#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

using Int = long long;

template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
#define COLOR(s) ("\x1b[" s "m")

////////////////////////////////////////////////////////////////////////////////
template <unsigned M_> struct ModInt {
  static constexpr unsigned M = M_;
  unsigned x;
  constexpr ModInt() : x(0U) {}
  constexpr ModInt(unsigned x_) : x(x_ % M) {}
  constexpr ModInt(unsigned long long x_) : x(x_ % M) {}
  constexpr ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
  constexpr ModInt(long long x_) : x(((x_ %= static_cast<long long>(M)) < 0) ? (x_ + static_cast<long long>(M)) : x_) {}
  ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; }
  ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; }
  ModInt &operator*=(const ModInt &a) { x = (static_cast<unsigned long long>(x) * a.x) % M; return *this; }
  ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); }
  ModInt pow(long long e) const {
    if (e < 0) return inv().pow(-e);
    ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b;
  }
  ModInt inv() const {
    unsigned a = M, b = x; int y = 0, z = 1;
    for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast<int>(q) * z; y = z; z = w; }
    assert(a == 1U); return ModInt(y);
  }
  ModInt operator+() const { return *this; }
  ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; }
  ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); }
  ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); }
  ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); }
  ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); }
  template <class T> friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); }
  template <class T> friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); }
  template <class T> friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); }
  template <class T> friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); }
  explicit operator bool() const { return x; }
  bool operator==(const ModInt &a) const { return (x == a.x); }
  bool operator!=(const ModInt &a) const { return (x != a.x); }
  friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; }
};
////////////////////////////////////////////////////////////////////////////////

constexpr unsigned MO = 998244353;
using Mint = ModInt<MO>;

constexpr int LIM_INV = 3'000'010;
Mint inv[LIM_INV], fac[LIM_INV], invFac[LIM_INV];

void prepare() {
  inv[1] = 1;
  for (int i = 2; i < LIM_INV; ++i) {
    inv[i] = -((Mint::M / i) * inv[Mint::M % i]);
  }
  fac[0] = invFac[0] = 1;
  for (int i = 1; i < LIM_INV; ++i) {
    fac[i] = fac[i - 1] * i;
    invFac[i] = invFac[i - 1] * inv[i];
  }
}
Mint binom(Int n, Int k) {
  if (n < 0) {
    if (k >= 0) {
      return ((k & 1) ? -1 : +1) * binom(-n + k - 1, k);
    } else if (n - k >= 0) {
      return (((n - k) & 1) ? -1 : +1) * binom(-k - 1, n - k);
    } else {
      return 0;
    }
  } else {
    if (0 <= k && k <= n) {
      assert(n < LIM_INV);
      return fac[n] * invFac[k] * invFac[n - k];
    } else {
      return 0;
    }
  }
}


/*
  F[n] := \sum[i+j+k=n] max{A+i,B+j,C+k} n!/i!j!k!
  for n >= 1 && i+j+k = n:
    n!/i!j!k! = (n-1)!/(i-1)!j!k! + (n-1)!/i!(j-1)!k! + (n-1)!/i!j!(k-1)!
    F[n] = 3 F[n-1]
           + \sum[i+j+k=n] (max{A+i,B+j,C+k} - max{A+i-1,B+j,C+k}) (n-1)!/(i-1)!j!k!
           + (cyclic)
         = 3 F[n-1]
           + \sum[i+j+k=n-1] [A+i >= max{B+j,C+k}] (n-1)!/i!j!k!
           + (cyclic)
  
  G[n] := \sum[i+j+k=n] [A+i >= max{B+j,C+k}] n!/i!j!k!
  for n >= 1 && i+j+k = n:
    G[n] = 3 G[n-1]
           + \sum[i+j+k=n] ([A+i >= max{B+j,C+k}] - [A+i-1 >= max{B+j,C+k}]) (n-1)!/(i-1)!j!k!
           + \sum[i+j+k=n] ([A+i >= max{B+j,C+k}] - [A+i >= max{B+j-1,C+k}]) (n-1)!/i!(j-1)!k!
           + \sum[i+j+k=n] ([A+i >= max{B+j,C+k}] - [A+i >= max{B+j,C+k-1}]) (n-1)!/i!j!(k-1)!
         = 3 G[n-1]
           + \sum[i+j+k=n-1] [A+i+1 = max{B+j,C+k}] (n-1)!/i!j!k!
           - \sum[i+j+k=n-1] [A+i = B+j >= C+k] (n-1)!/i!j!k!
           - \sum[i+j+k=n-1] [A+i = C+k >= B+j] (n-1)!/i!j!k!
  
  [A+i+1 = max{B+j,C+k}]
  = [A+i+1 = B+j >= C+k] + [A+i+1 = C+k >= B+j] - [A+i+1 = B+j = C+k]
  
  H[n] := \sum[i+j+k=n] [a+i = b+j >= C+k] n!/i!j!k!
  for n >= 2 && i+j+k = n && a+i = b+j:
    i = (n-a+b-k)/2
    j = (n+a-b-k)/2
    n!/i!j!k! = p (n-2)!/(i-1)!(j-1)!k! + q (n-1)!/i!j!(k-1)! + r (n-2)!/i!j!(k-2)!
      p = 4n(n-1) / (n-a+b)(n+a-b)
      q = n(2n-1) / (n-a+b)(n+a-b)
      r = -n(n-1) / (n-a+b)(n+a-b)
        for n < |a-b|: [a+i = b+j] = 0
    H[n] = p H[n-2] + q H[n-1] + r H[n-2]
           + p \sum[i+j+k=n] ([a+i = b+j >= C+k] - [a+i-1 = b+j-1 >= C+k]) (n-2)!/(i-1)!(j-1)!k!
           + q \sum[i+j+k=n] ([a+i = b+j >= C+k] - [a+i = b+j >= C+k-1]) (n-1)!/i!j!(k-1)!
           + r \sum[i+j+k=n] ([a+i = b+j >= C+k] - [a+i = b+j >= C+k-2]) (n-2)!/i!j!(k-2)!
         = p H[n-2] + q H[n-1] + r H[n-2]
           + p \sum[i+j+k=n-2] [a+i+1 = b+j+1 = C+k] (n-2)!/i!j!k!
           - q \sum[i+j+k=n-1] [a+i = b+j = C+k] (n-1)!/i!j!k!
           - r \sum[i+j+k=n-2] ([a+i = b+j = C+k] + [a+i = b+j = C+k+1]) (n-2)!/i!j!k!
*/

Mint path(int i, int j, int k) {
  return (i >= 0 && j >= 0 && k >= 0) ? (fac[i+j+k] * invFac[i] * invFac[j] * invFac[k]) : 0;
}

Mint same(int n, int a, int b, int c) {
  int m = a + b + c + n;
  if (m % 3 != 0) return 0;
  m /= 3;
  return path(m - a, m - b, m - c);
}

int main() {
  prepare();
  
  int A[3], N;
  for (; ~scanf("%d%d%d%d", &A[0], &A[1], &A[2], &N); ) {
    vector<Mint> H[3][2][2];
    for (int s = 0; s < 3; ++s) for (int u = 0; u < 2; ++u) for (int v = 0; v < 2; ++v) if (u + v <= 1) {
      const int a = A[s] + u;
      const int b = A[(s+1)%3] + v;
      const int c = A[(s+2)%3];
      auto &hs = H[s][u][v];
      hs.assign(N + 1, 0);
      for (int n = abs(a - b); n <= N; ++n) {
        if (n == 0) {
          if (a == b && a >= c) hs[n] += 1;
        } else if (n == 1) {
          if (a+1 == b && a+1 >= c) hs[n] += 1;
          if (a == b+1 && a >= c) hs[n] += 1;
          if (a == b && a >= c+1) hs[n] += 1;
        } else if (n == abs(a - b)) {
          if (max(a, b) >= c) hs[n] += 1;
        } else {
          const Mint p = 4LL * n * (n-1)   * inv[n-a+b] * inv[n+a-b];
          const Mint q = 1LL * n * (2*n-1) * inv[n-a+b] * inv[n+a-b];
          const Mint r = -1LL * n * (n-1)  * inv[n-a+b] * inv[n+a-b];
          hs[n] += p * hs[n-2];
          hs[n] += q * hs[n-1];
          hs[n] += r * hs[n-2];
          hs[n] += p * same(n-2, a+1, b+1, c);
          hs[n] -= q * same(n-1, a, b, c);
          hs[n] -= r * (same(n-2, a, b, c) + same(n-2, a, b, c+1));
#ifdef LOCAL
// cerr<<a<<" "<<b<<" "<<c<<" "<<n<<": "<<p<<" "<<q<<" "<<r<<endl;
for(int i=0;i<=n;++i)for(int j=0;j<=n-i;++j){const int k=n-i-j;
 if(a+i==b+j)assert(path(i,j,k)==p*path(i-1,j-1,k)+q*path(i,j,k-1)+r*path(i,j,k-2));
}
#endif
        }
      }
#ifdef LOCAL
vector<Mint>brt(N+1,0);
for(int i=0;i<=N;++i)for(int j=0;j<=N-i;++j)for(int k=0;k<=N-i-j;++k)if(a+i==b+j&&a+i>=c+k)brt[i+j+k]+=path(i,j,k);
// cerr<<"a = "<<a<<", b = "<<b<<", c = "<<c<<endl;
// cerr<<"  brt = "<<brt<<endl;
// cerr<<"  hs  = "<<hs<<endl;
assert(brt==hs);
#endif
    }
    
    vector<Mint> G[3];
    for (int s = 0; s < 3; ++s) {
      const int a = A[s];
      const int b = A[(s+1)%3];
      const int c = A[(s+2)%3];
      auto &gs = G[s];
      gs.assign(N + 1, 0);
      for (int n = 0; n <= N; ++n) {
        if (n == 0) {
          if (a >= b && a >= c) gs[n] += 1;
        } else {
          gs[n] += 3 * gs[n-1];
          gs[n] += (H[s][1][0][n-1] + H[(s+2)%3][0][1][n-1] - same(n-1, a+1, b, c));
          gs[n] -= H[s][0][0][n-1];
          gs[n] -= H[(s+2)%3][0][0][n-1];
        }
      }
#ifdef LOCAL
vector<Mint>brt(N+1,0);
for(int i=0;i<=N;++i)for(int j=0;j<=N-i;++j)for(int k=0;k<=N-i-j;++k)if(a+i>=b+j&&a+i>=c+k)brt[i+j+k]+=path(i,j,k);
// cerr<<"a = "<<a<<", b = "<<b<<", c = "<<c<<endl;
// cerr<<"  brt = "<<brt<<endl;
// cerr<<"  gs  = "<<gs<<endl;
assert(brt==gs);
#endif
    }
    
    vector<Mint> F(N + 1, 0);
    for (int n = 0; n <= N; ++n) {
      if (n == 0) {
        F[n] += max({A[0], A[1], A[2]});
      } else {
        F[n] += 3 * F[n-1];
        for (int s = 0; s < 3; ++s) {
          F[n] += G[s][n-1];
        }
      }
    }
#ifdef LOCAL
vector<Mint>brt(N+1,0);
for(int i=0;i<=N;++i)for(int j=0;j<=N-i;++j)for(int k=0;k<=N-i-j;++k)brt[i+j+k]+=max({A[0]+i,A[1]+j,A[2]+k})*path(i,j,k);
// cerr<<"A = ";pv(A,A+3);
// cerr<<"  brt = "<<brt<<endl;
// cerr<<"  F   = "<<F<<endl;
assert(brt==F);
#endif
    
    {
      Mint t = 1;
      for (int n = 0; n <= N; ++n) {
        F[n] *= t;
        t /= 3;
      }
    }
    for (int n = 1; n <= N; ++n) {
      printf("%u\n", F[n].x);
    }
#ifdef LOCAL
cerr<<"========"<<endl;
#endif
  }
  return 0;
}