Submission #70276868

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Source Code Expand

#include <bits/stdc++.h>
#include <atcoder/all>
using namespace std;
using namespace atcoder;
//using mint = modint1000000007;
//const int mod = 1000000007;
using mint = modint998244353;
const int mod = 998244353;
//const int INF = 1e9;
//const long long LINF = 1e18;
#define rep(i, n) for (int i = 0; i < (n); ++i)
#define rep2(i,l,r)for(int i=(l);i<(r);++i)
#define rrep(i, n) for (int i = (n) - 1; i >= 0; --i)
#define rrep2(i,l,r)for(int i=(r) - 1;i>=(l);--i)
#define all(x) (x).begin(),(x).end()
#define allR(x) (x).rbegin(),(x).rend()
#define P pair<int,int>
template<typename A, typename B> inline bool chmax(A & a, const B & b) { if (a < b) { a = b; return true; } return false; }
template<typename A, typename B> inline bool chmin(A & a, const B & b) { if (a > b) { a = b; return true; } return false; }
// combination mod prime
// https://www.youtube.com/watch?v=8uowVvQ_-Mo&feature=youtu.be&t=1619
struct combination {
	std::vector<mint> fact, ifact;
	combination(int n) :fact(n + 1), ifact(n + 1) {
		assert(n < mod);
		fact[0] = 1;
		for (int i = 1; i <= n; ++i) fact[i] = fact[i - 1] * i;
		ifact[n] = fact[n].inv();
		for (int i = n; i >= 1; --i) ifact[i - 1] = ifact[i] * i;
	}
	mint operator()(int n, int k) { return com(n, k); }
	mint com(int n, int k) {
		//負の二項係数を考慮する場合にコメントアウトを外す
		//if (n < 0) return com(-n, k) * (k % 2 ? -1 : 1);
		if (k < 0 || k > n) return 0;
		return fact[n] * ifact[k] * ifact[n - k];
	}
	mint comsub(long long n, long long k) {
		if (n - k < k) k = n - k;
		assert(k < (int)fact.size());
		mint val = ifact[k];
		for (int i = 0; i < k; ++i) val *= n - i;
		return val;
	}
	template <typename ...Ms, std::enable_if_t<std::conjunction_v<std::is_integral<Ms>...>, std::nullptr_t> = nullptr>
	mint polynom(const int n, const Ms & ...ms) {
		mint res = fact[n];
		int sum = 0;
		for (int m : { ms... }) {
			if (m < 0 or m > n) return 0;
			res *= ifact[m];
			sum += m;
		}
		if (sum > n)return 0;
		res *= ifact[n - sum];
		return res;
	}
	mint div(int x) {
		if (x >= (int)fact.size())return mint(x).inv();
		return fact[x - 1] * ifact[x];
	}
	mint inv(int n, int k) {
		//if (n < 0) return inv(-n, k) * (k % 2 ? -1 : 1);
		if (k < 0 || k > n) return 0;
		return ifact[n] * fact[k] * fact[n - k];
	}
	mint p(int n, int k) { return fact[n] * ifact[n - k]; }
}c(2000006);

int main() {
	std::ios::sync_with_stdio(false);
	std::cin.tie(nullptr);
	int n, u; cin >> n >> u;
	vector<int>b(n);
	rep(i, n)cin >> b[i];

	vector<int>cnt(u + 1);
	rep(i, n)cnt[b[i]]++;

	vector dp(21, vector<mint>(u + 1));
	dp[0][1] = 1;
	rep(i, 20) {
		rep2(j, 1, u + 1) {
			for (int k = 1; j * k <= u; k++) {
				dp[i + 1][j * k] += dp[i][j] * cnt[k];
			}
		}
	}

	vector<mint> ans(u + 1);
	vector tmp(u + 1, vector<int>(21));
	{
		rep2(i, 2, u + 1) {
			long long ni = i;
			long long pw = 1;
			while (ni <= u) {
				// i^pw = ni
				tmp[ni][pw] = i;
				ni *= i;
				pw++;
			}
		}
	}//return 0;

	rep2(i, 1, 21) {
		mint inv = mint(i).inv();
		rep2(j, 2, u + 1) {
			// i個、使って積がjのものにポリアする
			rep2(x, 1, i + 1) {
				int p = i / gcd(i, x);
				int q = i / p;
				int r = tmp[j][p];//(j)^(1/z);
				ans[j] += dp[q][r] * inv;
			}
		}
	}
	rep2(i, 2, u + 1)cout << ans[i].val() << endl;
	return 0;
}

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