#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 <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 = 998244353U;
constexpr unsigned MO2 = 2U * MO;
constexpr int FFT_MAX = 23;
using Mint = ModInt<MO>;
constexpr Mint FFT_ROOTS[FFT_MAX + 1] = {1U, 998244352U, 911660635U, 372528824U, 929031873U, 452798380U, 922799308U, 781712469U, 476477967U, 166035806U, 258648936U, 584193783U, 63912897U, 350007156U, 666702199U, 968855178U, 629671588U, 24514907U, 996173970U, 363395222U, 565042129U, 733596141U, 267099868U, 15311432U};
constexpr Mint INV_FFT_ROOTS[FFT_MAX + 1] = {1U, 998244352U, 86583718U, 509520358U, 337190230U, 87557064U, 609441965U, 135236158U, 304459705U, 685443576U, 381598368U, 335559352U, 129292727U, 358024708U, 814576206U, 708402881U, 283043518U, 3707709U, 121392023U, 704923114U, 950391366U, 428961804U, 382752275U, 469870224U};
constexpr Mint FFT_RATIOS[FFT_MAX] = {911660635U, 509520358U, 369330050U, 332049552U, 983190778U, 123842337U, 238493703U, 975955924U, 603855026U, 856644456U, 131300601U, 842657263U, 730768835U, 942482514U, 806263778U, 151565301U, 510815449U, 503497456U, 743006876U, 741047443U, 56250497U, 867605899U};
constexpr Mint INV_FFT_RATIOS[FFT_MAX] = {86583718U, 372528824U, 373294451U, 645684063U, 112220581U, 692852209U, 155456985U, 797128860U, 90816748U, 860285882U, 927414960U, 354738543U, 109331171U, 293255632U, 535113200U, 308540755U, 121186627U, 608385704U, 438932459U, 359477183U, 824071951U, 103369235U};

// as[rev(i)] <- \sum_j \zeta^(ij) as[j]
void fft(Mint *as, int n) {
  assert(!(n & (n - 1))); assert(1 <= n); assert(n <= 1 << FFT_MAX);
  int m = n;
  if (m >>= 1) {
    for (int i = 0; i < m; ++i) {
      const unsigned x = as[i + m].x;  // < MO
      as[i + m].x = as[i].x + MO - x;  // < 2 MO
      as[i].x += x;  // < 2 MO
    }
  }
  if (m >>= 1) {
    Mint prod = 1U;
    for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {
      for (int i = i0; i < i0 + m; ++i) {
        const unsigned x = (prod * as[i + m]).x;  // < MO
        as[i + m].x = as[i].x + MO - x;  // < 3 MO
        as[i].x += x;  // < 3 MO
      }
      prod *= FFT_RATIOS[__builtin_ctz(++h)];
    }
  }
  for (; m; ) {
    if (m >>= 1) {
      Mint prod = 1U;
      for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {
        for (int i = i0; i < i0 + m; ++i) {
          const unsigned x = (prod * as[i + m]).x;  // < MO
          as[i + m].x = as[i].x + MO - x;  // < 4 MO
          as[i].x += x;  // < 4 MO
        }
        prod *= FFT_RATIOS[__builtin_ctz(++h)];
      }
    }
    if (m >>= 1) {
      Mint prod = 1U;
      for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {
        for (int i = i0; i < i0 + m; ++i) {
          const unsigned x = (prod * as[i + m]).x;  // < MO
          as[i].x = (as[i].x >= MO2) ? (as[i].x - MO2) : as[i].x;  // < 2 MO
          as[i + m].x = as[i].x + MO - x;  // < 3 MO
          as[i].x += x;  // < 3 MO
        }
        prod *= FFT_RATIOS[__builtin_ctz(++h)];
      }
    }
  }
  for (int i = 0; i < n; ++i) {
    as[i].x = (as[i].x >= MO2) ? (as[i].x - MO2) : as[i].x;  // < 2 MO
    as[i].x = (as[i].x >= MO) ? (as[i].x - MO) : as[i].x;  // < MO
  }
}

// as[i] <- (1/n) \sum_j \zeta^(-ij) as[rev(j)]
void invFft(Mint *as, int n) {
  assert(!(n & (n - 1))); assert(1 <= n); assert(n <= 1 << FFT_MAX);
  int m = 1;
  if (m < n >> 1) {
    Mint prod = 1U;
    for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {
      for (int i = i0; i < i0 + m; ++i) {
        const unsigned long long y = as[i].x + MO - as[i + m].x;  // < 2 MO
        as[i].x += as[i + m].x;  // < 2 MO
        as[i + m].x = (prod.x * y) % MO;  // < MO
      }
      prod *= INV_FFT_RATIOS[__builtin_ctz(++h)];
    }
    m <<= 1;
  }
  for (; m < n >> 1; m <<= 1) {
    Mint prod = 1U;
    for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {
      for (int i = i0; i < i0 + (m >> 1); ++i) {
        const unsigned long long y = as[i].x + MO2 - as[i + m].x;  // < 4 MO
        as[i].x += as[i + m].x;  // < 4 MO
        as[i].x = (as[i].x >= MO2) ? (as[i].x - MO2) : as[i].x;  // < 2 MO
        as[i + m].x = (prod.x * y) % MO;  // < MO
      }
      for (int i = i0 + (m >> 1); i < i0 + m; ++i) {
        const unsigned long long y = as[i].x + MO - as[i + m].x;  // < 2 MO
        as[i].x += as[i + m].x;  // < 2 MO
        as[i + m].x = (prod.x * y) % MO;  // < MO
      }
      prod *= INV_FFT_RATIOS[__builtin_ctz(++h)];
    }
  }
  if (m < n) {
    for (int i = 0; i < m; ++i) {
      const unsigned y = as[i].x + MO2 - as[i + m].x;  // < 4 MO
      as[i].x += as[i + m].x;  // < 4 MO
      as[i + m].x = y;  // < 4 MO
    }
  }
  const Mint invN = Mint(n).inv();
  for (int i = 0; i < n; ++i) {
    as[i] *= invN;
  }
}

void fft(vector<Mint> &as) {
  fft(as.data(), as.size());
}
void invFft(vector<Mint> &as) {
  invFft(as.data(), as.size());
}

vector<Mint> convolve(vector<Mint> as, vector<Mint> bs) {
  if (as.empty() || bs.empty()) return {};
  const int len = as.size() + bs.size() - 1;
  int n = 1;
  for (; n < len; n <<= 1) {}
  as.resize(n); fft(as);
  bs.resize(n); fft(bs);
  for (int i = 0; i < n; ++i) as[i] *= bs[i];
  invFft(as);
  as.resize(len);
  return as;
}
vector<Mint> square(vector<Mint> as) {
  if (as.empty()) return {};
  const int len = as.size() + as.size() - 1;
  int n = 1;
  for (; n < len; n <<= 1) {}
  as.resize(n); fft(as);
  for (int i = 0; i < n; ++i) as[i] *= as[i];
  invFft(as);
  as.resize(len);
  return as;
}
////////////////////////////////////////////////////////////////////////////////


// 0 = \sum_{j=0}^d (\sum_{k=0}^e css[j][k] i^k) as[i - j]  (d <= i < |as|)
template <unsigned M>
vector<vector<ModInt<M>>> findPRecurrence(const vector<ModInt<M>> &as, int e,
                                          bool verbose = false) {
  using Mint = ModInt<M>;
  const int asLen = as.size();
  // asLen - d >= (d + 1) (e + 1) - 1  (otherwise definitely  dim Ker >= 2)
  const int d0 = (asLen + 2) / (e + 2) - 1;
  if (d0 < 0) {
    if (verbose) {
      fprintf(stderr, "[findPRecurrence] |as| >= e  must hold.\n");
      fflush(stderr);
    }
    return {};
  }
  const int m = asLen - d0, n = (d0 + 1) * (e + 1);
  vector<vector<Mint>> bss(m, vector<Mint>(n, 0));
  for (int i = d0; i < asLen; ++i) for (int j = 0; j <= d0; ++j) {
    Mint pw = 1;
    for (int k = 0; k <= e; ++k) {
      bss[i - d0][j * (e + 1) + k] = pw * as[i - j];
      pw *= i;
    }
  }
  int r = 0;
  vector<int> hs;
  for (int h = 0; h < n; ++h) {
    for (int i = r; i < m; ++i) if (bss[i][h]) {
      bss[r].swap(bss[i]);
      break;
    }
    if (r < m && bss[r][h]) {
      const Mint s = bss[r][h].inv();
      for (int j = h; j < n; ++j) bss[r][j] *= s;
      for (int i = 0; i < m; ++i) if (i != r) {
        const Mint t = bss[i][h];
        for (int j = h; j < n; ++j) bss[i][j] -= t * bss[r][j];
      }
      ++r;
    } else {
      hs.push_back(h);
    }
  }
  if (hs.empty()) {
    if (verbose) {
      fprintf(stderr, "[findPRecurrence] Not found: d = %d, e = %d.\n", d0, e);
      fflush(stderr);
    }
    return {};
  }
  vector<vector<Mint>> css(d0 + 1, vector<Mint>(e + 1, 0));
  for (int j = 0; j <= d0; ++j) for (int k = 0; k <= e; ++k) {
    const int h = j * (e + 1) + k;
    css[j][k] = (h < hs[0]) ? -bss[h][hs[0]] : (h == hs[0]) ? 1 : 0;
  }
  int d = hs[0] / (e + 1);
  for (int i = d0; i < asLen; ++i) {
    Mint sum = 0;
    for (int j = 0; j <= d0; ++j) {
      Mint coef = 0, pw = 1;
      for (int k = 0; k <= e; ++k) {
        coef += css[j][k] * pw;
        pw *= i;
      }
      sum += coef * as[i - j];
    }
    for (; sum; ) {
      if (i - ++d < 0) break;
      assert(d <= d0);
      Mint coef = 0, pw = 1;
      for (int k = 0; k <= e; ++k) {
        coef += css[d][k] * pw;
        pw *= i;
      }
      sum += coef * as[i - d];
    }
  }
  css.resize(d + 1);
  if (verbose) {
    const int hsLen = hs.size();
    if (hsLen > d0 - d + 1) {
      fprintf(stderr, "[findPRecurrence] Degenerate? (dim Ker = %d)\n", hsLen);
    }
    fprintf(stderr, "[findPRecurrence] d = %d, e = %d, non-trivial: %d\n", d, e,
            asLen - d - (d + 1) * (e + 1) + 1);
    fprintf(stderr, "{\n");
    for (int j = 0; j <= d; ++j) {
      fprintf(stderr, "  {");
      for (int k = 0; k <= e; ++k) {
        const unsigned c = css[j][k].x;
        if (k > 0) fprintf(stderr, ", ");
        fprintf(stderr, "%d", static_cast<int>((c < M - c) ? c : (c - M)));
      }
      fprintf(stderr, "},\n");
    }
    fprintf(stderr, "}\n");
    fflush(stderr);
  }
  return css;
}

// 0 = \sum_{j=0}^d (\sum_{k=0}^e css[j][k] i^k) as[i - j]  (d <= i < |as|)
template <unsigned M>
vector<ModInt<M>> extendPRecurrence(vector<ModInt<M>> as,
                                    const vector<vector<ModInt<M>>> &css,
                                    int n) {
  using Mint = ModInt<M>;
  assert(!css.empty());
  const int d = css.size() - 1, e = css[0].size() - 1;
  for (int j = 0; j <= d; ++j) assert(static_cast<int>(css[j].size()) == e + 1);
  const int asLen = as.size();
  as.resize(n);
  for (int i = asLen; i < n; ++i) {
    Mint sum = 0;
    for (int j = 1; j <= d; ++j) {
      Mint coef = 0, pw = 1;
      for (int k = 0; k <= e; ++k) {
        coef += css[j][k] * pw;
        pw *= i;
      }
      sum += coef * as[i - j];
    }
    {
      Mint coef = 0, pw = 1;
      for (int k = 0; k <= e; ++k) {
        coef += css[0][k] * pw;
        pw *= i;
      }
      as[i] = -sum / coef;
    }
  }
  return as;
}

////////////////////////////////////////////////////////////////////////////////


constexpr int LIM_INV = 400'010;
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;
    }
  }
}


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

constexpr int MAX_T = 100'010;
constexpr int MAX_PQ = 10;

Mint S2[MAX_PQ][MAX_PQ];

int T, C, P, Q, L;
int N[MAX_T], M[MAX_T];
Mint F[MAX_T][MAX_PQ];


namespace expr {
Mint dp[110][110][210];
void belowDiag(int lim) {
  memset(dp, 0, sizeof(dp));
  dp[0][0][0] = 1;
  for (int x = 0; x <= lim; ++x) for (int y = 0; y <= lim; ++y) {
    if (y <= x) {
      for (int k = x + y + 1; k >= 1; --k) dp[x][y][k] = dp[x][y][k - 1];
      dp[x][y][0] = 0;
    }
    for (int k = 0; k <= x + y + 1; ++k) dp[x + 1][y][k] += dp[x][y][k];
    for (int k = 0; k <= x + y + 1; ++k) dp[x][y + 1][k] += dp[x][y][k];
  }
  for (int x = 0; x <= lim; ++x) {
    Mint g = 0, h = 0;
    for (int k = 0; k <= x + x + 1; ++k) {
      g += dp[x][x][k] * k;
      h += dp[x][x][k] * (x + x + 1 - k);
    }
    cerr << x << ": " << g + h << " " << g << " " << h << "; "; pv(dp[x][x], dp[x][x] + (x + x + 1 + 1));
  }
}
void all(int lim) {
  for (int p = 0; p < 4; ++p) for (int q = 0; q < 4; ++q) {
    vector<vector<Mint>> tab(lim + 1, vector<Mint>(lim + 1, 0));
    for (int n = 0; n <= lim; ++n) for (int m = 0; m <= lim; ++m) {
      for (int x = 0; x <= n; ++x) for (int y = 0; y <= m; ++y) {
        tab[n][m] += path(x, y) * path(n - x, m - y) * binom(x, p) * binom(y, q);
      }
    }
    cerr << "binom(x, " << p << ") binom(y, " << q << ")" << endl;
    for (int n = 0; n <= lim; ++n) {
      cerr << n << ": " << tab[n] << endl;
    }
    for (int n = 0; n <= lim; ++n) for (int m = 0; m <= lim; ++m) {
      const Mint val = path(p, q) * binom(n + m + 1, p + q + 1) * path(n - p, m - q);
      assert(tab[n][m] == val);
    }
  }
}
}  // expr


namespace brute {
constexpr int SMALL = 1010;
Mint dp[MAX_PQ][SMALL][SMALL][2];
vector<Mint> run() {
  memset(dp, 0, sizeof(dp));
  for (int p = 0; p < P; ++p) for (int q = 0; q < Q; ++q) {
    const int id = p * Q + q;
    dp[id][0][0][0] = 1;
    for (int x = 0; x <= L; ++x) for (int y = 0; y <= L + C; ++y) {
      if (y <= x) {
        dp[id][x][y][1] += dp[id][x][y][0] * Mint(x).pow(p) * Mint(y).pow(q);
      }
      dp[id][x + 1][y][0] += dp[id][x][y][0];
      dp[id][x + 1][y][1] += dp[id][x][y][1];
      dp[id][x][y + 1][0] += dp[id][x][y][0];
      dp[id][x][y + 1][1] += dp[id][x][y][1];
    }
// cerr<<"p = "<<p<<", q = "<<q<<endl;
// for(int x=0;x<=L;++x){for(int y=0;y<=L+C;++y)cerr<<dp[id][x][y][0]<<","<<dp[id][x][y][1]<<" ";cerr<<endl;}
  }
  vector<Mint> ans(T, 0);
  for (int t = 0; t < T; ++t) {
    for (int p = 0; p < P; ++p) for (int q = 0; q < Q; ++q) {
      const int id = p * Q + q;
      ans[t] += F[t][id] * dp[id][N[t]][M[t]][1];
    }
  }
  return ans;
}
}  // brute


namespace sub4 {
vector<Mint> run() {
  vector<Mint> gs(L + 1, 0), hs(L + 1, 0);
  for (int n = 0; n <= L; ++n) {
    gs[n] = ((2 * n + 1) * path(n, n) + Mint(4).pow(n)) / 2;
    hs[n] = path(n, n) * (2 * n + 1) - gs[n];
  }
// cerr<<"gs = "<<gs<<endl;
// cerr<<"hs = "<<hs<<endl;
  vector<Mint> ggs, hhs;
  if (C >= 0) {
    vector<Mint> ps(L + 1, 0);
    for (int n = 1; n <= L; ++n) {
      ps[n] = path(n, n + C - 1) - path(n + C, n - 1);
    }
    ps[0] = 1;
    ggs = convolve(gs, ps);
    ggs.resize(L + 1);
// cerr<<"ps = "<<ps<<", ggs = "<<ggs<<endl;
  } else {
    vector<Mint> ps(L + 1, 0);
    for (int m = 1; m <= L; ++m) {
      ps[m] = path(m - C - 1, m) - path(m - 1, m - C);
    }
    ps[0] = 1;
    hhs = convolve(hs, ps);
    hhs.resize(L + 1);
// cerr<<"ps = "<<ps<<", hhs = "<<hhs<<endl;
  }
  vector<Mint> ans(T, 0);
  for (int t = 0; t < T; ++t) {
    if (C >= 0) {
      /*
      Mint sum = 0;
      for (int x = 0; x < N[t]; ++x) {
        // (x, x) -> (x, x+1)
        sum += gs[x] * (path(N[t] - x, M[t] - (x+1)) - path(M[t] - x, N[t] - (x+1)));
      }
      sum += gs[N[t]];
      ans[t] += F[t][0] * sum;
      */
      ans[t] += F[t][0] * ggs[N[t]];
    } else {
      /*
      Mint sum = 0;
      for (int y = 0; y < M[t]; ++y) {
        // (y, y) -> (y+1, y)
        sum += hs[y] * (path(N[t] - (y+1), M[t] - y) - path(M[t] - (y+1), N[t] - y));
      }
      sum += hs[M[t]];
      ans[t] += F[t][0] * sum;
      */
      ans[t] += F[t][0] * (path(N[t], M[t]) * (N[t] + M[t] + 1) - hhs[M[t]]);
    }
  }
  return ans;
}
}  // sub4


namespace fast {
constexpr int SZ = 200;
Mint dp[SZ + 1][SZ + 1][2];
vector<Mint> gss[MAX_PQ];
vector<Mint> run() {
  for (int p = 0; p < P; ++p) for (int q = 0; q < Q; ++q) {
    memset(dp, 0, sizeof(dp));
    dp[0][0][0] = 1;
    for (int x = 0; x < SZ; ++x) for (int y = 0; y < SZ; ++y) {
      if ((C >= 0) == (y <= x)) {
        dp[x][y][1] += dp[x][y][0] * Mint(x).pow(p) * Mint(y).pow(q);
      }
      dp[x + 1][y][0] += dp[x][y][0];
      dp[x + 1][y][1] += dp[x][y][1];
      dp[x][y + 1][0] += dp[x][y][0];
      dp[x][y + 1][1] += dp[x][y][1];
    }
    vector<Mint> as(SZ);
    for (int x = 0; x < SZ; ++x) {
      as[x] = dp[x][x][1];
    }
    // cerr << "x^" << p << " y^" << q << endl;
    // findPRecurrence(as, 1, true);
    const auto css = findPRecurrence(as, 1, false);
    gss[p * Q + q] = extendPRecurrence(as, css, L + 1);
  }
  {
    vector<Mint> ps(L + 1, 0);
    if (C >= 0) {
      for (int n = 1; n <= L; ++n) {
        ps[n] = path(n, n + C - 1) - path(n + C, n - 1);
      }
      ps[0] = 1;
    } else {
      for (int m = 1; m <= L; ++m) {
        ps[m] = path(m - C - 1, m) - path(m - 1, m - C);
      }
      ps[0] = 1;
    }
    for (int id = 0; id < P * Q; ++id) {
      gss[id] = convolve(gss[id], ps);
      gss[id].resize(L + 1);
    }
  }
  vector<Mint> ans(T, 0);
  for (int t = 0; t < T; ++t) {
    if (C >= 0) {
      for (int id = 0; id < P * Q; ++id) {
        ans[t] += F[t][id] * gss[id][N[t]];
      }
    } else {
      // x^p y^q -> binom(x, p') binom(y, q')
      Mint f[MAX_PQ] = {};
      for (int p = 0; p < P; ++p) for (int q = 0; q < Q; ++q) {
        for (int pp = 0; pp <= p; ++pp) for (int qq = 0; qq <= q; ++qq) {
          f[pp * Q + qq] += fac[pp] * fac[qq] * S2[p][pp] * S2[q][qq] * F[t][p * Q + q];
        }
      }
      for (int p = 0; p < P; ++p) for (int q = 0; q < Q; ++q) {
        ans[t] += f[p * Q + q] * path(p, q) * binom(N[t] + M[t] + 1, p + q + 1) * path(N[t] - p, M[t] - q);
      }
      for (int id = 0; id < P * Q; ++id) {
        ans[t] -= F[t][id] * gss[id][M[t]];
      }
    }
  }
  return ans;
}
}  // fast


int main() {
  prepare();
  
  for (int n = 0; n < MAX_PQ; ++n) {
    S2[n][0] = 0;
    S2[n][n] = 1;
    for (int k = 1; k < n; ++k) {
      S2[n][k] = S2[n - 1][k - 1] + k * S2[n - 1][k];
    }
  }
  
  // expr::belowDiag(10);
  // expr::all(10);
  
  for (; ~scanf("%d%d%d%d%d", &T, &C, &P, &Q, &L); ) {
    ++P;
    ++Q;
    for (int t = 0; t < T; ++t) {
      scanf("%d%d", &N[t], &M[t]);
      assert(N[t] >= 0);
      assert(M[t] >= 0);
      assert(N[t] + C == M[t]);
      for (int p = 0; p < P; ++p) for (int q = 0; q < Q; ++q) {
        scanf("%u", &F[t][p * Q + q].x);
      }
    }
    
    const auto ans = fast::run();
    for (int t = 0; t < T; ++t) {
      printf("%u\n", ans[t].x);
    }
#ifdef LOCAL
const auto brt=brute::run();
for(int t=0;t<T;++t)if(brt[t]!=ans[t]){
 cerr<<N[t]<<" "<<M[t]<<"; ";pv(F[t],F[t]+P*Q);
 cerr<<"brt[t] = "<<brt[t]<<endl;
 cerr<<"ans[t] = "<<ans[t]<<endl;
 break;
}
assert(brt==ans);
#endif
  }
  return 0;
}