Problem: Our child likes computer science very much, especially he likes binary trees.

Consider the sequence of n distinct positive integers: c1, c2, ..., cn. The child calls a vertex-weighted rooted binary tree good if and only if for every vertex v, the weight of v is in the set {c1, c2, ..., cn}. Also our child thinks that the weight of a vertex-weighted tree is the sum of all vertices' weights.

Given an integer m, can you for all s (1 ≤ s ≤ m) calculate the number of good vertex-weighted rooted binary trees with weight s? Please, check the samples for better understanding what trees are considered different.

We only want to know the answer modulo 998244353 (7 × 17 × 223 + 1, a prime number).

Input

The first line contains two integers n, m (1 ≤ n ≤ 105; 1 ≤ m ≤ 105). The second line contains n space-separated pairwise distinct integers c1, c2, ..., cn. (1 ≤ ci ≤ 105).

Output

Print m lines, each line containing a single integer. The i-th line must contain the number of good vertex-weighted rooted binary trees whose weight exactly equal to i. Print the answers modulo 998244353 (7 × 17 × 223 + 1, a prime number).

Examples

Input

2 3
1 2


Output

1
3
9


Input

3 10
9 4 3


Output

0
0
1
1
0
2
4
2
6
15


Input

5 10
13 10 6 4 15


Output

0
0
0
1
0
1
0
2
0
5

Note

In the first example, there are 9 good vertex-weighted rooted binary trees whose weight exactly equal to 3:

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Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
using Int = long long;
constexpr int bmds(int x) {
  const int v[] = {1012924417, 924844033, 998244353, 897581057, 645922817};
  return v[x];
}
constexpr int brts(int x) {
  const int v[] = {5, 5, 3, 3, 3};
  return v[x];
}
template <int X>
struct NTT {
  static constexpr int md = bmds(X);
  static constexpr int rt = brts(X);
  inline int add(int a, int b) {
    a += b;
    if (a >= md) a -= md;
    return a;
  }
  inline int mul(int a, int b) { return 1LL * a * b % md; }
  inline int pow(int a, int b) {
    int res = 1;
    while (b) {
      if (b & 1) res = mul(res, a);
      a = mul(a, a);
      b >>= 1;
    }
    return res;
  }
  inline int inv(int x) { return pow(x, md - 2); }
  inline int sqrt(int a) {
    if (a == 0) return 0;
    if (pow(a, (md - 1) / 2) != 1) return -1;
    int q = md - 1, m = 0;
    while (~q & 1) q >>= 1, m++;
    mt19937 mt;
    int z = mt() % md;
    while (pow(z, (md - 1) / 2) != md - 1) z = mt() % md;
    int c = pow(z, q), t = pow(a, q), r = pow(a, (q + 1) / 2);
    while (m > 1) {
      if (pow(t, 1 << (m - 2)) != 1) r = mul(r, c), t = mul(t, mul(c, c));
      c = mul(c, c);
      m--;
    }
    return r;
  }
  vector<vector<int> > rts, rrts;
  void ensure_base(int n) {
    if ((int)rts.size() >= n) return;
    rts.resize(n);
    rrts.resize(n);
    for (int i = 1; i < n; i <<= 1) {
      if (!rts[i].empty()) continue;
      int w = pow(rt, (md - 1) / (i << 1));
      int rw = inv(w);
      rts[i].resize(i);
      rrts[i].resize(i);
      rts[i][0] = 1;
      rrts[i][0] = 1;
      for (int k = 1; k < i; k++) {
        rts[i][k] = mul(rts[i][k - 1], w);
        rrts[i][k] = mul(rrts[i][k - 1], rw);
      }
    }
  }
  void ntt(vector<int> &a, bool f, int n = -1) {
    if (n == -1) n = a.size();
    assert((n & (n - 1)) == 0);
    for (int i = 0, j = 1; j + 1 < n; j++) {
      for (int k = n >> 1; k > (i ^= k); k >>= 1)
        ;
      if (i > j) swap(a[i], a[j]);
    }
    for (int i = 1; i < n; i <<= 1) {
      for (int j = 0; j < n; j += i * 2) {
        for (int k = 0; k < i; k++) {
          int z = mul(a[i + j + k], f ? rrts[i][k] : rts[i][k]);
          a[i + j + k] = add(a[j + k], md - z);
          a[j + k] = add(a[j + k], z);
        }
      }
    }
    if (f) {
      int tmp = inv(n);
      for (Int i = 0; i < n; i++) a[i] = mul(a[i], tmp);
    }
  }
  vector<int> add(vector<int> as, vector<int> bs) {
    int sz = max(as.size(), bs.size());
    vector<int> cs(sz, 0);
    for (int i = 0; i < (int)as.size(); i++) cs[i] = add(cs[i], as[i]);
    for (int i = 0; i < (int)bs.size(); i++) cs[i] = add(cs[i], bs[i]);
    return cs;
  }
  vector<int> sub(vector<int> as, vector<int> bs) {
    int sz = max(as.size(), bs.size());
    vector<int> cs(sz, 0);
    for (int i = 0; i < (int)as.size(); i++) cs[i] = add(cs[i], as[i]);
    for (int i = 0; i < (int)bs.size(); i++) cs[i] = add(cs[i], md - bs[i]);
    return cs;
  }
  vector<int> multiply(vector<int> as, vector<int> bs) {
    int need = as.size() + bs.size() - 1;
    int sz = 1;
    while (sz < need) sz <<= 1;
    ensure_base(sz);
    vector<int> f(sz), g(sz);
    for (int i = 0; i < (int)as.size(); i++) f[i] = as[i];
    for (int i = 0; i < (int)bs.size(); i++) g[i] = bs[i];
    ntt(f, 0);
    ntt(g, 0);
    for (int i = 0; i < sz; i++) f[i] = mul(f[i], g[i]);
    ntt(f, 1);
    f.resize(need);
    return f;
  }
  vector<int> divide(vector<int> as, vector<int> bs) {
    assert(bs != vector<int>(bs.size(), 0));
    if (as == vector<int>(as.size(), 0)) return {0};
    assert(as.size() >= bs.size());
    int need = as.size() - bs.size() + 1;
    as.resize(need);
    if (bs[0] == 0) {
      reverse(as.begin(), as.end());
      reverse(bs.begin(), bs.end());
      while (bs.back() == 0) {
        assert(as.back() == 0);
        as.pop_back();
        bs.pop_back();
      }
      reverse(as.begin(), as.end());
      reverse(bs.begin(), bs.end());
    }
    int sz = 1;
    vector<int> rs({inv(bs[0])});
    while (sz < need) {
      sz <<= 1;
      vector<int> ts(min(sz, (int)bs.size()));
      for (int i = 0; i < (int)ts.size(); i++) ts[i] = bs[i];
      rs = sub(add(rs, rs), multiply(multiply(rs, rs), ts));
      rs.resize(sz);
    }
    while (as.back() == 0) as.pop_back();
    while (rs.back() == 0) rs.pop_back();
    auto cs = multiply(as, rs);
    cs.resize(need, 0);
    return cs;
  }
  vector<int> sqrt(vector<int> as) {
    if (as == vector<int>(as.size(), 0)) return {0};
    int dg = 0;
    if (as[0] == 0) {
      reverse(as.begin(), as.end());
      while (as.back() == 0) {
        dg++;
        as.pop_back();
        assert(as.back() == 0);
        as.pop_back();
      }
      reverse(as.begin(), as.end());
    }
    int sz = 1, inv2 = inv(2);
    vector<int> ss({sqrt(as[0])});
    while (sz < (int)as.size()) {
      sz <<= 1;
      vector<int> ts(min(sz + sz / 2 - 1, (int)as.size()));
      for (int i = 0; i < (int)ts.size(); i++) ts[i] = as[i];
      ss = add(ss, divide(ts, ss));
      ss.resize(sz);
      for (int &x : ss) x = mul(x, inv2);
    }
    if (dg) {
      reverse(ss.begin(), ss.end());
      for (int i = 0; i < dg; i++) ss.emplace_back(0);
      reverse(ss.begin(), ss.end());
    }
    return ss;
  }
};
signed ATC001_C() {
  cin.tie(0);
  ios::sync_with_stdio(0);
  int n;
  cin >> n;
  vector<int> as(n + 1, 0), bs(n + 1, 0);
  for (int i = 1; i <= n; i++) cin >> as[i] >> bs[i];
  NTT<0> ntt;
  auto cs = ntt.multiply(as, bs);
  for (int i = 1; i <= n * 2; i++) cout << cs[i] << "\n";
  cout << flush;
  return 0;
}
signed HAPPYQUERY_E() {
  cin.tie(0);
  ios::sync_with_stdio(0);
  int n, m, q;
  cin >> n >> m >> q;
  vector<int> ls(q), rs(q);
  for (int i = 0; i < q; i++) cin >> ls[i] >> rs[i], ls[i]--;
  vector<int> as(n);
  for (int i = 0; i < n; i++) cin >> as[i];
  vector<int> cnt(n - m + 1, 0);
  for (int l : ls) cnt[l]++;
  NTT<0> ntt;
  auto bs = ntt.divide(as, cnt);
  assert((int)bs.size() == m);
  for (int i = 0; i < m; i++) {
    if (i) cout << " ";
    cout << bs[i];
  }
  cout << endl;
  return 0;
}
signed CFR250_E() {
  cin.tie(0);
  ios::sync_with_stdio(0);
  int n, m;
  cin >> n >> m;
  vector<int> cs(n);
  for (int i = 0; i < n; i++) cin >> cs[i];
  NTT<2> ntt;
  vector<int> as(1 << 18, 0);
  as[0] = 1;
  for (int c : cs) as[c] = ntt.add(as[c], ntt.md - 4);
  vector<int> bs = ntt.sqrt(as);
  bs[0] = ntt.add(bs[0], 1);
  while (bs.back() == 0) bs.pop_back();
  vector<int> vs(bs.size() + m, 0);
  vs[0] = 2;
  vector<int> ans = ntt.divide(vs, bs);
  for (int i = 1; i <= m; i++) cout << ans[i] << "\n";
  cout << flush;
  return 0;
}
signed main() {
  CFR250_E();
  return 0;
}