結果
| 問題 | No.2580 Hyperinflation |
| ユーザー |
 suisen
|
| 提出日時 | 2023-12-08 02:20:05 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 33,958 bytes |
| コンパイル時間 | 7,222 ms |
| コンパイル使用メモリ | 226,592 KB |
| 実行使用メモリ | 245,072 KB |
| 最終ジャッジ日時 | 2024-09-27 02:35:54 |
| 合計ジャッジ時間 | 19,075 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge3 |
（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 | 196 ms
245,072 KB |
| testcase_01 | AC | 178 ms
120,548 KB |
| testcase_02 | AC | 178 ms
120,640 KB |
| testcase_03 | AC | 178 ms
120,656 KB |
| testcase_04 | AC | 182 ms
120,668 KB |
| testcase_05 | AC | 177 ms
120,580 KB |
| testcase_06 | AC | 178 ms
120,576 KB |
| testcase_07 | AC | 181 ms
120,676 KB |
| testcase_08 | AC | 177 ms
120,492 KB |
| testcase_09 | AC | 176 ms
120,576 KB |
| testcase_10 | AC | 177 ms
120,552 KB |
| testcase_11 | AC | 181 ms
120,576 KB |
| testcase_12 | AC | 183 ms
120,596 KB |
| testcase_13 | AC | 180 ms
120,576 KB |
| testcase_14 | AC | 187 ms
120,768 KB |
| testcase_15 | AC | 188 ms
120,796 KB |
| testcase_16 | AC | 187 ms
120,624 KB |
| testcase_17 | AC | 179 ms
120,548 KB |
| testcase_18 | AC | 680 ms
121,952 KB |
| testcase_19 | AC | 683 ms
122,112 KB |
| testcase_20 | AC | 690 ms
122,084 KB |
| testcase_21 | AC | 680 ms
121,984 KB |
| testcase_22 | AC | 691 ms
121,984 KB |
| testcase_23 | TLE | - |
| testcase_24 | -- | - |
| testcase_25 | -- | - |
| testcase_26 | -- | - |
| testcase_27 | -- | - |
| testcase_28 | -- | - |
| testcase_29 | -- | - |
| testcase_30 | -- | - |
| testcase_31 | -- | - |
| testcase_32 | -- | - |
| testcase_33 | -- | - |
ソースコード
// N^3
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include <bit>
#include <iostream>
#include <vector>
#include <atcoder/modint>
#include <atcoder/convolution>
using mint = atcoder::modint998244353;
#include <cassert>
#include <vector>
#include <iomanip>
#include <iostream>
#include <sstream>
#include <vector>
#include <atcoder/convolution>
namespace suisen::internal {
template <typename T, typename R = T>
std::vector<R> convolution_naive(const std::vector<T>& a, const std::vector<T>& b) {
const int n = a.size(), m = b.size();
std::vector<R> c(n + m - 1);
if (n < m) {
for (int j = 0; j < m; j++) for (int i = 0; i < n; i++) c[i + j] += R(a[i]) * b[j];
} else {
for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) c[i + j] += R(a[i]) * b[j];
}
return c;
}
} // namespace suisen
namespace suisen {
template <typename mint, atcoder::internal::is_modint_t<mint>* = nullptr>
std::vector<mint> arbitrary_mod_convolution(const std::vector<mint>& a, const std::vector<mint>& b) {
int n = int(a.size()), m = int(b.size());
if constexpr (atcoder::internal::is_static_modint<mint>::value) {
int maxz = 1;
while (not ((mint::mod() - 1) & maxz)) maxz <<= 1;
int z = 1;
while (z < n + m - 1) z <<= 1;
if (z <= maxz) return atcoder::convolution<mint>(a, b);
}
if (n == 0 or m == 0) return {};
if (std::min(n, m) <= 120) return internal::convolution_naive(a, b);
static constexpr long long MOD1 = 754974721; // 2^24
static constexpr long long MOD2 = 167772161; // 2^25
static constexpr long long MOD3 = 469762049; // 2^26
static constexpr long long M1M2 = MOD1 * MOD2;
static constexpr long long INV_M1_MOD2 = atcoder::internal::inv_gcd(MOD1, MOD2).second;
static constexpr long long INV_M1M2_MOD3 = atcoder::internal::inv_gcd(M1M2, MOD3).second;
std::vector<int> a2(n), b2(m);
for (int i = 0; i < n; ++i) a2[i] = a[i].val();
for (int i = 0; i < m; ++i) b2[i] = b[i].val();
auto c1 = atcoder::convolution<MOD1>(a2, b2);
auto c2 = atcoder::convolution<MOD2>(a2, b2);
auto c3 = atcoder::convolution<MOD3>(a2, b2);
const long long m1m2 = mint(M1M2).val();
std::vector<mint> c(n + m - 1);
for (int i = 0; i < n + m - 1; ++i) {
// Garner's Algorithm
// X = x1 + x2 * m1 + x3 * m1 * m2
// x1 = c1[i], x2 = (c2[i] - x1) / m1 (mod m2), x3 = (c3[i] - x1 - x2 * m1) / m2 (mod m3)
long long x1 = c1[i];
long long x2 = (atcoder::static_modint<MOD2>(c2[i] - x1) * INV_M1_MOD2).val();
long long x3 = (atcoder::static_modint<MOD3>(c3[i] - x1 - x2 * MOD1) * INV_M1M2_MOD3).val();
c[i] = x1 + x2 * MOD1 + x3 * m1m2;
}
return c;
}
std::vector<__uint128_t> convolution_int(const std::vector<int> &a, const std::vector<int> &b) {
int n = int(a.size()), m = int(b.size());
auto check_nonnegative = [](int e) { return e >= 0; };
assert(std::all_of(a.begin(), a.end(), check_nonnegative));
assert(std::all_of(b.begin(), b.end(), check_nonnegative));
if (n == 0 or m == 0) return {};
if (std::min(n, m) <= 120) return internal::convolution_naive<int, __uint128_t>(a, b);
static constexpr long long MOD1 = 754974721; // 2^24
static constexpr long long MOD2 = 167772161; // 2^25
static constexpr long long MOD3 = 469762049; // 2^26
static constexpr long long M1M2 = MOD1 * MOD2;
static constexpr long long INV_M1_MOD2 = atcoder::internal::inv_gcd(MOD1, MOD2).second;
static constexpr long long INV_M1M2_MOD3 = atcoder::internal::inv_gcd(M1M2, MOD3).second;
auto c1 = atcoder::convolution<MOD1>(a, b);
auto c2 = atcoder::convolution<MOD2>(a, b);
auto c3 = atcoder::convolution<MOD3>(a, b);
std::vector<__uint128_t> c(n + m - 1);
for (int i = 0; i < n + m - 1; ++i) {
// Garner's Algorithm
// X = x1 + x2 * m1 + x3 * m1 * m2
// x1 = c1[i], x2 = (c2[i] - x1) / m1 (mod m2), x3 = (c3[i] - x1 - x2 * m1) / m2 (mod m3)
int x1 = c1[i];
int x2 = (atcoder::static_modint<MOD2>(c2[i] - x1) * INV_M1_MOD2).val();
int x3 = (atcoder::static_modint<MOD3>(c3[i] - x1 - x2 * MOD1) * INV_M1M2_MOD3).val();
c[i] = x1 + x2 * MOD1 + __uint128_t(x3) * M1M2;
}
return c;
}
} // namespace suisen
namespace suisen {
struct unsigned_bigint : private std::vector<int> {
static constexpr int D = 1000000000;
static constexpr int LogD = 9;
static inline struct { operator unsigned_bigint() const { return unsigned_bigint{}; }; } const ZERO{};
static inline struct { operator unsigned_bigint() const { return unsigned_bigint{ 1 }; }; } const ONE{};
unsigned_bigint() : vector() {}
template <typename T, std::enable_if_t<std::is_integral_v<T>, std::nullptr_t> = nullptr>
unsigned_bigint(T v) {
if constexpr (std::is_signed_v<T>) {
assert(v >= 0);
}
for (; v; v /= D) {
this->push_back(v % D);
}
}
unsigned_bigint(const std::string& s) : vector() {
int siz = s.size();
for (int i = siz; i > 0; i -= LogD) {
int l = std::max(0, i - LogD);
int r = i;
int& v = this->emplace_back();
for (int j = l; j < r; ++j) {
int d = s[j] - '0';
assert(0 <= d and d <= 9);
v = v * 10 + d;
}
}
}
unsigned_bigint(const char* s) : unsigned_bigint(std::string(s)) {}
operator bool() const {
return not this->empty();
}
friend bool operator==(const unsigned_bigint& a, const unsigned_bigint& b) {
if (a.size() != b.size()) {
return false;
}
for (size_t i = 0; i < a.size(); ++i) {
if (a[i] != b[i]) return false;
}
return true;
}
friend bool operator!=(const unsigned_bigint& a, const unsigned_bigint& b) {
return not (a == b);
}
friend bool operator<(const unsigned_bigint& a, const unsigned_bigint& b) {
if (a.size() != b.size()) {
return a.size() < b.size();
}
for (size_t i = a.size(); i-- > 0;) {
if (a[i] != b[i]) return a[i] < b[i];
}
return false;
}
friend bool operator<=(const unsigned_bigint& a, const unsigned_bigint& b) {
return not (b < a);
}
friend bool operator>(const unsigned_bigint& a, const unsigned_bigint& b) {
return b < a;
}
friend bool operator>=(const unsigned_bigint& a, const unsigned_bigint& b) {
return not (a < b);
}
friend unsigned_bigint& operator<<=(unsigned_bigint& a, int shamt) {
if (a) a.insert(a.begin(), shamt, 0);
return a;
}
friend unsigned_bigint operator<<(unsigned_bigint a, int shamt) {
a <<= shamt;
return a;
}
friend unsigned_bigint& operator>>=(unsigned_bigint& a, int shamt) {
a.erase(a.begin(), a.begin() + std::min<int>(shamt, a.size()));
return a;
}
friend unsigned_bigint operator>>(unsigned_bigint a, int shamt) {
a >>= shamt;
return a;
}
unsigned_bigint& operator++() {
return _incr_assign(*this);
}
unsigned_bigint operator++(int) {
unsigned_bigint res = *this;
_incr_assign(*this);
return res;
}
unsigned_bigint& operator--() {
return _decr_assign(*this);
}
unsigned_bigint operator--(int) {
unsigned_bigint res = *this;
_decr_assign(*this);
return res;
}
friend unsigned_bigint& operator+=(unsigned_bigint& a, const unsigned_bigint& b) {
return _add_assign(a, b);
}
friend unsigned_bigint operator+(const unsigned_bigint& a, const unsigned_bigint& b) {
unsigned_bigint c = a;
c += b;
return c;
}
friend unsigned_bigint& operator-=(unsigned_bigint& a, const unsigned_bigint& b) {
return _sub_assign(a, b);
}
friend unsigned_bigint operator-(const unsigned_bigint& a, const unsigned_bigint& b) {
unsigned_bigint c = a;
c -= b;
return c;
}
friend unsigned_bigint& operator*=(unsigned_bigint& a, const unsigned_bigint& b) {
return a = a * b;
}
friend unsigned_bigint operator*(const unsigned_bigint& a, const unsigned_bigint& b) {
return _mul_fft(a, b);
}
static std::pair<unsigned_bigint, unsigned_bigint> divmod(unsigned_bigint a, unsigned_bigint b) {
return _divmod(a, b);
}
friend unsigned_bigint& operator/=(unsigned_bigint& a, const unsigned_bigint& b) {
return a = a / b;
}
friend unsigned_bigint operator/(const unsigned_bigint& a, const unsigned_bigint& b) {
return divmod(a, b).first;
}
friend unsigned_bigint& operator%=(unsigned_bigint& a, const unsigned_bigint& b) {
return a = a % b;
}
friend unsigned_bigint operator%(const unsigned_bigint& a, const unsigned_bigint& b) {
return divmod(a, b).second;
}
#define CAST_PRIMITIVE(type) \
operator type() const { \
type res = 0; \
for (auto it = this->rbegin(); it != this->rend(); ++it) { \
res = res * D + *it; \
} \
return res; \
} \
CAST_PRIMITIVE(unsigned int)
CAST_PRIMITIVE(unsigned long)
CAST_PRIMITIVE(unsigned long long)
CAST_PRIMITIVE(__uint128_t)
CAST_PRIMITIVE(float)
CAST_PRIMITIVE(double)
CAST_PRIMITIVE(long double)
#undef CAST_PRIMITIVE
#define CAST_SIGNED_INT(type) \
operator type() const { \
return static_cast<std::make_unsigned_t<type>>(*this); \
} \
CAST_SIGNED_INT(int)
CAST_SIGNED_INT(long)
CAST_SIGNED_INT(long long)
#undef CAST_SIGNED_INT
operator __int128_t() const {
return static_cast<__uint128_t>(*this);
}
operator std::string() const {
return _to_string();
}
friend std::istream& operator>>(std::istream& in, unsigned_bigint& v) {
std::string s;
in >> s, v = s;
return in;
}
friend std::ostream& operator<<(std::ostream& out, const unsigned_bigint& v) {
return out << v._to_string();
}
private:
using std::vector<int>::vector;
void _check_leading_zeros() const {
assert(this->empty() or this->back());
}
void _cut_leading_zeros() {
while (this->size() and this->back() == 0) this->pop_back();
}
static unsigned_bigint& _incr_assign(unsigned_bigint& a) {
for (int& e : a) {
if (++e != D) return a;
e -= D;
}
a.push_back(1);
return a;
}
static unsigned_bigint& _decr_assign(unsigned_bigint& a) {
assert(a.size());
for (int& e : a) {
if (--e >= 0) break;
e += D;
}
a._cut_leading_zeros();
return a;
}
static unsigned_bigint& _add_assign(unsigned_bigint& a, const unsigned_bigint& b) {
if (a.size() < b.size()) a.resize(b.size());
int carry = 0;
for (size_t i = 0; i < a.size(); ++i) {
if (i >= b.size()) {
if (carry) {
++a[i];
} else break;
} else {
a[i] += b[i] + carry;
}
if (a[i] >= D) {
a[i] -= D;
carry = 1;
} else {
carry = 0;
}
}
if (carry) a.push_back(1);
return a;
}
static unsigned_bigint& _sub_assign(unsigned_bigint& a, const unsigned_bigint& b) {
assert(a.size() >= b.size());
int borrow = 0;
for (size_t i = 0; i < a.size(); ++i) {
if (i >= b.size()) {
if (borrow) {
--a[i];
} else break;
} else {
a[i] -= b[i] + borrow;
}
if (a[i] < 0) {
a[i] += D;
borrow = 1;
} else {
borrow = 0;
}
}
assert(not borrow);
a._cut_leading_zeros();
return a;
}
unsigned_bigint _cut(int l, int r) const {
r = std::min(r, static_cast<int>(this->size()));
unsigned_bigint v = l < r ? unsigned_bigint(this->begin() + l, this->begin() + r) : ZERO;
v._cut_leading_zeros();
return v;
}
template <typename T>
static unsigned_bigint _build(const std::vector<T>& dat) {
unsigned_bigint res;
T carry = 0;
for (auto v : dat) {
carry += v;
res.push_back(carry % D);
carry /= D;
}
while (carry) {
res.push_back(carry % D);
carry /= D;
}
res._cut_leading_zeros();
return res;
}
static unsigned_bigint _mul_naive(const unsigned_bigint& a, const unsigned_bigint& b) {
return _build(suisen::internal::convolution_naive<int, __int128_t>(a, b));
}
static unsigned_bigint _mul_karatsuba(const unsigned_bigint& a, const unsigned_bigint& b) {
if (std::min(a.size(), b.size()) <= 64) {
return _mul_naive(a, b);
}
const int m = std::max(a.size(), b.size()) / 2;
unsigned_bigint lo_a = a._cut(0, m), hi_a = a._cut(m, a.size());
unsigned_bigint lo_b = b._cut(0, m), hi_b = b._cut(m, b.size());
unsigned_bigint lo_c = lo_a * lo_b;
unsigned_bigint hi_c = hi_a * hi_b;
bool neg = true;
unsigned_bigint md_a;
if (hi_a >= lo_a) md_a = hi_a - lo_a;
else md_a = lo_a - hi_a, neg = not neg;
unsigned_bigint md_b;
if (hi_b >= lo_b) md_b = hi_b - lo_b;
else md_b = lo_b - hi_b, neg = not neg;
unsigned_bigint md_ab = md_a * md_b;
unsigned_bigint md_c = (hi_c << m) + lo_c + hi_c + lo_c._cut(m, lo_c.size());
if (neg) md_c -= md_ab;
else md_c += md_ab;
unsigned_bigint c = (md_c << m) + lo_c._cut(0, m);
c._cut_leading_zeros();
return c;
}
static unsigned_bigint _mul_fft(const unsigned_bigint& a, const unsigned_bigint& b) {
if (std::min(a.size(), b.size()) <= 64) {
return _mul_naive(a, b);
}
if (std::max(a.size(), b.size()) <= 200) {
return _mul_karatsuba(a, b);
}
return _build(suisen::convolution_int(a, b));
}
// compare(a, D^k)
static int _compare_powD(const unsigned_bigint& a, int k) {
const int dA = a.size();
if (dA <= k) return -1;
if (dA >= k + 2) return +1;
if (a[k] != 1) return +1;
for (int i = 0; i < k; ++i) {
if (a[i]) return +1;
}
return 0;
}
static unsigned_bigint _powD(int k) {
return ONE << k;
}
static std::pair<unsigned_bigint, unsigned_bigint> _divmod_int(const unsigned_bigint& a, const unsigned_bigint& b) {
assert(b.size() == 1);
const int b0 = b.front();
unsigned_bigint q;
long long r = 0;
for (auto it = a.rbegin(); it != a.rend(); ++it) {
r = r * D + *it;
q.push_back(r / b0);
r %= b0;
}
std::reverse(q.begin(), q.end());
q._cut_leading_zeros();
return { q, r ? unsigned_bigint{ int(r) } : ZERO };
}
static std::pair<unsigned_bigint, unsigned_bigint> _divmod_naive(unsigned_bigint& a, unsigned_bigint& b) {
if (b.size() == 1) {
return _divmod_int(a, b);
}
if (a < b) {
return { ZERO, a };
}
const unsigned_bigint coef{ D / (b.back() + 1) };
a *= coef;
b *= coef;
assert(2 * b.back() >= D);
unsigned_bigint q, r(a.end() - b.size(), a.end());
for (int i = a.size() - b.size(); i >= 0; --i) {
if (r.size() < b.size()) {
q.push_back(0);
} else if (r.size() == b.size()) {
if (r >= b) {
q.push_back(1);
r -= b;
} else {
q.push_back(0);
}
} else {
assert(r.size() == b.size() + 1);
int x = (static_cast<long long>(r.end()[-1]) * D + r.end()[-2]) / b.back();
unsigned_bigint bx = b * unsigned_bigint{ x };
while (bx > r) bx -= b, --x;
while (bx + b <= r) bx += b, ++x;
q.push_back(x);
r = r - bx;
}
if (i) {
r.insert(r.begin(), a[i - 1]);
}
}
std::reverse(q.begin(), q.end());
q._cut_leading_zeros();
r._cut_leading_zeros();
return { q, _divmod_int(r, coef).first };
}
static std::pair<unsigned_bigint, unsigned_bigint> _divmod_naive(const unsigned_bigint& a, const unsigned_bigint& b) {
unsigned_bigint a_ = a, b_ = b;
return _divmod_naive(a_, b_);
}
// floor(D^n/b)
static unsigned_bigint _div_powD(int n, unsigned_bigint b) {
assert(b.size() and 2 * b.back() >= D);
const int dB = b.size();
int k = n - dB;
while (k > 64) k = (k + 1) >> 1;
k = std::min(n, dB + k);
unsigned_bigint c = _divmod_naive(_powD(k), b).first;
unsigned_bigint bc = b * c;
for (; k < n; k = 2 * k - dB) {
// loop invariant: c = floor(D^k/B)
bc.resize(k + 1);
int carry = 0;
for (int i = 0; i < k; ++i) {
bc[i] = D - bc[i] + (i ? carry - 1 : 0);
if (bc[i] >= D) {
bc[i] -= D;
carry = 1;
} else {
carry = 0;
}
}
++bc[k];
c *= bc;
c.erase(c.begin(), c.begin() + dB);
bc = b * c;
if (_compare_powD(bc + b, 2 * k - dB) <= 0) {
++c, bc += b;
}
assert(_compare_powD(bc + b, 2 * k - dB) > 0);
}
// c = floor(D^k/b)
c >>= k - n;
return c;
}
static std::pair<unsigned_bigint, unsigned_bigint> _divmod(unsigned_bigint a, unsigned_bigint b) {
assert(b.size());
if (std::min(static_cast<int>(b.size()), static_cast<int>(a.size()) - static_cast<int>(b.size())) <= 64) {
return _divmod_naive(a, b);
}
if (a < b) {
return { ZERO, a };
}
const unsigned_bigint coef{ D / (b.back() + 1) };
a *= coef;
b *= coef;
assert(2 * b.back() >= D);
const int dA = a.size(), dB = b.size();
if (dA == dB) {
return { ONE, _divmod_int(a - b, coef).first };
}
unsigned_bigint invB = _div_powD(dA, b);
unsigned_bigint q = a * invB;
q.erase(q.begin(), q.begin() + dA);
unsigned_bigint qb = q * b, qb2 = qb + b;
if (qb2 <= a) {
return { ++q, _divmod_int(a - qb2, coef).first };
} else {
return { q, _divmod_int(a - qb, coef).first };
}
}
std::string _to_string() const {
if (this->empty()) return "0";
std::ostringstream oss;
auto it = this->rbegin();
oss << *it;
while (++it != this->rend()) {
oss << std::setw(9) << std::setfill('0') << *it;
}
return oss.str();
}
};
} // namespace suisen
namespace suisen {
struct bigint {
static inline struct { operator bigint() const { return bigint{ unsigned_bigint::ZERO }; }; } const ZERO{};
static inline struct { operator bigint() const { return bigint{ unsigned_bigint::ONE }; }; } const ONE{};
bigint() : _neg(false), _dat{} {}
template <typename T, std::enable_if_t<std::is_integral_v<T>, std::nullptr_t> = nullptr>
bigint(T v) {
_neg = false;
if constexpr (std::is_signed_v<T>) {
if (v < 0) {
_neg = true;
v = -v;
}
}
_dat = unsigned_bigint(v);
}
bigint(const std::string& s) {
if (s.front() == '-') {
_neg = true;
_dat = unsigned_bigint(s.substr(1));
fix_sign();
} else {
_neg = false;
_dat = unsigned_bigint(s);
}
}
bigint(const char* s) : bigint(std::string(s)) {}
bigint(const unsigned_bigint& dat) : _neg(false), _dat(dat) {}
bigint(unsigned_bigint&& dat) : _neg(false), _dat(std::move(dat)) {}
operator bool() const {
return bool(_dat);
}
friend bool operator==(const bigint& a, const bigint& b) {
if (a._neg xor b._neg) {
return false;
} else {
return a._dat == b._dat;
}
}
friend bool operator!=(const bigint& a, const bigint& b) {
return not (a == b);
}
friend bool operator<(const bigint& a, const bigint& b) {
if (a._neg xor b._neg) {
return a._neg;
} else if (a._neg) {
return a._dat > b._dat;
} else {
return a._dat < b._dat;
}
}
friend bool operator<=(const bigint& a, const bigint& b) {
return not (b < a);
}
friend bool operator>(const bigint& a, const bigint& b) {
return b < a;
}
friend bool operator>=(const bigint& a, const bigint& b) {
return not (a < b);
}
friend bigint& operator<<=(bigint& a, int shamt) {
a._dat <<= shamt;
return a;
}
friend bigint operator<<(bigint a, int shamt) {
a <<= shamt;
return a;
}
friend bigint& operator>>=(bigint& a, int shamt) {
a._dat >>= shamt;
a.fix_sign();
return a;
}
friend bigint operator>>(bigint a, int shamt) {
a >>= shamt;
a.fix_sign();
return a;
}
bigint operator+() const {
return *this;
}
bigint operator-() const {
return bigint(_dat, not _neg);
}
bigint& operator++() {
if (_neg) {
--_dat;
fix_sign();
} else {
++_dat;
}
return *this;
}
bigint operator++(int) {
bigint res = *this;
++*this;
return res;
}
bigint& operator--() {
if (_neg) {
++_dat;
} else if (_dat) {
--_dat;
} else {
_neg = true;
_dat = unsigned_bigint::ONE;
}
return *this;
}
bigint operator--(int) {
bigint res = *this;
--*this;
return res;
}
friend bigint& operator+=(bigint& a, const bigint& b) {
if (a._neg xor b._neg) {
if (a._dat >= b._dat) {
a._dat -= b._dat;
} else {
a._dat = b._dat - a._dat;
a._neg = not a._neg;
}
a.fix_sign();
} else {
a._dat += b._dat;
}
return a;
}
friend bigint operator+(const bigint& a, const bigint& b) {
bigint c = a;
c += b;
return c;
}
friend bigint& operator-=(bigint& a, const bigint& b) {
if (a._neg xor b._neg) {
a._dat += b._dat;
} else {
if (a._dat >= b._dat) {
a._dat -= b._dat;
} else {
a._dat = b._dat - a._dat;
a._neg = not a._neg;
}
a.fix_sign();
}
return a;
}
friend bigint operator-(const bigint& a, const bigint& b) {
bigint c = a;
c -= b;
return c;
}
friend bigint& operator*=(bigint& a, const bigint& b) {
return a = a * b;
}
friend bigint operator*(const bigint& a, const bigint& b) {
return bigint(a._dat * b._dat, a._neg xor b._neg);
}
static std::pair<bigint, bigint> divmod(bigint a, bigint b) {
auto [q, r] = unsigned_bigint::divmod(a._dat, b._dat);
return { bigint(std::move(q), a._neg xor b._neg), bigint(std::move(r), a._neg) };
}
friend bigint& operator/=(bigint& a, const bigint& b) {
return a = a / b;
}
friend bigint operator/(const bigint& a, const bigint& b) {
return divmod(a, b).first;
}
friend bigint& operator%=(bigint& a, const bigint& b) {
return a = a % b;
}
friend bigint operator%(const bigint& a, const bigint& b) {
return divmod(a, b).second;
}
#define CAST_PRIMITIVE(type) \
operator type() const { \
type res = _dat; \
return _neg ? -res : res; \
} \
CAST_PRIMITIVE(unsigned int)
CAST_PRIMITIVE(unsigned long)
CAST_PRIMITIVE(unsigned long long)
CAST_PRIMITIVE(__uint128_t)
CAST_PRIMITIVE(float)
CAST_PRIMITIVE(double)
CAST_PRIMITIVE(long double)
#undef CAST_PRIMITIVE
#define CAST_SIGNED_INT(type) \
operator type() const { \
return static_cast<std::make_unsigned_t<type>>(*this); \
} \
CAST_SIGNED_INT(int)
CAST_SIGNED_INT(long)
CAST_SIGNED_INT(long long)
#undef CAST_SIGNED_INT
operator __int128_t() const {
return static_cast<__uint128_t>(*this);
}
operator unsigned_bigint() const {
assert(not _neg);
return _dat;
}
operator std::string() const {
if (_neg) {
return '-' + std::string(_dat);
} else {
return std::string(_dat);
}
}
friend std::istream& operator>>(std::istream& in, bigint& v) {
std::string s;
in >> s, v = s;
return in;
}
friend std::ostream& operator<<(std::ostream& out, const bigint& v) {
return out << std::string(v);
}
private:
bigint(const unsigned_bigint& dat, bool neg) : _neg(neg), _dat(dat) { fix_sign(); }
bigint(unsigned_bigint&& dat, bool neg) : _neg(neg), _dat(std::move(dat)) { fix_sign(); }
bool _neg;
unsigned_bigint _dat;
void fix_sign() {
if (_neg and not _dat) _neg = false;
}
};
} // namespace suisen
#include <cassert>
namespace suisen {
template <typename T, typename U = T>
struct factorial {
factorial() = default;
factorial(int n) { ensure(n); }
static void ensure(const int n) {
int sz = _fac.size();
if (n + 1 <= sz) return;
int new_size = std::max(n + 1, sz * 2);
_fac.resize(new_size), _fac_inv.resize(new_size);
for (int i = sz; i < new_size; ++i) _fac[i] = _fac[i - 1] * i;
_fac_inv[new_size - 1] = U(1) / _fac[new_size - 1];
for (int i = new_size - 1; i > sz; --i) _fac_inv[i - 1] = _fac_inv[i] * i;
}
T fac(const int i) {
ensure(i);
return _fac[i];
}
T operator()(int i) {
return fac(i);
}
U fac_inv(const int i) {
ensure(i);
return _fac_inv[i];
}
U binom(const int n, const int r) {
if (n < 0 or r < 0 or n < r) return 0;
ensure(n);
return _fac[n] * _fac_inv[r] * _fac_inv[n - r];
}
template <typename ...Ds, std::enable_if_t<std::conjunction_v<std::is_integral<Ds>...>, std::nullptr_t> = nullptr>
U polynom(const int n, const Ds& ...ds) {
if (n < 0) return 0;
ensure(n);
int sumd = 0;
U res = _fac[n];
for (int d : { ds... }) {
if (d < 0 or d > n) return 0;
sumd += d;
res *= _fac_inv[d];
}
if (sumd > n) return 0;
res *= _fac_inv[n - sumd];
return res;
}
U perm(const int n, const int r) {
if (n < 0 or r < 0 or n < r) return 0;
ensure(n);
return _fac[n] * _fac_inv[n - r];
}
private:
static std::vector<T> _fac;
static std::vector<U> _fac_inv;
};
template <typename T, typename U>
std::vector<T> factorial<T, U>::_fac{ 1 };
template <typename T, typename U>
std::vector<U> factorial<T, U>::_fac_inv{ 1 };
} // namespace suisen
using suisen::bigint;
mint solve(int N, std::vector<bigint>& A, bigint M) {
suisen::factorial<mint> fact(10000000);
std::vector<bigint> Mt(N + 1);
Mt[N] = M;
for (int i = N - 1; i >= 0; --i) {
Mt[i] = Mt[i + 1] / A[i];
}
std::vector<mint> pd(N + 1);
for (int x = 0; x <= N; ++x) {
auto binom = [](bigint n, int r) -> mint {
if (r < 0 or bigint(r) > n) return 0;
mint n2 = (int) bigint::divmod(n, mint::mod()).second;
mint num = 1, den = 1;
for (int i = 0; i < r; ++i) {
num *= n2 - i;
den *= 1 + i;
}
return num / den;
};
pd[x] = binom(bigint(N) + (Mt[0] - bigint(x)), N);
}
std::vector<int> fac(5000000), ifac(5000000);
for (int i = 0; i < 5000000; ++i) {
fac[i] = fact.fac(i).val();
ifac[i] = fact.fac_inv(i).val();
}
for (int t = 1; t <= N; ++t) {
const int At = A[t - 1];
// x_i,...,x_n < At
const int u = N - t;
const int Rt = Mt[t] % bigint(At);
std::vector<mint> a(N + 1);
for (int i = 0; i <= N; ++i) {
a[i] = (i & 1 ? -1 : 1) * fact.binom(u + 1, i);
}
std::reverse(pd.begin(), pd.end());
std::vector<mint> f = atcoder::convolution(a, pd);
f.resize(N + 1);
std::reverse(f.begin(), f.end());
std::vector<mint> dp(N + 1);
for (int i = 0; i <= N; ++i) {
const int T = At * i + Rt;
const int maxk = std::min(N, T);
const mint fi = f[i];
for (int k = 0; k <= maxk; ++k) {
dp[k] += (long long) (fac[T + u - k]) * ifac[T - k] * fi;
}
}
for (int k = 0; k <= N; ++k) {
dp[k] *= ifac[u];
}
pd.swap(dp);
}
return pd[0];
}
int main() {
int N;
std::cin >> N;
--N;
std::vector<bigint> A(N);
for (auto& e : A) std::cin >> e;
std::reverse(A.begin(), A.end());
bigint M;
std::cin >> M;
std::cout << solve(N, A, M).val() << std::endl;
}