#include #include #include #include using mint = atcoder::modint; #include #include #include namespace suisen::internal { template std::vector convolution_naive(const std::vector& a, const std::vector& b) { const int n = a.size(), m = b.size(); std::vector c(n + m - 1); if (n < m) { for (int j = 0; j < m; j++) for (int i = 0; i < n; i++) c[i + j] += a[i] * b[j]; } else { for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) c[i + j] += a[i] * b[j]; } return c; } } // namespace suisen namespace suisen { template * = nullptr> std::vector arbitrary_mod_convolution(const std::vector& a, const std::vector& b) { int n = int(a.size()), m = int(b.size()); if (n == 0 or m == 0) return {}; if (std::min(n, m) <= 60) return internal::convolution_naive(a, b); static constexpr long long MOD1 = 754974721; // 2^24 static constexpr long long MOD2 = 167772161; // 2^25 static constexpr long long MOD3 = 469762049; // 2^26 static constexpr long long M1M2 = MOD1 * MOD2; static constexpr long long INV_M1_MOD2 = atcoder::internal::inv_gcd(MOD1, MOD2).second; static constexpr long long INV_M1M2_MOD3 = atcoder::internal::inv_gcd(M1M2, MOD3).second; std::vector a2(n), b2(m); for (int i = 0; i < n; ++i) a2[i] = a[i].val(); for (int i = 0; i < m; ++i) b2[i] = b[i].val(); auto c1 = atcoder::convolution(a2, b2); auto c2 = atcoder::convolution(a2, b2); auto c3 = atcoder::convolution(a2, b2); const long long m1m2 = mint(M1M2).val(); std::vector c(n + m - 1); for (int i = 0; i < n + m - 1; ++i) { // Garner's Algorithm // X = x1 + x2 * m1 + x3 * m1 * m2 // x1 = c1[i], x2 = (c2[i] - x1) / m1 (mod m2), x3 = (c3[i] - x1 - x2 * m1) / m2 (mod m3) long long x1 = c1[i]; long long x2 = (atcoder::static_modint(c2[i] - x1) * INV_M1_MOD2).val(); long long x3 = (atcoder::static_modint(c3[i] - x1 - x2 * MOD1) * INV_M1M2_MOD3).val(); c[i] = x1 + x2 * MOD1 + x3 * m1m2; } return c; } } // namespace suisen constexpr int N = 100000; int main() { int n, m, c; std::cin >> n >> m >> c; mint::set_mod(m); int s = 0; std::vector> binom(n + 1, std::vector(n + 1)); binom[0][0] = 1; for (int i = 1; i <= n; ++i) { binom[i][0] = binom[i][i] = 1; for (int j = 1; j < i; ++j) { binom[i][j] = binom[i - 1][j - 1] + binom[i - 1][j]; } } std::array cnt{}; for (int i = 0; i < n; ++i) { int e; std::cin >> e; s += e; ++cnt[e]; } std::vector dp(c + 1, std::vector(s + 1)); dp[0][0] = 1; for (int val = N; val >= 1; --val) { const int p = cnt[val]; if (p == 0) continue; std::vector g(p + 1); for (int i = 0; i <= p; ++i) { g[i] = binom[p][i]; } for (int sum_mod = 0; sum_mod < val; ++sum_mod) { const int max_diff = (s - sum_mod) / val; for (int diff = 0; diff <= max_diff; ++diff) { const int max_num = std::min(c, (s - sum_mod) / val - diff); std::vector f(max_num + 1); for (int num = 0; num <= max_num; ++num) { f[num] = dp[num][(num + diff) * val + sum_mod]; } std::vector h = suisen::arbitrary_mod_convolution(f, g); for (int num = 0; num <= max_num; ++num) { dp[num][(num + diff) * val + sum_mod] = h[num]; } } } } for (int sum = 1; sum <= s; ++sum) { std::cout << dp[c][sum].val() << " \n"[sum == s]; } return 0; }