-l>1){
        ll m=(l+r)/2;
        vector<Mint> A(k), C(k + 1);
        for(int i=0; i<k; i++){
            if(a[i]>=m) A[i]=1;
        }
        C[0]=1;
        for(int i=1; i<=k; i++){
            if(b[k-i]>=m) C[i]=-1;
        }
        const Mint ans = linearRecurrenceAt(A, C, n);
        if(ans.x!=0) l=m;
        else r=m;
    }
    cout<<l<<endl;
    return 0;
}
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