%%%dkw
话说这是个论文题来着...
考虑生成函数(OGF)
对于价值为(v)的物品，由于有(10^5)的件数，可以看做无限个
那么，其生成函数为(x^0 + x^{v} + x^{2v} + ... = frac{1}{1 - x^v})
我们所需的答案即([x^n] prod frac{1}{1 - x^{v_i}})
只需考虑求出(A = prod frac{1}{1 - x^{v_i}})
自然地想到取对数
(In(A) = sum In(frac{1}{1 - x^{v_i}}))
不难发现
(In(frac{1}{1 - x^v}) = - In(1 - x^v))
考虑用麦克劳林级数来模拟，那么
由于(In^{(n)}(1 - x) = - frac{1}{(1 - x)^n} * (n - 1)!)
(-In(1 - x^v) = sum frac{x^{vi}}{i})
于是，我们可以直接枚举倍数，在(O(m log m))的时间内完成计算
最后只要(O(m log m))的(exp)一下即可
#include <cmath>
#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
#define ri register int
#define rep(io, st, ed) for(ri io = st; io <= ed; io ++)
#define drep(io, ed, st) for(ri io = ed; io >= st; io --)
#define gc getchar
inline int read() {
int p = 0, w = 1; char c = gc();
while(c > '9' || c < '0') { if(c == '-') w = -1; c = gc(); }
while(c >= '0' && c <= '9') p = p * 10 + c - '0', c = gc();
return p * w;
}
const int sid = 500050;
const int mod = 998244353;
int n, m;
int V[sid], F[sid], inv[sid], rev[sid], ans[sid];
inline int Inc(int a, int b) { return (a + b >= mod) ? a + b - mod : a + b; }
inline int Dec(int a, int b) { return (a - b < 0) ? a - b + mod : a - b; }
inline int mul(int a, int b) { return 1ll * a * b % mod; }
inline int fp(int a, int k) {
int ret = 1;
for( ; k; k >>= 1, a = mul(a, a))
if(k & 1) ret = mul(ret, a);
return ret;
}
inline void init(int Maxn, int &n, int &lg) {
n = 1; lg = 0;
while(n < Maxn) n <<= 1, lg ++;
}
inline void NTT(int *a, int n, int opt) {
for(ri i = 0; i < n; i ++) if(i < rev[i]) swap(a[i], a[rev[i]]);
for(ri i = 1; i < n; i <<= 1)
for(ri j = 0, g = fp(3, (mod - 1) / (i << 1)); j < n; j += (i << 1))
for(ri k = j, G = 1; k < i + j; k ++, G = mul(G, g)) {
int x = a[k], y = mul(G, a[i + k]);
a[k] = (x + y >= mod) ? x + y - mod : x + y;
a[i + k] = (x - y < 0) ? x - y + mod : x - y;
}
if(opt == -1) {
int ivn = fp(n, mod - 2);
reverse(a + 1, a + n);
rep(i, 0, n) a[i] = mul(a[i], ivn);
}
}
int ia[sid], ib[sid];
inline void Inv(int *a, int *b, int n) {
if(n == 1) { b[0] = fp(a[0], mod - 2); return; }
Inv(a, b, n >> 1);
int N = 1, lg = 0; init(n + n, N, lg);
for(ri i = 0; i < N; i ++)
rev[i] = (rev[i >> 1] >> 1) | ((i & 1) << (lg - 1));
for(ri i = 0; i < N; i ++) ia[i] = ib[i] = 0;
for(ri i = 0; i < n; i ++) ia[i] = a[i], ib[i] = b[i];
NTT(ia, N, 1); NTT(ib, N, 1);
for(ri i = 0; i < N; i ++)
ia[i] = Dec((ib[i] << 1) % mod, mul(ia[i], mul(ib[i], ib[i])));
NTT(ia, N, -1);
for(ri i = 0; i < n; i ++) b[i] = ia[i];
}
inline void Inv_init(int n) {
inv[0] = inv[1] = 1;
rep(i, 2, n) inv[i] = mul(inv[mod % i], mod - mod / i);
}
inline void wf(int *a, int *b, int n) { for(ri i = 1; i < n; i ++) b[i - 1] = mul(a[i], i); }
inline void jf(int *a, int *b, int n) { for(ri i = 1; i < n; i ++) b[i] = mul(a[i - 1], inv[i]); }
int iv[sid], dx[sid];
inline void In(int *a, int *b, int n) {
for(ri i = 0; i < n + n; i ++) iv[i] = dx[i] = 0;
Inv(a, iv, n); wf(a, dx, n);
int N = 1, lg = 0; init(n + n, N, lg);
for(ri i = 0; i < N; i ++)
rev[i] = (rev[i >> 1] >> 1) | ((i & 1) << (lg - 1));
NTT(iv, N, 1); NTT(dx, N, 1);
for(ri i = 0; i < N; i ++) iv[i] = mul(iv[i], dx[i]);
NTT(iv, N, -1); jf(iv, b, n);
}
int inb[sid], fb[sid];
inline void Exp(int *a, int *b, int n) {
if(n == 1) { b[0] = 1; return; }
Exp(a, b, n >> 1);
for(ri i = 0; i < n + n; i ++) inb[i] = fb[i] = 0;
In(b, inb, n);
int N = 1, lg = 0; init(n + n, N, lg);
for(ri i = 0; i < N; i ++)
rev[i] = (rev[i >> 1] >> 1) | ((i & 1) << (lg - 1));
for(ri i = 0; i < n; i ++) fb[i] = Dec(a[i], inb[i]); fb[0] ++;
for(ri i = 0; i < n; i ++) inb[i] = b[i];
NTT(inb, N, 1); NTT(fb, N, 1);
for(ri i = 0; i < N; i ++) fb[i] = mul(fb[i], inb[i]);
NTT(fb, N, -1);
for(ri i = 0; i < n; i ++) b[i] = fb[i], b[i + n] = 0;
}
inline void calc() {
int N = 1, lg = 0;
init(m + 5, N, lg); Inv_init(N);
for(ri i = 1; i <= m; i ++)
for(ri j = i; j <= m; j += i)
F[j] = Inc(F[j], mul(V[i], inv[j / i]));
Exp(F, ans, N);
rep(i, 1, m) printf("%d
", ans[i]);
}
int main() {
n = read(); m = read();
rep(i, 1, n) V[read()] ++;
calc();
return 0;
}