結果
| 問題 | No.1068 #いろいろな色 / Red and Blue and more various colors (Hard) |
| ユーザー |
 keijak
|
| 提出日時 | 2020-10-23 07:17:00 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 34,860 bytes |
| コンパイル時間 | 3,957 ms |
| コンパイル使用メモリ | 255,192 KB |
| 実行使用メモリ | 364,684 KB |
| 最終ジャッジ日時 | 2024-07-21 09:45:48 |
| 合計ジャッジ時間 | 11,184 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 | 2 ms
10,624 KB |
| testcase_01 | AC | 2 ms
5,376 KB |
| testcase_02 | AC | 2 ms
5,376 KB |
| testcase_03 | AC | 334 ms
17,544 KB |
| testcase_04 | AC | 236 ms
15,296 KB |
| testcase_05 | AC | 287 ms
16,224 KB |
| testcase_06 | AC | 194 ms
14,196 KB |
| testcase_07 | AC | 190 ms
14,052 KB |
| testcase_08 | AC | 278 ms
16,232 KB |
| testcase_09 | AC | 329 ms
17,704 KB |
| testcase_10 | AC | 102 ms
11,988 KB |
| testcase_11 | AC | 213 ms
14,044 KB |
| testcase_12 | AC | 100 ms
11,844 KB |
| testcase_13 | TLE | - |
| testcase_14 | -- | - |
| testcase_15 | -- | - |
| testcase_16 | -- | - |
| testcase_17 | -- | - |
| testcase_18 | -- | - |
| testcase_19 | -- | - |
| testcase_20 | -- | - |
| testcase_21 | -- | - |
| testcase_22 | -- | - |
| testcase_23 | -- | - |
| testcase_24 | -- | - |
| testcase_25 | -- | - |
| testcase_26 | -- | - |
| testcase_27 | -- | - |
| testcase_28 | -- | - |
| testcase_29 | -- | - |
| testcase_30 | -- | - |
| testcase_31 | -- | - |
ソースコード
#include <bits/stdc++.h>
#include <algorithm>
#include <array>
#ifdef _MSC_VER
#include <intrin.h>
#endif
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
#include <utility>
#ifdef _MSC_VER
#include <intrin.h>
#endif
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
#include <cassert>
#include <numeric>
#include <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
#include <cassert>
#include <numeric>
#include <type_traits>
#ifdef _MSC_VER
#include <intrin.h>
#endif
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
#include <cassert>
#include <type_traits>
#include <vector>
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
using i64 = long long;
using u64 = unsigned long long;
#define REP(i, n) for (int i = 0, REP_N_ = int(n); i < REP_N_; ++i)
#define ALL(x) std::begin(x), std::end(x)
template <class T>
inline bool chmax(T &a, T b) {
return a < b and ((a = std::move(b)), true);
}
template <class T>
inline bool chmin(T &a, T b) {
return a > b and ((a = std::move(b)), true);
}
template <typename T>
using V = std::vector<T>;
template <typename T>
std::istream &operator>>(std::istream &is, std::vector<T> &a) {
for (auto &x : a) is >> x;
return is;
}
template <typename Container>
std::ostream &pprint(const Container &a, std::string_view sep = " ",
std::string_view ends = "\n", std::ostream *os = nullptr) {
if (os == nullptr) os = &std::cout;
auto b = std::begin(a), e = std::end(a);
for (auto it = std::begin(a); it != e; ++it) {
if (it != b) *os << sep;
*os << *it;
}
return *os << ends;
}
template <typename T, typename = void>
struct is_iterable : std::false_type {};
template <typename T>
struct is_iterable<T, std::void_t<decltype(std::begin(std::declval<T>())),
decltype(std::end(std::declval<T>()))>>
: std::true_type {};
template <typename T,
typename = std::enable_if_t<is_iterable<T>::value &&
!std::is_same<T, std::string>::value>>
std::ostream &operator<<(std::ostream &os, const T &a) {
return pprint(a, ", ", "", &(os << "{")) << "}";
}
template <typename T, typename U>
std::ostream &operator<<(std::ostream &os, const std::pair<T, U> &a) {
return os << "(" << a.first << ", " << a.second << ")";
}
#ifdef ENABLE_DEBUG
template <typename T>
void pdebug(const T &value) {
std::cerr << value;
}
template <typename T, typename... Ts>
void pdebug(const T &value, const Ts &... args) {
pdebug(value);
std::cerr << ", ";
pdebug(args...);
}
#define DEBUG(...) \
do { \
std::cerr << " \033[33m (L" << __LINE__ << ") "; \
std::cerr << #__VA_ARGS__ << ":\033[0m "; \
pdebug(__VA_ARGS__); \
std::cerr << std::endl; \
} while (0)
#else
#define pdebug(...)
#define DEBUG(...)
#endif
using namespace std;
// Formal Power Series (dense format).
template <typename T, int DMAX>
struct DenseFPS {
// Coefficients of terms from x^0 to x^DMAX.
std::vector<T> coeff_;
DenseFPS() : coeff_(DMAX + 1) {} // zero-initialized
explicit DenseFPS(std::vector<T> c) : coeff_(std::move(c)) {
assert((int)coeff_.size() == DMAX + 1);
}
DenseFPS(const DenseFPS &other) : coeff_(other.coeff_) {}
DenseFPS(DenseFPS &&other) : coeff_(std::move(other.coeff_)) {}
DenseFPS &operator=(const DenseFPS &other) {
coeff_ = other.coeff_;
return *this;
}
DenseFPS &operator=(DenseFPS &&other) {
coeff_ = std::move(other.coeff_);
return *this;
}
static constexpr int size() { return DMAX + 1; }
// Returns the coefficient of x^d.
const T &operator[](int d) const { return coeff_[d]; }
DenseFPS &operator+=(const T &scalar) {
coeff_[0] += scalar;
return *this;
}
friend DenseFPS operator+(const DenseFPS &x, const T &scalar) {
DenseFPS res = x;
res += scalar;
return res;
}
DenseFPS &operator+=(const DenseFPS &other) {
for (int i = 0; i < size(); ++i) coeff_[i] += other[i];
return *this;
}
friend DenseFPS operator+(const DenseFPS &x, const DenseFPS &y) {
DenseFPS res = x;
res += y;
return res;
}
DenseFPS &operator-=(const DenseFPS &other) {
for (int i = 0; i < size(); ++i) coeff_[i] -= other[i];
return *this;
}
friend DenseFPS operator-(const DenseFPS &x, const DenseFPS &y) {
DenseFPS res = x;
res -= y;
return res;
}
DenseFPS &operator*=(const T &scalar) {
for (auto &x : coeff_) x *= scalar;
return *this;
}
friend DenseFPS operator*(const DenseFPS &x, const T &scalar) {
DenseFPS res = x;
res *= scalar;
return res;
}
DenseFPS &operator*=(const DenseFPS &other) {
*this = this->mul_naive(other);
return *this;
}
friend DenseFPS operator*(const DenseFPS &x, const DenseFPS &y) {
return x.mul_naive(y);
}
private:
// Naive multiplication. O(N^2)
DenseFPS mul_naive(const DenseFPS &other) const {
DenseFPS res;
for (int i = 0; i < size(); ++i) {
for (int j = 0; i + j < size(); ++j) {
res.coeff_[i + j] += (*this)[i] * other[j];
}
}
return res;
}
};
namespace fps {
// Fast polynomial multiplication by single NTT.
template <typename ModInt, int DMAX>
DenseFPS<ModInt, DMAX> mul_ntt(const DenseFPS<ModInt, DMAX> &x,
const DenseFPS<ModInt, DMAX> &y) {
static_assert(ModInt::mod() != 1'000'000'007); // Must be a NTT-friendly MOD!
auto z = atcoder::convolution(x.coeff_, y.coeff_);
z.resize(DMAX + 1); // Maybe shrink.
return DenseFPS<ModInt, DMAX>(std::move(z));
}
// Polynomial multiplication by NTT + Garner (arbitrary mod).
template <typename ModInt, int DMAX>
DenseFPS<ModInt, DMAX> mul_mod(const DenseFPS<ModInt, DMAX> &x,
const DenseFPS<ModInt, DMAX> &y) {
std::vector<i64> xll(x.size()), yll(y.size());
for (int i = 0; i < x.size(); ++i) {
xll[i] = x[i].val();
}
for (int i = 0; i < y.size(); ++i) {
yll[i] = y[i].val();
}
auto zll = atcoder::convolution_ll(xll, yll);
DenseFPS<ModInt, DMAX> res;
int n = std::min<int>(res.size(), zll.size());
for (int i = 0; i < n; ++i) {
res.coeff_[i] = zll[i];
}
return res;
}
// Polynomial multiplication by NTT + Garner (long long).
template <int DMAX>
DenseFPS<i64, DMAX> mul_ll(const DenseFPS<i64, DMAX> &x,
const DenseFPS<i64, DMAX> &y) {
auto z = atcoder::convolution_ll(x.coeff_, y.coeff_);
z.resize(DMAX + 1); // Maybe shrink.
return DenseFPS<i64, DMAX>(std::move(z));
}
template <typename T, int DMAX, typename Func>
DenseFPS<T, DMAX> pow_generic(const DenseFPS<T, DMAX> &x, u64 t, Func mulfunc) {
DenseFPS<T, DMAX> base = x, res;
res.coeff_[0] = 1;
while (t) {
if (t & 1) res = mulfunc(res, base);
base = mulfunc(base, base);
t >>= 1;
}
return res;
}
template <typename ModInt, int DMAX>
DenseFPS<ModInt, DMAX> pow_ntt(const DenseFPS<ModInt, DMAX> &x, u64 t) {
return pow_generic(x, t, mul_ntt);
}
template <typename ModInt, int DMAX>
DenseFPS<ModInt, DMAX> pow_mod(const DenseFPS<ModInt, DMAX> &x, u64 t) {
return pow_generic(x, t, mul_mod);
}
template <int DMAX>
DenseFPS<i64, DMAX> pow_ll(const DenseFPS<i64, DMAX> &x, u64 t) {
return pow_generic(x, t, mul_ll);
}
} // namespace fps
// Formal Power Series (sparse format).
template <typename T>
struct SparseFPS {
int size_;
std::vector<int> degree_;
std::vector<T> coeff_;
SparseFPS() : size_(0) {}
explicit SparseFPS(std::vector<std::pair<int, T>> terms)
: size_(terms.size()), degree_(size_), coeff_(size_) {
// Sort by degree_ in ascending order.
sort(terms.begin(), terms.end());
for (int i = 0; i < size_; ++i) {
degree_[i] = terms[i].first;
coeff_[i] = terms[i].second;
}
}
inline int size() const { return size_; }
inline int degree(int i) const { return degree_[i]; }
inline const T &coeff(int i) const { return coeff_[i]; }
int DMAX() const { return (size_ == 0) ? 0 : degree_.back(); }
void emplace_back(int d, T c) {
if (not degree_.empty()) {
assert(d > degree_.back());
}
degree_.push_back(std::move(d));
coeff_.push_back(std::move(c));
++size_;
}
// Returns the coefficient of x^d.
T operator[](int d) const {
auto it = std::lower_bound(degree_.begin(), degree_.end(), d);
if (it == degree_.end() or *it != d) return (T)(0);
int j = std::distance(degree_.begin(), it);
return coeff_[j];
}
SparseFPS &operator+=(const T &scalar) {
for (auto &x : coeff_) x += scalar;
return *this;
}
friend SparseFPS operator+(const SparseFPS &x, const T &scalar) {
SparseFPS res = x;
res += scalar;
return res;
}
SparseFPS &operator+=(const SparseFPS &other) {
*this = this->add(other);
return *this;
}
friend SparseFPS operator+(const SparseFPS &x, const SparseFPS &y) {
return x.add(y);
}
SparseFPS &operator*=(const T &scalar) {
for (auto &x : coeff_) x *= scalar;
return *this;
}
friend SparseFPS operator*(const SparseFPS &x, const T &scalar) {
SparseFPS res = x;
res *= scalar;
return res;
}
SparseFPS &operator-=(const SparseFPS &other) {
*this = this->add(other * -1);
return *this;
}
friend SparseFPS operator-(const SparseFPS &x, const SparseFPS &y) {
return x.add(y * -1);
}
SparseFPS mul(const SparseFPS &other, int max_degree) const {
std::map<int, T> terms;
for (int i = 0; i < size(); ++i) {
int di = degree(i);
T ci = coeff(i);
for (int j = 0; j < other.size(); ++j) {
int dj = other.degree(j);
if (di + dj > max_degree) break;
terms[di + dj] += ci * other.coeff(j);
}
}
SparseFPS res;
for (auto &[d, c] : terms) {
res.emplace_back(d, c);
}
return res;
}
private:
SparseFPS add(const SparseFPS &other) const {
SparseFPS res;
int j = 0;
for (int i = 0; i < size();) {
const int deg = this->degree(i);
for (; j < other.size() and other.degree(j) < deg; ++j) {
res.emplace_back(other.degree(j), other.coeff(j));
}
T c = this->coeff(i);
if (j < other.size() and other.degree(j) == deg) {
c += other.coeff(j);
++j;
}
if (c != 0) {
res.emplace_back(deg, c);
}
}
for (; j < other.size(); ++j) {
res.emplace_back(other.degree(j), other.coeff(j));
}
return res;
}
};
// Polynomial addition (dense + sparse).
template <typename ModInt, int DMAX>
DenseFPS<ModInt, DMAX> &operator+=(DenseFPS<ModInt, DMAX> &x,
const SparseFPS<ModInt> &y) {
for (int i = 0; i < y.size(); ++i) {
if (y.degree(i) > DMAX) break; // ignore
x.coeff_[y.degree(i)] += y.coeff(i);
}
return x;
}
template <typename ModInt, int DMAX>
DenseFPS<ModInt, DMAX> operator+(const DenseFPS<ModInt, DMAX> &x,
const SparseFPS<ModInt> &y) {
DenseFPS<ModInt, DMAX> res = x;
res += y;
return res;
}
template <typename ModInt, int DMAX>
DenseFPS<ModInt, DMAX> operator+(const SparseFPS<ModInt> &x,
const DenseFPS<ModInt, DMAX> &y) {
return y + x; // commutative
}
// Polynomial multiplication (dense * sparse).
template <typename ModInt, int DMAX>
DenseFPS<ModInt, DMAX> &operator*=(DenseFPS<ModInt, DMAX> &x,
const SparseFPS<ModInt> &y) {
if (y.size() == 0) {
return x *= 0;
}
ModInt c0 = 0;
int j0 = 0;
if (y.degree(0) == 0) {
c0 = y.coeff(0);
++j0;
}
for (int i = DMAX; i >= 0; --i) {
x.coeff_[i] *= c0;
for (int j = j0; j < y.size(); ++j) {
int d = y.degree(j);
if (d > i) break;
x.coeff_[i] += x[i - d] * y.coeff(j);
}
}
return x;
}
template <typename ModInt, int DMAX>
DenseFPS<ModInt, DMAX> operator*(const DenseFPS<ModInt, DMAX> &x,
const SparseFPS<ModInt> &y) {
DenseFPS<ModInt, DMAX> res = x;
res *= y;
return res;
}
template <typename ModInt, int DMAX>
DenseFPS<ModInt, DMAX> operator*(const SparseFPS<ModInt> &x,
const DenseFPS<ModInt, DMAX> &y) {
return y * x; // commutative
}
// Polynomial division (dense / sparse).
template <typename ModInt, int DMAX>
DenseFPS<ModInt, DMAX> &operator/=(DenseFPS<ModInt, DMAX> &x,
const SparseFPS<ModInt> &y) {
assert(y.size() > 0 and y.degree(0) == 0 and y.coeff(0) != 0);
ModInt inv_c0 = y.coeff(0).inv();
for (int i = 0; i < x.size(); ++i) {
for (int j = 1; j < y.size(); ++j) {
int d = y.degree(j);
if (d > i) break;
x.coeff_[i] -= x.coeff_[i - d] * y.coeff[j];
}
x.coeff_[i] *= inv_c0;
}
return x;
}
template <typename ModInt, int DMAX>
DenseFPS<ModInt, DMAX> operator/(const DenseFPS<ModInt, DMAX> &x,
const SparseFPS<ModInt> &y) {
DenseFPS<ModInt, DMAX> res = x;
res /= y;
return res;
}
using mint = atcoder::modint998244353;
const int MOD = 998244353;
const int BMAX = 200'000;
template <class T>
struct Factorials {
// factorials and inverse factorials.
std::vector<T> fact, ifact;
// n: max cached value.
Factorials(size_t n) : fact(n + 1), ifact(n + 1) {
assert(n > 0 and n < MOD);
fact[0] = 1;
for (size_t i = 1; i <= n; ++i) fact[i] = fact[i - 1] * i;
ifact[n] = fact[n].inv();
for (size_t i = n; i >= 1; --i) ifact[i - 1] = ifact[i] * i;
}
// Combination (nCk)
T C(int n, int k) {
if (k < 0 || k > n) return 0;
return fact[n] * ifact[k] * ifact[n - k];
}
// Permutation (nPk)
T P(int n, int k) {
if (k < 0 || k > n) return 0;
return fact[n] * ifact[n - k];
}
};
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
int N, Q;
cin >> N >> Q;
V<int> A(N);
cin >> A;
deque<SparseFPS<mint>> q;
REP(i, N) {
SparseFPS<mint> g;
g.emplace_back(0, mint(A[i] - 1));
g.emplace_back(1, mint(1));
q.push_back(move(g));
}
deque<DenseFPS<mint, BMAX>> qd;
while (q.size() > 1) {
SparseFPS<mint> p = q[0].mul(q[1], BMAX);
q.pop_front();
q.pop_front();
if (p.size() < 500) {
q.push_back(move(p));
} else {
DenseFPS<mint, BMAX> d;
REP(i, p.size()) { d.coeff_[p.degree(i)] = p.coeff(i); }
qd.push_back(move(d));
}
}
if (q.size() == 1) {
SparseFPS<mint> p = q.front();
DenseFPS<mint, BMAX> d;
REP(i, p.size()) { d.coeff_[p.degree(i)] = p.coeff(i); }
qd.push_back(move(d));
}
while (qd.size() > 1) {
DenseFPS<mint, BMAX> p = fps::mul_ntt(qd[0], qd[1]);
qd.pop_front();
qd.pop_front();
qd.push_back(move(p));
}
const auto &f = qd.front();
REP(i, Q) {
int b;
cin >> b;
cout << f[b].val() << '\n';
}
}