#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using lint = long long; using pint = pair; using plint = pair; 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##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template void ndarray(vector& vec, const V& val, int len) { vec.assign(len, val); } template void ndarray(vector& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); } template bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; } template bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; } int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); } template pair operator+(const pair &l, const pair &r) { return make_pair(l.first + r.first, l.second + r.second); } template pair operator-(const pair &l, const pair &r) { return make_pair(l.first - r.first, l.second - r.second); } template vector sort_unique(vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template int arglb(const std::vector &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); } template int argub(const std::vector &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); } template istream &operator>>(istream &is, vector &vec) { for (auto &v : vec) is >> v; return is; } template ostream &operator<<(ostream &os, const vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const array &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; } #if __cplusplus >= 201703L template istream &operator>>(istream &is, tuple &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template ostream &operator<<(ostream &os, const tuple &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; } #endif template ostream &operator<<(ostream &os, const deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const pair &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; } template ostream &operator<<(ostream &os, const map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_map &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) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl #define dbgif(cond, x) ((cond) ? cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl : cerr) #else #define dbg(x) 0 #define dbgif(cond, x) 0 #endif #include #include #include #include #include // Solve ax+by=gcd(a, b) template Int extgcd(Int a, Int b, Int &x, Int &y) { Int d = a; if (b != 0) { d = extgcd(b, a % b, y, x), y -= (a / b) * x; } else { x = 1, y = 0; } return d; } // Calculate a^(-1) (MOD m) s if gcd(a, m) == 1 // Calculate x s.t. ax == gcd(a, m) MOD m template Int mod_inverse(Int a, Int m) { Int x, y; extgcd(a, m, x, y); x %= m; return x + (x < 0) * m; } // Require: 1 <= b // return: (g, x) s.t. g = gcd(a, b), xa = g MOD b, 0 <= x < b/g template /* constexpr */ std::pair inv_gcd(Int a, Int b) { a %= b; if (a < 0) a += b; if (a == 0) return {b, 0}; Int s = b, t = a, m0 = 0, m1 = 1; while (t) { Int u = s / t; s -= t * u, m0 -= m1 * u; auto tmp = s; s = t, t = tmp, tmp = m0, m0 = m1, m1 = tmp; } if (m0 < 0) m0 += b / s; return {s, m0}; } template /* constexpr */ std::pair crt(const std::vector &r, const std::vector &m) { assert(r.size() == m.size()); int n = int(r.size()); // Contracts: 0 <= r0 < m0 Int r0 = 0, m0 = 1; for (int i = 0; i < n; i++) { assert(1 <= m[i]); Int r1 = r[i] % m[i], m1 = m[i]; if (r1 < 0) r1 += m1; if (m0 < m1) { std::swap(r0, r1); std::swap(m0, m1); } if (m0 % m1 == 0) { if (r0 % m1 != r1) return {0, 0}; continue; } Int g, im; std::tie(g, im) = inv_gcd(m0, m1); Int u1 = m1 / g; if ((r1 - r0) % g) return {0, 0}; Int x = (r1 - r0) / g % u1 * im % u1; r0 += x * m0; m0 *= u1; if (r0 < 0) r0 += m0; } return {r0, m0}; } // 蟻本 P.262 // 中国剰余定理を利用して,色々な素数で割った余りから元の値を復元 // 連立線形合同式 A * x = B mod M の解 // Requirement: M[i] > 0 // Output: x = first MOD second (if solution exists), (0, 0) (otherwise) template std::pair linear_congruence(const std::vector &A, const std::vector &B, const std::vector &M) { Int r = 0, m = 1; assert(A.size() == M.size()); assert(B.size() == M.size()); for (int i = 0; i < (int)A.size(); i++) { assert(M[i] > 0); const Int ai = A[i] % M[i]; Int a = ai * m, b = B[i] - ai * r, d = std::__gcd(M[i], a); if (b % d != 0) { return std::make_pair(0, 0); // 解なし } Int t = b / d * mod_inverse(a / d, M[i] / d) % (M[i] / d); r += m * t; m *= M[i] / d; } return std::make_pair((r < 0 ? r + m : r), m); } vector solve_md(const vector &A, int hi, int C, unsigned short md) { vector dp(C + 1, vector(hi + 1)); dp[0][0] = 1; for (auto a : A) { IREP(c, C) { REP(i, hi - a + 1) { dp[c + 1][i + a] += dp[c][i]; if (dp[c + 1][i + a] >= md) dp[c + 1][i + a] -= md; } } } return dp.back(); } int main() { vector<__int128> mods{32533, 32537, 32561, 32563, 32569, 32573, 32579, 4253}; int N, M, C; cin >> N >> M >> C; vector A(N); cin >> A; const int maxi = accumulate(A.begin(), A.end(), 0); int c_use = min(C, N - C); vector> answers; for (int md : mods) { auto sol = solve_md(A, maxi, c_use, M); answers.push_back(sol); } vector ret(maxi + 1); REP(i, ret.size()) { vector<__int128> B; REP(d, mods.size()) B.push_back(answers[d][i]); ret[i] = crt(B, mods).first % M; } if (C != c_use) reverse(ALL(ret)); ret.erase(ret.begin()); for (auto x : ret) cout << x << ' '; cout << '\n'; }