結果
| 問題 | No.1353 Limited Sequence |
| ユーザー |
 PCTprobability
|
| 提出日時 | 2021-01-14 16:33:11 |
| 言語 | C++17(clang) (17.0.6 + boost 1.83.0) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 30,085 bytes |
| コンパイル時間 | 3,679 ms |
| コンパイル使用メモリ | 172,928 KB |
| 実行使用メモリ | 28,872 KB |
| 最終ジャッジ日時 | 2024-11-24 11:50:27 |
| 合計ジャッジ時間 | 81,190 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge5 |
（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 | 1 ms
13,640 KB |
| testcase_01 | WA | - |
| testcase_02 | WA | - |
| testcase_03 | WA | - |
| testcase_04 | WA | - |
| testcase_05 | WA | - |
| testcase_06 | WA | - |
| testcase_07 | WA | - |
| testcase_08 | WA | - |
| testcase_09 | WA | - |
| testcase_10 | WA | - |
| testcase_11 | WA | - |
| testcase_12 | TLE | - |
| testcase_13 | TLE | - |
| testcase_14 | WA | - |
| testcase_15 | WA | - |
| testcase_16 | WA | - |
| testcase_17 | WA | - |
| testcase_18 | TLE | - |
| testcase_19 | TLE | - |
| testcase_20 | WA | - |
| testcase_21 | WA | - |
| testcase_22 | WA | - |
| testcase_23 | TLE | - |
| testcase_24 | TLE | - |
| testcase_25 | TLE | - |
| testcase_26 | TLE | - |
| testcase_27 | WA | - |
| testcase_28 | WA | - |
| testcase_29 | WA | - |
| testcase_30 | TLE | - |
| testcase_31 | WA | - |
| testcase_32 | TLE | - |
| testcase_33 | WA | - |
| testcase_34 | TLE | - |
| testcase_35 | WA | - |
| testcase_36 | TLE | - |
| testcase_37 | TLE | - |
| testcase_38 | TLE | - |
| testcase_39 | TLE | - |
| testcase_40 | TLE | - |
| testcase_41 | TLE | - |
| testcase_42 | TLE | - |
| testcase_43 | TLE | - |
| testcase_44 | TLE | - |
| testcase_45 | TLE | - |
| testcase_46 | TLE | - |
| testcase_47 | TLE | - |
コンパイルメッセージ
main.cpp:709:27: warning: unqualified call to 'std::move' [-Wunqualified-std-cast-call]
709 | auto c2 = convolution(move(a2), move(b2));
| ^
| std::
main.cpp:737:15: note: in instantiation of function template specialization 'atcoder::convolution<754974721U, long long, nullptr>' requested here
737 | auto c1 = convolution<MOD1>(a, b);
| ^
main.cpp:709:37: warning: unqualified call to 'std::move' [-Wunqualified-std-cast-call]
709 | auto c2 = convolution(move(a2), move(b2));
| ^
| std::
main.cpp:709:27: warning: unqualified call to 'std::move' [-Wunqualified-std-cast-call]
709 | auto c2 = convolution(move(a2), move(b2));
| ^
| std::
main.cpp:738:15: note: in instantiation of function template specialization 'atcoder::convolution<167772161U, long long, nullptr>' requested here
738 | auto c2 = convolution<MOD2>(a, b);
| ^
main.cpp:709:37: warning: unqualified call to 'std::move' [-Wunqualified-std-cast-call]
709 | auto c2 = convolution(move(a2), move(b2));
| ^
| std::
main.cpp:709:27: warning: unqualified call to 'std::move' [-Wunqualified-std-cast-call]
709 | auto c2 = convolution(move(a2), move(b2));
| ^
| std::
main.cpp:739:15: note: in instantiation of function template specialization 'atcoder::convolution<469762049U, long long, nullptr>' requested here
739 | auto c3 = convolution<MOD3>(a, b);
| ^
main.cpp:709:37: warning: unqualified call to 'std::move' [-Wunqualified-std-cast-call]
709 | auto c2 = convolution(move(a2), move(b2));
| ^
|
ソースコード
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
#define all(s) (s).begin(),(s).end()
#define vcin(n) for(ll i=0;i<ll(n.size());i++) cin>>n[i]
#define rever(vec) reverse(vec.begin(), vec.end())
#define sor(vec) sort(vec.begin(), vec.end())
#define fi first
#define se second
//const ll mod = 998244353;
const ll mod = 1000000007;
const ll inf = 2000000000000000000ll;
static const long double pi = 3.141592653589793;
template<class T,class U> void chmax(T& t,const U& u){if(t<u) t=u;}
template<class T,class U> void chmin(T& t,const U& u){if(t>u) t=u;}
ll modPow(ll a, ll n, ll mod) { ll ret = 1; ll p = a % mod; while (n) { if (n & 1) ret = ret * p % mod; p = p * p % mod; n >>= 1; } return ret; }
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
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
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
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
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 namespace atcoder;
template<class T>
struct FormalPowerSeries:vector<T>{
using vector<T>::vector;
using vector<T>::operator=;
using F = FormalPowerSeries;
F operator-() const{
F res(*this);
for(auto &e:res) e=-e;
return res;
}
F &operator*=(const T &g){
for(auto &e:*this) e*=g;
return *this;
}
F &operator/=(const T &g){
assert(g!=T(0));
*this*=g.inv();
return *this;
}
F &operator+=(const F &g){
int n=(*this).size(),m=g.size();
for(int i=0;i<min(n,m);i++){
(*this)[i]+=g[i];
}
return *this;
}
F &operator-=(const F &g){
int n=(*this).size(),m=g.size();
for(int i=0;i<min(n,m);i++){
(*this)[i]-=g[i];
}
return *this;
}
F &operator<<=(const int d) {
int n=(*this).size();
(*this).insert((*this).begin(),d,0);
(*this).resize(n);
return *this;
}
F &operator>>=(const int d) {
int n=(*this).size();
(*this).erase((*this).begin(),(*this).begin()+min(n, d));
(*this).resize(n);
return *this;
}
F inv(int d=-1) const{
int n=(*this).size();
assert(n!=0&&(*this)[0]!=0);
if(d==-1) d=n;
assert(d>0);
F res{(*this)[0].inv()};
while(res.size()<d){
int m=size(res);
F f(begin(*this),begin(*this)+min(n,2*m));
F r(res);
f.resize(2*m);
r.resize(2*m);
vector<T> s=convolution(f,r);
s.resize(2*m);
for(int i=0;i<2*m;i++){
s[i]=-s[i];
}
s[0]+=2;
vector<T> g=convolution(s,r);
g.resize(2*m);
res=g;
}
res.resize(n);
return res;
}
F &operator*=(const F &g){
int n=(*this).size();
*this=convolution(*this,g);
(*this).resize(n);
return (*this);
}
F &operator/=(const F &g){
int n=(*this).size();
*this=convolution(*this,g.inv());
(*this).resize(n);
return (*this);
}
void onemul(const int d,const T c){
int n=(*this).size();
if(c==T(1)){
for(int i=n-d-1;i>=0;i--){
(*this)[i+d]+=(*this)[i];
}
}
else if(c==T(-1)){
for(int i=n-d-1;i>=0;i--){
(*this)[i+d]-=(*this)[i];
}
}
else{
for(int i=n-d-1;i>=0;i--){
(*this)[i+d]+=(*this)[i]*c;
}
}
}
void onediv(const int d,const T c){
int n=(*this).size();
for(int i=0;i<n-d;i++){
(*this)[i+d]-=(*this)[i]*c;
}
}
void spacemul(vector<pair<int, T>> g) {
int n = (*this).size();
auto [d, c] = g.front();
if (d == 0) g.erase(g.begin());
else c = 0;
for(int i=n-1;i>=0;i--){
(*this)[i] *= c;
for (auto &[j, b] : g) {
if (j > i) break;
(*this)[i] += (*this)[i-j] * b;
}
}
}
void spacediv(vector<pair<int, T>> g) {
int n = (*this).size();
auto [d, c] = g.front();
assert(d == 0 && c != T(0));
T ic = c.inv();
g.erase(g.begin());
for(int i=0;i<n;i++){
for (auto &[j, b] : g) {
if (j > i) break;
(*this)[i] -= (*this)[i-j] * b;
}
(*this)[i] *= ic;
}
}
T eval(const T &a) const {
T x(1),res(0);
for(auto e:*this) res+=e*x,x*=a;
return res;
}
F differential() const {
int n=(*this).size();
F res(n);
for(int i=0;i<n-1;i++){
res[i]=T(i+1)*(*this)[i+1];
}
res[n-1]=0;
return res;
}
F Integral() const {
int n=(*this).size();
F res(n);
for(int i=1;i<n;i++){
res[i]=(*this)[i-1]/T(i);
}
res[0]=0;
return res;
}
F log() const{
assert((*this)[0]==1);
int n=(*this).size();
F u=(*this).differential();
F d=(*this);
u/=d;
u=u.Integral();
u.resize(n);
return u;
}
F exp(int d=-1) const{
int n=(*this).size();
assert(n!=0&&(*this)[0]==0);
if(d==-1) d=n;
assert(d>0);
F res{1};
while(res.size()<d){
int m=size(res);
F f(begin(*this),begin(*this)+min(n,2*m));
F r(res);
f.resize(2*m);
r.resize(2*m);
r=r.log();
f-=r;
f[0]++;
F g=f*res;
g.resize(2*m);
res=g;
}
res.resize(n);
return res;
}
F pow(int a){
int n=(*this).size();
F res(n);
for(int i=0;i<n;i++){
res[i]=(*this)[i];
}
if(a==0){
F s(n);
if(n>0){
s[0]=T(1);
}
for(int i=0;i<n;i++){
res[i]=s[i];
}
return res;
}
int l=0;
while(l<n&&res[l]==0) l++;
if(l>(n-1)/a||l==n){
F s(n);
for(int i=0;i<n;i++){
res[i]=s[i];
}
return res;
}
T t=res[l];
res.erase(res.begin(),res.begin()+l);
res/=t;
F g=res.log();
for(int i=0;i<n;i++){
res[i]=g[i];
}
res*=a;
g=res.exp();
for(int i=0;i<n;i++){
res[i]=g[i];
}
res*=t.pow(a);
res.insert(res.begin(),l*a,0);
return res;
}
F sqrt(int k=-1){
int n=(*this).size();
if(k==-1){
k=n;
}
ll m=T::mod();
if((*this)[0]==T(0)){
for(int i=1;i<int((*this).size());i++){
if((*this)[i]!=T(0)){
if(i&1) return {};
if(n-i/2<=0)break;
auto ret=(*this>>i).sqrt(n-i/2)<<(i/2);
if(int(ret.size())<n) return {};
return ret;
}
}
F g(n);
for(int i=0;i<n;i++){
g[i]=0;
}
return g;
}
else{
if(modsqrt((*this)[0].val(),m)==-1){
return {};
}
F ret{T(modsqrt((*this)[0].val(),m))};
for(int i=1;i<n;i<<=1){
ret.resize(2*i);
ret=(ret+(*this)/ret);
ret/=T(2);
}
return ret;
}
}
F operator*(const T &g) const { return F(*this)*=g;}
F operator-(const T &g) const { return F(*this)-=g;}
F operator*(const F &g) const { return F(*this)*=g;}
F operator-(const F &g) const { return F(*this)-=g;}
F operator+(const F &g) const { return F(*this)+=g;}
F operator/(const F &g) const { return F(*this)/=g;}
F operator<<(const int d) const { return F(*this)<<=d;}
F operator>>(const int d) const { return F(*this)>>=d;}
};
using mint=modint998244353;
using fps = FormalPowerSeries<mint>;
using sfps = vector<pair<int, mint>>;
int main() {
/* mod は 1e9+7 */
ios::sync_with_stdio(false);
std::cin.tie(nullptr);
cout<< fixed << setprecision(10);
ll n,r,l;
cin>>n>>r>>l;
vector<ll> a(n);
vcin(a);
/* for(int i=0;i<n;i++){
a[i]=1;
}*/
mint ans=0;
vector<fps> dp(n);
for(int i=0;i<n;i++){
fps f(l+1);
f[0]=1;
f.onemul((i+1)*a[i],-1);
f.onediv((i+1),-1);
f<<=i+1;
dp[i]=f;
ans+=f[l];
}
bool s=true;
ll g=n;
while(s){
fps f(l+1);
for(int j=0;j<g;j++){
f+=dp[j];
}
for(int j=0;j<g;j++){
fps g=f;
g-=dp[j];
g.onediv((j+1),-1);
g.onemul((j+1)*a[j],-1);
g<<=j+1;
dp[j]=g;
}
bool t=false;
for(int j=g-1;j>=0;j--){
bool r=false;
for(int k=0;k<=l;k++){
if(k>=r){
ans+=dp[j][k];
}
if(dp[j][k]!=0){
t=true;
r=true;
}
}
if(r==false){
g--;
}
}
s=t;
}
cout<<ans.val()<<endl;
}