結果
| 問題 | No.2810 Have Another Go (Hard) |
| ユーザー |
 hitonanode
|
| 提出日時 | 2024-07-12 22:16:39 |
| 言語 | C++23 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 28,351 bytes |
| コンパイル時間 | 3,236 ms |
| コンパイル使用メモリ | 202,600 KB |
| 実行使用メモリ | 6,948 KB |
| 最終ジャッジ日時 | 2024-07-12 22:17:51 |
| 合計ジャッジ時間 | 56,975 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge1 |
（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 | 3 ms
6,812 KB |
| testcase_01 | AC | 1,434 ms
6,940 KB |
| testcase_02 | AC | 1,413 ms
6,940 KB |
| testcase_03 | AC | 1,375 ms
6,940 KB |
| testcase_04 | AC | 1,418 ms
6,944 KB |
| testcase_05 | AC | 1,401 ms
6,944 KB |
| testcase_06 | AC | 1,411 ms
6,940 KB |
| testcase_07 | AC | 1,387 ms
6,940 KB |
| testcase_08 | AC | 1,384 ms
6,940 KB |
| testcase_09 | AC | 1,392 ms
6,944 KB |
| testcase_10 | AC | 1,403 ms
6,940 KB |
| testcase_11 | AC | 11 ms
6,940 KB |
| testcase_12 | AC | 11 ms
6,944 KB |
| testcase_13 | AC | 5 ms
6,940 KB |
| testcase_14 | AC | 14 ms
6,940 KB |
| testcase_15 | AC | 10 ms
6,944 KB |
| testcase_16 | AC | 324 ms
6,944 KB |
| testcase_17 | AC | 1,315 ms
6,940 KB |
| testcase_18 | AC | 795 ms
6,944 KB |
| testcase_19 | AC | 1,230 ms
6,944 KB |
| testcase_20 | AC | 187 ms
6,940 KB |
| testcase_21 | AC | 441 ms
6,940 KB |
| testcase_22 | AC | 795 ms
6,940 KB |
| testcase_23 | AC | 538 ms
6,940 KB |
| testcase_24 | AC | 920 ms
6,940 KB |
| testcase_25 | AC | 1,378 ms
6,940 KB |
| testcase_26 | AC | 1,442 ms
6,940 KB |
| testcase_27 | AC | 1,455 ms
6,940 KB |
| testcase_28 | AC | 1,497 ms
6,944 KB |
| testcase_29 | AC | 1,500 ms
6,944 KB |
| testcase_30 | AC | 1,464 ms
6,940 KB |
| testcase_31 | AC | 1,477 ms
6,944 KB |
| testcase_32 | AC | 1,453 ms
6,940 KB |
| testcase_33 | AC | 1,469 ms
6,940 KB |
| testcase_34 | AC | 1,451 ms
6,944 KB |
| testcase_35 | AC | 1,490 ms
6,944 KB |
| testcase_36 | AC | 1,472 ms
6,940 KB |
| testcase_37 | AC | 1,479 ms
6,940 KB |
| testcase_38 | AC | 1,526 ms
6,940 KB |
| testcase_39 | AC | 1,501 ms
6,944 KB |
| testcase_40 | AC | 1,467 ms
6,940 KB |
| testcase_41 | AC | 1,486 ms
6,940 KB |
| testcase_42 | AC | 1,477 ms
6,940 KB |
| testcase_43 | AC | 1,482 ms
6,940 KB |
| testcase_44 | AC | 1,505 ms
6,940 KB |
| testcase_45 | AC | 1,458 ms
6,940 KB |
| testcase_46 | WA | - |
| testcase_47 | WA | - |
| testcase_48 | WA | - |
| testcase_49 | WA | - |
| testcase_50 | WA | - |
| testcase_51 | WA | - |
| testcase_52 | WA | - |
| testcase_53 | WA | - |
| testcase_54 | WA | - |
| testcase_55 | WA | - |
| testcase_56 | WA | - |
| testcase_57 | WA | - |
| testcase_58 | WA | - |
| testcase_59 | WA | - |
| testcase_60 | WA | - |
ソースコード
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <numeric>
#include <optional>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }
template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }
const std::vector<std::pair<int, int>> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <class T1, class T2> T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); }
template <class T1, class T2> std::pair<T1, T2> operator+(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first + r.first, l.second + r.second); }
template <class T1, class T2> std::pair<T1, T2> operator-(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first - r.first, l.second - r.second); }
template <class T> std::vector<T> sort_unique(std::vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <class T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }
template <class T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }
template <class IStream, class T> IStream &operator>>(IStream &is, std::vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec);
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr);
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const pair<T, U> &pa);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa);
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp);
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp);
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
template <class... T> std::istream &operator>>(std::istream &is, std::tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; }
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";
#define dbg(x) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl
#define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl : std::cerr)
#else
#define dbg(x) ((void)0)
#define dbgif(cond, x) ((void)0)
#endif
template <int md> struct ModInt {
using lint = long long;
constexpr static int mod() { return md; }
static int get_primitive_root() {
static int primitive_root = 0;
if (!primitive_root) {
primitive_root = [&]() {
std::set<int> fac;
int v = md - 1;
for (lint i = 2; i * i <= v; i++)
while (v % i == 0) fac.insert(i), v /= i;
if (v > 1) fac.insert(v);
for (int g = 1; g < md; g++) {
bool ok = true;
for (auto i : fac)
if (ModInt(g).pow((md - 1) / i) == 1) {
ok = false;
break;
}
if (ok) return g;
}
return -1;
}();
}
return primitive_root;
}
int val_;
int val() const noexcept { return val_; }
constexpr ModInt() : val_(0) {}
constexpr ModInt &_setval(lint v) { return val_ = (v >= md ? v - md : v), *this; }
constexpr ModInt(lint v) { _setval(v % md + md); }
constexpr explicit operator bool() const { return val_ != 0; }
constexpr ModInt operator+(const ModInt &x) const {
return ModInt()._setval((lint)val_ + x.val_);
}
constexpr ModInt operator-(const ModInt &x) const {
return ModInt()._setval((lint)val_ - x.val_ + md);
}
constexpr ModInt operator*(const ModInt &x) const {
return ModInt()._setval((lint)val_ * x.val_ % md);
}
constexpr ModInt operator/(const ModInt &x) const {
return ModInt()._setval((lint)val_ * x.inv().val() % md);
}
constexpr ModInt operator-() const { return ModInt()._setval(md - val_); }
constexpr ModInt &operator+=(const ModInt &x) { return *this = *this + x; }
constexpr ModInt &operator-=(const ModInt &x) { return *this = *this - x; }
constexpr ModInt &operator*=(const ModInt &x) { return *this = *this * x; }
constexpr ModInt &operator/=(const ModInt &x) { return *this = *this / x; }
friend constexpr ModInt operator+(lint a, const ModInt &x) { return ModInt(a) + x; }
friend constexpr ModInt operator-(lint a, const ModInt &x) { return ModInt(a) - x; }
friend constexpr ModInt operator*(lint a, const ModInt &x) { return ModInt(a) * x; }
friend constexpr ModInt operator/(lint a, const ModInt &x) { return ModInt(a) / x; }
constexpr bool operator==(const ModInt &x) const { return val_ == x.val_; }
constexpr bool operator!=(const ModInt &x) const { return val_ != x.val_; }
constexpr bool operator<(const ModInt &x) const {
return val_ < x.val_;
} // To use std::map<ModInt, T>
friend std::istream &operator>>(std::istream &is, ModInt &x) {
lint t;
return is >> t, x = ModInt(t), is;
}
constexpr friend std::ostream &operator<<(std::ostream &os, const ModInt &x) {
return os << x.val_;
}
constexpr ModInt pow(lint n) const {
ModInt ans = 1, tmp = *this;
while (n) {
if (n & 1) ans *= tmp;
tmp *= tmp, n >>= 1;
}
return ans;
}
static constexpr int cache_limit = std::min(md, 1 << 21);
static std::vector<ModInt> facs, facinvs, invs;
constexpr static void _precalculation(int N) {
const int l0 = facs.size();
if (N > md) N = md;
if (N <= l0) return;
facs.resize(N), facinvs.resize(N), invs.resize(N);
for (int i = l0; i < N; i++) facs[i] = facs[i - 1] * i;
facinvs[N - 1] = facs.back().pow(md - 2);
for (int i = N - 2; i >= l0; i--) facinvs[i] = facinvs[i + 1] * (i + 1);
for (int i = N - 1; i >= l0; i--) invs[i] = facinvs[i] * facs[i - 1];
}
constexpr ModInt inv() const {
if (this->val_ < cache_limit) {
if (facs.empty()) facs = {1}, facinvs = {1}, invs = {0};
while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2);
return invs[this->val_];
} else {
return this->pow(md - 2);
}
}
constexpr ModInt fac() const {
while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2);
return facs[this->val_];
}
constexpr ModInt facinv() const {
while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2);
return facinvs[this->val_];
}
constexpr ModInt doublefac() const {
lint k = (this->val_ + 1) / 2;
return (this->val_ & 1) ? ModInt(k * 2).fac() / (ModInt(2).pow(k) * ModInt(k).fac())
: ModInt(k).fac() * ModInt(2).pow(k);
}
constexpr ModInt nCr(int r) const {
if (r < 0 or this->val_ < r) return ModInt(0);
return this->fac() * (*this - r).facinv() * ModInt(r).facinv();
}
constexpr ModInt nPr(int r) const {
if (r < 0 or this->val_ < r) return ModInt(0);
return this->fac() * (*this - r).facinv();
}
static ModInt binom(int n, int r) {
static long long bruteforce_times = 0;
if (r < 0 or n < r) return ModInt(0);
if (n <= bruteforce_times or n < (int)facs.size()) return ModInt(n).nCr(r);
r = std::min(r, n - r);
ModInt ret = ModInt(r).facinv();
for (int i = 0; i < r; ++i) ret *= n - i;
bruteforce_times += r;
return ret;
}
// Multinomial coefficient, (k_1 + k_2 + ... + k_m)! / (k_1! k_2! ... k_m!)
// Complexity: O(sum(ks))
template <class Vec> static ModInt multinomial(const Vec &ks) {
ModInt ret{1};
int sum = 0;
for (int k : ks) {
assert(k >= 0);
ret *= ModInt(k).facinv(), sum += k;
}
return ret * ModInt(sum).fac();
}
// Catalan number, C_n = binom(2n, n) / (n + 1)
// C_0 = 1, C_1 = 1, C_2 = 2, C_3 = 5, C_4 = 14, ...
// https://oeis.org/A000108
// Complexity: O(n)
static ModInt catalan(int n) {
if (n < 0) return ModInt(0);
return ModInt(n * 2).fac() * ModInt(n + 1).facinv() * ModInt(n).facinv();
}
ModInt sqrt() const {
if (val_ == 0) return 0;
if (md == 2) return val_;
if (pow((md - 1) / 2) != 1) return 0;
ModInt b = 1;
while (b.pow((md - 1) / 2) == 1) b += 1;
int e = 0, m = md - 1;
while (m % 2 == 0) m >>= 1, e++;
ModInt x = pow((m - 1) / 2), y = (*this) * x * x;
x *= (*this);
ModInt z = b.pow(m);
while (y != 1) {
int j = 0;
ModInt t = y;
while (t != 1) j++, t *= t;
z = z.pow(1LL << (e - j - 1));
x *= z, z *= z, y *= z;
e = j;
}
return ModInt(std::min(x.val_, md - x.val_));
}
};
template <int md> std::vector<ModInt<md>> ModInt<md>::facs = {1};
template <int md> std::vector<ModInt<md>> ModInt<md>::facinvs = {1};
template <int md> std::vector<ModInt<md>> ModInt<md>::invs = {0};
using mint = ModInt<998244353>;
// Berlekamp–Massey algorithm
// https://en.wikipedia.org/wiki/Berlekamp%E2%80%93Massey_algorithm
// Complexity: O(N^2)
// input: S = sequence from field K
// return: L = degree of minimal polynomial,
// C_reversed = monic min. polynomial (size = L + 1, reversed order, C_reversed[0] = 1))
// Formula: convolve(S, C_reversed)[i] = 0 for i >= L
// Example:
// - [1, 2, 4, 8, 16] -> (1, [1, -2])
// - [1, 1, 2, 3, 5, 8] -> (2, [1, -1, -1])
// - [0, 0, 0, 0, 1] -> (5, [1, 0, 0, 0, 0, 998244352]) (mod 998244353)
// - [] -> (0, [1])
// - [0, 0, 0] -> (0, [1])
// - [-2] -> (1, [1, 2])
template <typename Tfield>
std::pair<int, std::vector<Tfield>> find_linear_recurrence(const std::vector<Tfield> &S) {
int N = S.size();
using poly = std::vector<Tfield>;
poly C_reversed{1}, B{1};
int L = 0, m = 1;
Tfield b = 1;
// adjust: C(x) <- C(x) - (d / b) x^m B(x)
auto adjust = [](poly C, const poly &B, Tfield d, Tfield b, int m) -> poly {
C.resize(std::max(C.size(), B.size() + m));
Tfield a = d / b;
for (unsigned i = 0; i < B.size(); i++) C[i + m] -= a * B[i];
return C;
};
for (int n = 0; n < N; n++) {
Tfield d = S[n];
for (int i = 1; i <= L; i++) d += C_reversed[i] * S[n - i];
if (d == 0)
m++;
else if (2 * L <= n) {
poly T = C_reversed;
C_reversed = adjust(C_reversed, B, d, b, m);
L = n + 1 - L;
B = T;
b = d;
m = 1;
} else
C_reversed = adjust(C_reversed, B, d, b, m++);
}
return std::make_pair(L, C_reversed);
}
// Calculate ^N \bmod f(x)$
// Known as `Kitamasa method`
// Input: f_reversed: monic, reversed (f_reversed[0] = 1)
// Complexity: (K^2 \log N)$ ($: deg. of $)
// Example: (4, [1, -1, -1]) -> [2, 3]
// ( x^4 = (x^2 + x + 2)(x^2 - x - 1) + 3x + 2 )
// Reference: http://misawa.github.io/others/fast_kitamasa_method.html
// http://sugarknri.hatenablog.com/entry/2017/11/18/233936
template <typename Tfield>
std::vector<Tfield> monomial_mod_polynomial(long long N, const std::vector<Tfield> &f_reversed) {
assert(!f_reversed.empty() and f_reversed[0] == 1);
int K = f_reversed.size() - 1;
if (!K) return {};
int D = 64 - __builtin_clzll(N);
std::vector<Tfield> ret(K, 0);
ret[0] = 1;
auto self_conv = [](std::vector<Tfield> x) -> std::vector<Tfield> {
int d = x.size();
std::vector<Tfield> ret(d * 2 - 1);
for (int i = 0; i < d; i++) {
ret[i * 2] += x[i] * x[i];
for (int j = 0; j < i; j++) ret[i + j] += x[i] * x[j] * 2;
}
return ret;
};
for (int d = D; d--;) {
ret = self_conv(ret);
for (int i = 2 * K - 2; i >= K; i--) {
for (int j = 1; j <= K; j++) ret[i - j] -= ret[i] * f_reversed[j];
}
ret.resize(K);
if ((N >> d) & 1) {
std::vector<Tfield> c(K);
c[0] = -ret[K - 1] * f_reversed[K];
for (int i = 1; i < K; i++) { c[i] = ret[i - 1] - ret[K - 1] * f_reversed[K - i]; }
ret = c;
}
}
return ret;
}
// Guess k-th element of the sequence, assuming linear recurrence
// initial_elements: 0-ORIGIN
// Verify: abc198f https://atcoder.jp/contests/abc198/submissions/21837815
template <typename Tfield>
Tfield guess_kth_term(const std::vector<Tfield> &initial_elements, long long k) {
assert(k >= 0);
if (k < static_cast<long long>(initial_elements.size())) return initial_elements[k];
const auto f = find_linear_recurrence<Tfield>(initial_elements).second;
const auto g = monomial_mod_polynomial<Tfield>(k, f);
Tfield ret = 0;
for (unsigned i = 0; i < g.size(); i++) ret += g[i] * initial_elements[i];
return ret;
}
#include <algorithm>
#include <cassert>
#include <cmath>
#include <iterator>
#include <type_traits>
#include <utility>
#include <vector>
namespace matrix_ {
struct has_id_method_impl {
template <class T_> static auto check(T_ *) -> decltype(T_::id(), std::true_type());
template <class T_> static auto check(...) -> std::false_type;
};
template <class T_> struct has_id : decltype(has_id_method_impl::check<T_>(nullptr)) {};
} // namespace matrix_
template <typename T> struct matrix {
int H, W;
std::vector<T> elem;
typename std::vector<T>::iterator operator[](int i) { return elem.begin() + i * W; }
inline T &at(int i, int j) { return elem[i * W + j]; }
inline T get(int i, int j) const { return elem[i * W + j]; }
int height() const { return H; }
int width() const { return W; }
std::vector<std::vector<T>> vecvec() const {
std::vector<std::vector<T>> ret(H);
for (int i = 0; i < H; i++) {
std::copy(elem.begin() + i * W, elem.begin() + (i + 1) * W, std::back_inserter(ret[i]));
}
return ret;
}
operator std::vector<std::vector<T>>() const { return vecvec(); }
matrix() = default;
matrix(int H, int W) : H(H), W(W), elem(H * W) {}
matrix(const std::vector<std::vector<T>> &d) : H(d.size()), W(d.size() ? d[0].size() : 0) {
for (auto &raw : d) std::copy(raw.begin(), raw.end(), std::back_inserter(elem));
}
template <typename T2, typename std::enable_if<matrix_::has_id<T2>::value>::type * = nullptr>
static T2 _T_id() {
return T2::id();
}
template <typename T2, typename std::enable_if<!matrix_::has_id<T2>::value>::type * = nullptr>
static T2 _T_id() {
return T2(1);
}
static matrix Identity(int N) {
matrix ret(N, N);
for (int i = 0; i < N; i++) ret.at(i, i) = _T_id<T>();
return ret;
}
matrix operator-() const {
matrix ret(H, W);
for (int i = 0; i < H * W; i++) ret.elem[i] = -elem[i];
return ret;
}
matrix operator*(const T &v) const {
matrix ret = *this;
for (auto &x : ret.elem) x *= v;
return ret;
}
matrix operator/(const T &v) const {
matrix ret = *this;
const T vinv = _T_id<T>() / v;
for (auto &x : ret.elem) x *= vinv;
return ret;
}
matrix operator+(const matrix &r) const {
matrix ret = *this;
for (int i = 0; i < H * W; i++) ret.elem[i] += r.elem[i];
return ret;
}
matrix operator-(const matrix &r) const {
matrix ret = *this;
for (int i = 0; i < H * W; i++) ret.elem[i] -= r.elem[i];
return ret;
}
matrix operator*(const matrix &r) const {
matrix ret(H, r.W);
for (int i = 0; i < H; i++) {
for (int k = 0; k < W; k++) {
for (int j = 0; j < r.W; j++) ret.at(i, j) += this->get(i, k) * r.get(k, j);
}
}
return ret;
}
matrix &operator*=(const T &v) { return *this = *this * v; }
matrix &operator/=(const T &v) { return *this = *this / v; }
matrix &operator+=(const matrix &r) { return *this = *this + r; }
matrix &operator-=(const matrix &r) { return *this = *this - r; }
matrix &operator*=(const matrix &r) { return *this = *this * r; }
bool operator==(const matrix &r) const { return H == r.H and W == r.W and elem == r.elem; }
bool operator!=(const matrix &r) const { return H != r.H or W != r.W or elem != r.elem; }
bool operator<(const matrix &r) const { return elem < r.elem; }
matrix pow(int64_t n) const {
matrix ret = Identity(H);
bool ret_is_id = true;
if (n == 0) return ret;
for (int i = 63 - __builtin_clzll(n); i >= 0; i--) {
if (!ret_is_id) ret *= ret;
if ((n >> i) & 1) ret *= (*this), ret_is_id = false;
}
return ret;
}
std::vector<T> pow_vec(int64_t n, std::vector<T> vec) const {
matrix x = *this;
while (n) {
if (n & 1) vec = x * vec;
x *= x;
n >>= 1;
}
return vec;
};
matrix transpose() const {
matrix ret(W, H);
for (int i = 0; i < H; i++) {
for (int j = 0; j < W; j++) ret.at(j, i) = this->get(i, j);
}
return ret;
}
// Gauss-Jordan elimination
// - Require inverse for every non-zero element
// - Complexity: O(H^2 W)
template <typename T2, typename std::enable_if<std::is_floating_point<T2>::value>::type * = nullptr>
static int choose_pivot(const matrix<T2> &mtr, int h, int c) noexcept {
int piv = -1;
for (int j = h; j < mtr.H; j++) {
if (mtr.get(j, c) and (piv < 0 or std::abs(mtr.get(j, c)) > std::abs(mtr.get(piv, c))))
piv = j;
}
return piv;
}
template <typename T2, typename std::enable_if<!std::is_floating_point<T2>::value>::type * = nullptr>
static int choose_pivot(const matrix<T2> &mtr, int h, int c) noexcept {
for (int j = h; j < mtr.H; j++) {
if (mtr.get(j, c) != T2()) return j;
}
return -1;
}
matrix gauss_jordan() const {
int c = 0;
matrix mtr(*this);
std::vector<int> ws;
ws.reserve(W);
for (int h = 0; h < H; h++) {
if (c == W) break;
int piv = choose_pivot(mtr, h, c);
if (piv == -1) {
c++;
h--;
continue;
}
if (h != piv) {
for (int w = 0; w < W; w++) {
std::swap(mtr[piv][w], mtr[h][w]);
mtr.at(piv, w) *= -_T_id<T>(); // To preserve sign of determinant
}
}
ws.clear();
for (int w = c; w < W; w++) {
if (mtr.at(h, w) != T()) ws.emplace_back(w);
}
const T hcinv = _T_id<T>() / mtr.at(h, c);
for (int hh = 0; hh < H; hh++)
if (hh != h) {
const T coeff = mtr.at(hh, c) * hcinv;
for (auto w : ws) mtr.at(hh, w) -= mtr.at(h, w) * coeff;
mtr.at(hh, c) = T();
}
c++;
}
return mtr;
}
int rank_of_gauss_jordan() const {
for (int i = H * W - 1; i >= 0; i--) {
if (elem[i] != 0) return i / W + 1;
}
return 0;
}
int rank() const { return gauss_jordan().rank_of_gauss_jordan(); }
T determinant_of_upper_triangle() const {
T ret = _T_id<T>();
for (int i = 0; i < H; i++) ret *= get(i, i);
return ret;
}
int inverse() {
assert(H == W);
std::vector<std::vector<T>> ret = Identity(H), tmp = *this;
int rank = 0;
for (int i = 0; i < H; i++) {
int ti = i;
while (ti < H and tmp[ti][i] == T()) ti++;
if (ti == H) {
continue;
} else {
rank++;
}
ret[i].swap(ret[ti]), tmp[i].swap(tmp[ti]);
T inv = _T_id<T>() / tmp[i][i];
for (int j = 0; j < W; j++) ret[i][j] *= inv;
for (int j = i + 1; j < W; j++) tmp[i][j] *= inv;
for (int h = 0; h < H; h++) {
if (i == h) continue;
const T c = -tmp[h][i];
for (int j = 0; j < W; j++) ret[h][j] += ret[i][j] * c;
for (int j = i + 1; j < W; j++) tmp[h][j] += tmp[i][j] * c;
}
}
*this = ret;
return rank;
}
friend std::vector<T> operator*(const matrix &m, const std::vector<T> &v) {
assert(m.W == int(v.size()));
std::vector<T> ret(m.H);
for (int i = 0; i < m.H; i++) {
for (int j = 0; j < m.W; j++) ret[i] += m.get(i, j) * v[j];
}
return ret;
}
friend std::vector<T> operator*(const std::vector<T> &v, const matrix &m) {
assert(int(v.size()) == m.H);
std::vector<T> ret(m.W);
for (int i = 0; i < m.H; i++) {
for (int j = 0; j < m.W; j++) ret[j] += v[i] * m.get(i, j);
}
return ret;
}
std::vector<T> prod(const std::vector<T> &v) const { return (*this) * v; }
std::vector<T> prod_left(const std::vector<T> &v) const { return v * (*this); }
template <class OStream> friend OStream &operator<<(OStream &os, const matrix &x) {
os << "[(" << x.H << " * " << x.W << " matrix)";
os << "\n[column sums: ";
for (int j = 0; j < x.W; j++) {
T s = T();
for (int i = 0; i < x.H; i++) s += x.get(i, j);
os << s << ",";
}
os << "]";
for (int i = 0; i < x.H; i++) {
os << "\n[";
for (int j = 0; j < x.W; j++) os << x.get(i, j) << ",";
os << "]";
}
os << "]\n";
return os;
}
template <class IStream> friend IStream &operator>>(IStream &is, matrix &x) {
for (auto &v : x.elem) is >> v;
return is;
}
};
int main() {
int N, M, K;
cin >> N >> M >> K;
vector<mint> init(50);
init.at(0) = 1;
REP(i, init.size()) {
FOR(v, 1, 7) {
int j = i + v;
if (j < (int)init.size()) init.at(j) += init.at(i);
}
}
dbg(init);
dbg(guess_kth_term(init, 0));
dbg(guess_kth_term(init, 1));
auto f = [&](const lint x) -> mint {
if (x < 0) return 0;
if (x == 0) return 1;
return guess_kth_term(init, x);
};
auto g = [&](const lint &x) -> mint {
if (x < 0) return 0;
if (x == 0) return 1;
mint ret = 0;
for (lint last = x - 6; last < x; ++last) {
if (last < 0) continue;
ret += guess_kth_term(init, last) * (7 - (x - last));
}
// mint ret = guess_kth_term(init, x);
return ret;
};
matrix<mint> J(5, 5);
REP(i, 5) REP(j, 5) {
int dist = 6 + j - i;
if (dist <= 6) J[j][i] += 1;
}
matrix<mint> L(5, 5);
REP(i, 5) REP(j, 5) {
int dist = N - 6 + j - i;
L[j][i] = f(dist);
}
FOR(x, 1, 20) dbg(make_tuple(x, g(x)));
const mint all = g(lint(N) * M);
dbg(all);
dbg(J);
dbg(L);
REP(_, K) {
lint C;
cin >> C;
mint ret = all;
vector<mint> state(5);
REP(i, 5) state.at(i) = f(C - 5 + i);
state = J * (L * J).pow(M - 1) * state;
dbg(make_tuple(C, state));
// if (C == N) {
// // cout << ret - accumulate(ALL(state), mint(0)) << '\n';
// } else {
REP(i, 5) {
lint rem = N - C - 1 - i;
ret -= g(rem) * state.at(i);
}
cout << ret << '\n';
// }
}
}