結果
| 問題 |
No.754 畳み込みの和
|
| コンテスト | |
| ユーザー |
 stoq
|
| 提出日時 | 2020-12-20 05:34:29 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 28,159 bytes |
| コンパイル時間 | 3,563 ms |
| コンパイル使用メモリ | 243,124 KB |
| 最終ジャッジ日時 | 2025-01-17 04:26:41 |
|
ジャッジサーバーID （参考情報） |
judge2 / judge5 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | WA * 3 |
ソースコード
#define MOD_TYPE 1
#pragma region Macros
#include <bits/stdc++.h>
using namespace std;
#if 0
#include <boost/multiprecision/cpp_int.hpp>
#include <boost/multiprecision/cpp_dec_float.hpp>
using Int = boost::multiprecision::cpp_int;
using lld = boost::multiprecision::cpp_dec_float_100;
#endif
#if 1
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#endif
using ll = long long int;
using ld = long double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using pld = pair<ld, ld>;
template <typename Q_type>
using smaller_queue = priority_queue<Q_type, vector<Q_type>, greater<Q_type>>;
constexpr ll MOD = (MOD_TYPE == 1 ? (ll)(1e9 + 7) : 998244353);
constexpr int INF = (int)1e9 + 10;
constexpr ll LINF = (ll)4e18;
constexpr double PI = acos(-1.0);
constexpr double EPS = 1e-7;
constexpr int Dx[] = {0, 0, -1, 1, -1, 1, -1, 1, 0};
constexpr int Dy[] = {1, -1, 0, 0, -1, -1, 1, 1, 0};
#define REP(i, m, n) for (ll i = m; i < (ll)(n); ++i)
#define rep(i, n) REP(i, 0, n)
#define REPI(i, m, n) for (int i = m; i < (int)(n); ++i)
#define repi(i, n) REPI(i, 0, n)
#define MP make_pair
#define MT make_tuple
#define YES(n) cout << ((n) ? "YES" : "NO") << "\n"
#define Yes(n) cout << ((n) ? "Yes" : "No") << "\n"
#define possible(n) cout << ((n) ? "possible" : "impossible") << "\n"
#define Possible(n) cout << ((n) ? "Possible" : "Impossible") << "\n"
#define all(v) v.begin(), v.end()
#define NP(v) next_permutation(all(v))
#define dbg(x) cerr << #x << ":" << x << "\n";
struct io_init
{
io_init()
{
cin.tie(0);
ios::sync_with_stdio(false);
cout << setprecision(30) << setiosflags(ios::fixed);
};
} io_init;
template <typename T>
inline bool chmin(T &a, T b)
{
if (a > b)
{
a = b;
return true;
}
return false;
}
template <typename T>
inline bool chmax(T &a, T b)
{
if (a < b)
{
a = b;
return true;
}
return false;
}
inline ll CEIL(ll a, ll b)
{
return (a + b - 1) / b;
}
template <typename A, size_t N, typename T>
inline void Fill(A (&array)[N], const T &val)
{
fill((T *)array, (T *)(array + N), val);
}
template <typename T, typename U>
constexpr istream &operator>>(istream &is, pair<T, U> &p) noexcept
{
is >> p.first >> p.second;
return is;
}
template <typename T, typename U>
constexpr ostream &operator<<(ostream &os, pair<T, U> &p) noexcept
{
os << p.first << " " << p.second;
return os;
}
#pragma endregion
// internal_bit
namespace atcoder
{
namespace internal
{
// @param n `0 <= n`
// @return minimum non-negative `x` s.t. `n <= 2**x`
int ceil_pow2(int n)
{
int x = 0;
while ((1U << x) < (unsigned int)(n))
x++;
return x;
}
// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
int bsf(unsigned int n)
{
#ifdef _MSC_VER
unsigned long index;
_BitScanForward(&index, n);
return index;
#else
return __builtin_ctz(n);
#endif
}
} // namespace internal
} // namespace atcoder
// internal_type_traits
namespace atcoder
{
namespace internal
{
#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value ||
std::is_same<T, __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int128 =
typename std::conditional<std::is_same<T, __uint128_t>::value ||
std::is_same<T, unsigned __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using make_unsigned_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value,
__uint128_t,
unsigned __int128>;
template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
is_signed_int128<T>::value ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
std::is_signed<T>::value) ||
is_signed_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<(is_integral<T>::value &&
std::is_unsigned<T>::value) ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<
is_signed_int128<T>::value,
make_unsigned_int128<T>,
typename std::conditional<std::is_signed<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type>::type;
#else
template <class T>
using is_integral = typename std::is_integral<T>;
template <class T>
using is_signed_int =
typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<is_integral<T>::value &&
std::is_unsigned<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type;
#endif
template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
template <class T>
using to_unsigned_t = typename to_unsigned<T>::type;
} // namespace internal
} // namespace atcoder
// internal_math
namespace atcoder
{
namespace internal
{
// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m)
{
x %= m;
if (x < 0)
x += m;
return x;
}
// Fast modular multiplication by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett
{
unsigned int _m;
unsigned long long im;
// @param m `1 <= m < 2^31`
barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
// @return m
unsigned int umod() const { return _m; }
// @param a `0 <= a < m`
// @param b `0 <= b < m`
// @return `a * b % m`
unsigned int mul(unsigned int a, unsigned int b) const
{
// [1] m = 1
// a = b = im = 0, so okay
// [2] m >= 2
// im = ceil(2^64 / m)
// -> im * m = 2^64 + r (0 <= r < m)
// let z = a*b = c*m + d (0 <= c, d < m)
// a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
// c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2
// ((ab * im) >> 64) == c or c + 1
unsigned long long z = a;
z *= b;
#ifdef _MSC_VER
unsigned long long x;
_umul128(z, im, &x);
#else
unsigned long long x =
(unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
unsigned int v = (unsigned int)(z - x * _m);
if (_m <= v)
v += _m;
return v;
}
};
// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr long long pow_mod_constexpr(long long x, long long n, int m)
{
if (m == 1)
return 0;
unsigned int _m = (unsigned int)(m);
unsigned long long r = 1;
unsigned long long y = safe_mod(x, m);
while (n)
{
if (n & 1)
r = (r * y) % _m;
y = (y * y) % _m;
n >>= 1;
}
return r;
}
// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
constexpr bool is_prime_constexpr(int n)
{
if (n <= 1)
return false;
if (n == 2 || n == 7 || n == 61)
return true;
if (n % 2 == 0)
return false;
long long d = n - 1;
while (d % 2 == 0)
d /= 2;
constexpr long long bases[3] = {2, 7, 61};
for (long long a : bases)
{
long long t = d;
long long y = pow_mod_constexpr(a, t, n);
while (t != n - 1 && y != 1 && y != n - 1)
{
y = y * y % n;
t <<= 1;
}
if (y != n - 1 && t % 2 == 0)
{
return false;
}
}
return true;
}
template <int n>
constexpr bool is_prime = is_prime_constexpr(n);
// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b)
{
a = safe_mod(a, b);
if (a == 0)
return {b, 0};
// Contracts:
// [1] s - m0 * a = 0 (mod b)
// [2] t - m1 * a = 0 (mod b)
// [3] s * |m1| + t * |m0| <= b
long long s = b, t = a;
long long m0 = 0, m1 = 1;
while (t)
{
long long u = s / t;
s -= t * u;
m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b
// [3]:
// (s - t * u) * |m1| + t * |m0 - m1 * u|
// <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
// = s * |m1| + t * |m0| <= b
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
// by [3]: |m0| <= b/g
// by g != b: |m0| < b/g
if (m0 < 0)
m0 += b / s;
return {s, m0};
}
// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
constexpr int primitive_root_constexpr(int m)
{
if (m == 2)
return 1;
if (m == 167772161)
return 3;
if (m == 469762049)
return 3;
if (m == 754974721)
return 11;
if (m == 998244353)
return 3;
int divs[20] = {};
divs[0] = 2;
int cnt = 1;
int x = (m - 1) / 2;
while (x % 2 == 0)
x /= 2;
for (int i = 3; (long long)(i)*i <= x; i += 2)
{
if (x % i == 0)
{
divs[cnt++] = i;
while (x % i == 0)
{
x /= i;
}
}
}
if (x > 1)
{
divs[cnt++] = x;
}
for (int g = 2;; g++)
{
bool ok = true;
for (int i = 0; i < cnt; i++)
{
if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1)
{
ok = false;
break;
}
}
if (ok)
return g;
}
}
template <int m>
constexpr int primitive_root = primitive_root_constexpr(m);
} // namespace internal
} // namespace atcoder
// modint
namespace atcoder
{
namespace internal
{
struct modint_base
{
};
struct static_modint_base : modint_base
{
};
template <class T>
using is_modint = std::is_base_of<modint_base, T>;
template <class T>
using is_modint_t = std::enable_if_t<is_modint<T>::value>;
} // namespace internal
template <int m, std::enable_if_t<(1 <= m)> * = nullptr>
struct static_modint : internal::static_modint_base
{
using mint = static_modint;
public:
static constexpr int mod() { return m; }
static mint raw(int v)
{
mint x;
x._v = v;
return x;
}
static_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T> * = nullptr>
static_modint(T v)
{
long long x = (long long)(v % (long long)(umod()));
if (x < 0)
x += umod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T> * = nullptr>
static_modint(T v)
{
_v = (unsigned int)(v % umod());
}
static_modint(bool v) { _v = ((unsigned int)(v) % umod()); }
unsigned int val() const { return _v; }
mint &operator++()
{
_v++;
if (_v == umod())
_v = 0;
return *this;
}
mint &operator--()
{
if (_v == 0)
_v = umod();
_v--;
return *this;
}
mint operator++(int)
{
mint result = *this;
++*this;
return result;
}
mint operator--(int)
{
mint result = *this;
--*this;
return result;
}
mint &operator+=(const mint &rhs)
{
_v += rhs._v;
if (_v >= umod())
_v -= umod();
return *this;
}
mint &operator-=(const mint &rhs)
{
_v -= rhs._v;
if (_v >= umod())
_v += umod();
return *this;
}
mint &operator*=(const mint &rhs)
{
unsigned long long z = _v;
z *= rhs._v;
_v = (unsigned int)(z % umod());
return *this;
}
mint &operator/=(const mint &rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const
{
assert(0 <= n);
mint x = *this, r = 1;
while (n)
{
if (n & 1)
r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const
{
if (prime)
{
assert(_v);
return pow(umod() - 2);
}
else
{
auto eg = internal::inv_gcd(_v, m);
assert(eg.first == 1);
return eg.second;
}
}
friend mint operator+(const mint &lhs, const mint &rhs)
{
return mint(lhs) += rhs;
}
friend mint operator-(const mint &lhs, const mint &rhs)
{
return mint(lhs) -= rhs;
}
friend mint operator*(const mint &lhs, const mint &rhs)
{
return mint(lhs) *= rhs;
}
friend mint operator/(const mint &lhs, const mint &rhs)
{
return mint(lhs) /= rhs;
}
friend bool operator==(const mint &lhs, const mint &rhs)
{
return lhs._v == rhs._v;
}
friend bool operator!=(const mint &lhs, const mint &rhs)
{
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static constexpr unsigned int umod() { return m; }
static constexpr bool prime = internal::is_prime<m>;
};
template <int id>
struct dynamic_modint : internal::modint_base
{
using mint = dynamic_modint;
public:
static int mod() { return (int)(bt.umod()); }
static void set_mod(int m)
{
assert(1 <= m);
bt = internal::barrett(m);
}
static mint raw(int v)
{
mint x;
x._v = v;
return x;
}
dynamic_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T> * = nullptr>
dynamic_modint(T v)
{
long long x = (long long)(v % (long long)(mod()));
if (x < 0)
x += mod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T> * = nullptr>
dynamic_modint(T v)
{
_v = (unsigned int)(v % mod());
}
dynamic_modint(bool v) { _v = ((unsigned int)(v) % mod()); }
unsigned int val() const { return _v; }
mint &operator++()
{
_v++;
if (_v == umod())
_v = 0;
return *this;
}
mint &operator--()
{
if (_v == 0)
_v = umod();
_v--;
return *this;
}
mint operator++(int)
{
mint result = *this;
++*this;
return result;
}
mint operator--(int)
{
mint result = *this;
--*this;
return result;
}
mint &operator+=(const mint &rhs)
{
_v += rhs._v;
if (_v >= umod())
_v -= umod();
return *this;
}
mint &operator-=(const mint &rhs)
{
_v += mod() - rhs._v;
if (_v >= umod())
_v -= umod();
return *this;
}
mint &operator*=(const mint &rhs)
{
_v = bt.mul(_v, rhs._v);
return *this;
}
mint &operator/=(const mint &rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const
{
assert(0 <= n);
mint x = *this, r = 1;
while (n)
{
if (n & 1)
r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const
{
auto eg = internal::inv_gcd(_v, mod());
assert(eg.first == 1);
return eg.second;
}
friend mint operator+(const mint &lhs, const mint &rhs)
{
return mint(lhs) += rhs;
}
friend mint operator-(const mint &lhs, const mint &rhs)
{
return mint(lhs) -= rhs;
}
friend mint operator*(const mint &lhs, const mint &rhs)
{
return mint(lhs) *= rhs;
}
friend mint operator/(const mint &lhs, const mint &rhs)
{
return mint(lhs) /= rhs;
}
friend bool operator==(const mint &lhs, const mint &rhs)
{
return lhs._v == rhs._v;
}
friend bool operator!=(const mint &lhs, const mint &rhs)
{
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static internal::barrett bt;
static unsigned int umod() { return bt.umod(); }
};
template <int id>
internal::barrett dynamic_modint<id>::bt = 998244353;
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
namespace internal
{
template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;
template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;
template <class>
struct is_dynamic_modint : public std::false_type
{
};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type
{
};
template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;
} // namespace internal
} // namespace atcoder
// convolution
namespace atcoder
{
namespace internal
{
template <class mint, internal::is_static_modint_t<mint> * = nullptr>
void butterfly(std::vector<mint> &a)
{
static constexpr int g = internal::primitive_root<mint::mod()>;
int n = int(a.size());
int h = internal::ceil_pow2(n);
static bool first = true;
static mint sum_e[30]; // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i]
if (first)
{
first = false;
mint es[30], ies[30]; // es[i]^(2^(2+i)) == 1
int cnt2 = bsf(mint::mod() - 1);
mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
for (int i = cnt2; i >= 2; i--)
{
// e^(2^i) == 1
es[i - 2] = e;
ies[i - 2] = ie;
e *= e;
ie *= ie;
}
mint now = 1;
for (int i = 0; i <= cnt2 - 2; i++)
{
sum_e[i] = es[i] * now;
now *= ies[i];
}
}
for (int ph = 1; ph <= h; ph++)
{
int w = 1 << (ph - 1), p = 1 << (h - ph);
mint now = 1;
for (int s = 0; s < w; s++)
{
int offset = s << (h - ph + 1);
for (int i = 0; i < p; i++)
{
auto l = a[i + offset];
auto r = a[i + offset + p] * now;
a[i + offset] = l + r;
a[i + offset + p] = l - r;
}
now *= sum_e[bsf(~(unsigned int)(s))];
}
}
}
template <class mint, internal::is_static_modint_t<mint> * = nullptr>
void butterfly_inv(std::vector<mint> &a)
{
static constexpr int g = internal::primitive_root<mint::mod()>;
int n = int(a.size());
int h = internal::ceil_pow2(n);
static bool first = true;
static mint sum_ie[30]; // sum_ie[i] = es[0] * ... * es[i - 1] * ies[i]
if (first)
{
first = false;
mint es[30], ies[30]; // es[i]^(2^(2+i)) == 1
int cnt2 = bsf(mint::mod() - 1);
mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
for (int i = cnt2; i >= 2; i--)
{
// e^(2^i) == 1
es[i - 2] = e;
ies[i - 2] = ie;
e *= e;
ie *= ie;
}
mint now = 1;
for (int i = 0; i <= cnt2 - 2; i++)
{
sum_ie[i] = ies[i] * now;
now *= es[i];
}
}
for (int ph = h; ph >= 1; ph--)
{
int w = 1 << (ph - 1), p = 1 << (h - ph);
mint inow = 1;
for (int s = 0; s < w; s++)
{
int offset = s << (h - ph + 1);
for (int i = 0; i < p; i++)
{
auto l = a[i + offset];
auto r = a[i + offset + p];
a[i + offset] = l + r;
a[i + offset + p] =
(unsigned long long)(mint::mod() + l.val() - r.val()) *
inow.val();
}
inow *= sum_ie[bsf(~(unsigned int)(s))];
}
}
}
} // namespace internal
template <class mint, internal::is_static_modint_t<mint> * = nullptr>
std::vector<mint> convolution(std::vector<mint> a, std::vector<mint> b)
{
int n = int(a.size()), m = int(b.size());
if (!n || !m)
return {};
if (std::min(n, m) <= 60)
{
if (n < m)
{
std::swap(n, m);
std::swap(a, b);
}
std::vector<mint> ans(n + m - 1);
for (int i = 0; i < n; i++)
{
for (int j = 0; j < m; j++)
{
ans[i + j] += a[i] * b[j];
}
}
return ans;
}
int z = 1 << internal::ceil_pow2(n + m - 1);
a.resize(z);
internal::butterfly(a);
b.resize(z);
internal::butterfly(b);
for (int i = 0; i < z; i++)
{
a[i] *= b[i];
}
internal::butterfly_inv(a);
a.resize(n + m - 1);
mint iz = mint(z).inv();
for (int i = 0; i < n + m - 1; i++)
a[i] *= iz;
return a;
}
template <unsigned int mod = 998244353,
class T,
std::enable_if_t<internal::is_integral<T>::value> * = nullptr>
std::vector<T> convolution(const std::vector<T> &a, const std::vector<T> &b)
{
int n = int(a.size()), m = int(b.size());
if (!n || !m)
return {};
using mint = static_modint<mod>;
std::vector<mint> a2(n), b2(m);
for (int i = 0; i < n; i++)
{
a2[i] = mint(a[i]);
}
for (int i = 0; i < m; i++)
{
b2[i] = mint(b[i]);
}
auto c2 = convolution(move(a2), move(b2));
std::vector<T> c(n + m - 1);
for (int i = 0; i < n + m - 1; i++)
{
c[i] = c2[i].val();
}
return c;
}
std::vector<long long> convolution_ll(const std::vector<long long> &a,
const std::vector<long long> &b)
{
int n = int(a.size()), m = int(b.size());
if (!n || !m)
return {};
static constexpr unsigned long long MOD1 = 754974721; // 2^24
static constexpr unsigned long long MOD2 = 167772161; // 2^25
static constexpr unsigned long long MOD3 = 469762049; // 2^26
static constexpr unsigned long long M2M3 = MOD2 * MOD3;
static constexpr unsigned long long M1M3 = MOD1 * MOD3;
static constexpr unsigned long long M1M2 = MOD1 * MOD2;
static constexpr unsigned long long M1M2M3 = MOD1 * MOD2 * MOD3;
static constexpr unsigned long long i1 =
internal::inv_gcd(MOD2 * MOD3, MOD1).second;
static constexpr unsigned long long i2 =
internal::inv_gcd(MOD1 * MOD3, MOD2).second;
static constexpr unsigned long long i3 =
internal::inv_gcd(MOD1 * MOD2, MOD3).second;
auto c1 = convolution<MOD1>(a, b);
auto c2 = convolution<MOD2>(a, b);
auto c3 = convolution<MOD3>(a, b);
std::vector<long long> c(n + m - 1);
for (int i = 0; i < n + m - 1; i++)
{
unsigned long long x = 0;
x += (c1[i] * i1) % MOD1 * M2M3;
x += (c2[i] * i2) % MOD2 * M1M3;
x += (c3[i] * i3) % MOD3 * M1M2;
// B = 2^63, -B <= x, r(real value) < B
// (x, x - M, x - 2M, or x - 3M) = r (mod 2B)
// r = c1[i] (mod MOD1)
// focus on MOD1
// r = x, x - M', x - 2M', x - 3M' (M' = M % 2^64) (mod 2B)
// r = x,
// x - M' + (0 or 2B),
// x - 2M' + (0, 2B or 4B),
// x - 3M' + (0, 2B, 4B or 6B) (without mod!)
// (r - x) = 0, (0)
// - M' + (0 or 2B), (1)
// -2M' + (0 or 2B or 4B), (2)
// -3M' + (0 or 2B or 4B or 6B) (3) (mod MOD1)
// we checked that
// ((1) mod MOD1) mod 5 = 2
// ((2) mod MOD1) mod 5 = 3
// ((3) mod MOD1) mod 5 = 4
long long diff =
c1[i] - internal::safe_mod((long long)(x), (long long)(MOD1));
if (diff < 0)
diff += MOD1;
static constexpr unsigned long long offset[5] = {
0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3};
x -= offset[diff % 5];
c[i] = x;
}
return c;
}
} // namespace atcoder
#pragma region mint
template <int MOD>
struct Fp
{
long long val;
constexpr Fp(long long v = 0) noexcept : val(v % MOD)
{
if (val < 0)
v += MOD;
}
constexpr int getmod()
{
return MOD;
}
constexpr Fp operator-() const noexcept
{
return val ? MOD - val : 0;
}
constexpr Fp operator+(const Fp &r) const noexcept
{
return Fp(*this) += r;
}
constexpr Fp operator-(const Fp &r) const noexcept
{
return Fp(*this) -= r;
}
constexpr Fp operator*(const Fp &r) const noexcept
{
return Fp(*this) *= r;
}
constexpr Fp operator/(const Fp &r) const noexcept
{
return Fp(*this) /= r;
}
constexpr Fp &operator+=(const Fp &r) noexcept
{
val += r.val;
if (val >= MOD)
val -= MOD;
return *this;
}
constexpr Fp &operator-=(const Fp &r) noexcept
{
val -= r.val;
if (val < 0)
val += MOD;
return *this;
}
constexpr Fp &operator*=(const Fp &r) noexcept
{
val = val * r.val % MOD;
if (val < 0)
val += MOD;
return *this;
}
constexpr Fp &operator/=(const Fp &r) noexcept
{
long long a = r.val, b = MOD, u = 1, v = 0;
while (b)
{
long long t = a / b;
a -= t * b;
swap(a, b);
u -= t * v;
swap(u, v);
}
val = val * u % MOD;
if (val < 0)
val += MOD;
return *this;
}
constexpr bool operator==(const Fp &r) const noexcept
{
return this->val == r.val;
}
constexpr bool operator!=(const Fp &r) const noexcept
{
return this->val != r.val;
}
friend constexpr ostream &operator<<(ostream &os, const Fp<MOD> &x) noexcept
{
return os << x.val;
}
friend constexpr istream &operator>>(istream &is, Fp<MOD> &x) noexcept
{
return is >> x.val;
}
};
Fp<MOD> modpow(const Fp<MOD> &a, long long n) noexcept
{
if (n == 0)
return 1;
auto t = modpow(a, n / 2);
t = t * t;
if (n & 1)
t = t * a;
return t;
}
using mint = Fp<MOD>;
#pragma endregion
void solve()
{
int n;
cin >> n;
vector<ll> a(n + 1), b(n + 1);
rep(i, n + 1) cin >> a[i];
rep(i, n + 1) cin >> b[i];
auto c = atcoder::convolution<MOD>(a, b);
mint sum = 0;
rep(i, n + 1) sum += c[i];
cout << sum << "\n";
}
int main()
{
solve();
}