#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using namespace atcoder; typedef long long ll; #define rep(i, n) for (int i = 0; i < (int)(n); i++) #define repr(i, n) for (int i = (int)(n) - 1; i >= 0; i--) #define repk(i, k, n) for (int i = k; i < (int)(n); i++) #define all(v) v.begin(), v.end() #define mod1 1000000007 #define mod2 998244353 #define mod3 100000007 #define vi vector #define vs vector #define vc vector #define vl vector #define vb vector #define vvi vector> #define vvc vector> #define vvl vector> #define vvb vector> #define vvvi vector>> #define vvvl vector>> #define pii pair #define pil pair #define pli pair #define pll pair #define vpii vector> #define vpll vector> #define vvpii vector>> #define vvpll vector>> template void debug(T e) { cerr << e << endl; } template void debug(vector &v) { rep(i, v.size()) { cerr << v[i] << " "; } cerr << endl; } template void debug(vector> &v) { rep(i, v.size()) { rep(j, v[i].size()) { cerr << v[i][j] << " "; } cerr << endl; } } template void debug(vector> &v) { rep(i, v.size()) { cerr << v[i].first << " " << v[i].second << endl; } } template void debug(set &st) { for (auto itr = st.begin(); itr != st.end(); itr++) { cerr << *itr << " "; } cerr << endl; } template void debug(multiset &ms) { for (auto itr = ms.begin(); itr != ms.end(); itr++) { cerr << *itr << " "; } cerr << endl; } template void debug(map &mp) { for (auto itr = mp.begin(); itr != mp.end(); itr++) { cerr << itr->first << " " << itr->second << endl; } } void debug_out() { cerr << endl; } template void debug_out(Head H, Tail... T) { cerr << H << " "; debug_out(T...); } using mint = modint998244353; void debug_mint1(vector &vec) { for (int i = 0; i < vec.size(); i++) { cerr << vec[i].val() << " "; } cerr << endl; } void debug_mint2(vector> &vec) { for (int i = 0; i < vec.size(); i++) { for (int j = 0; j < vec[i].size(); j++) { cerr << vec[i][j].val() << " "; } cerr << endl; } } int main() { ll MAX_X = 9000000; vector fact(MAX_X + 1); fact[0] = mint(1); for (ll i = 0; i < MAX_X; i++){ fact[i + 1] = fact[i] * mint(i + 1); } vector finv(MAX_X + 1); finv[MAX_X] = mint(1) / fact[MAX_X]; for (ll i = MAX_X - 1; i >= 0; i--){ finv[i] = finv[i + 1] * mint(i + 1); } auto comb = [&fact, &finv](ll n, ll r){ if (n < r) return mint(0); if (r < 0) return mint(0); return fact[n] * finv[n - r] * finv[r]; }; ll N, M, K, L; cin >> N >> M >> K >> L; // 第 1 項目が L 以上であるものの数は? // 第 1 項目は全探索できそう mint ans = mint(0); for (ll y = L; y <= M; y++){ mint plus_sub = mint(0); mint minus_sub = mint(0); for (ll j = 0; j <= N - 1; j++){ if (j % 2 == 0){ plus_sub += comb(N - 1, j) * comb(M * K - y - (M + 1) * j + N - 2, N - 2); } else{ plus_sub -= comb(N - 1, j) * comb(M * K - y - (M + 1) * j + N - 2, N - 2); } } ans += plus_sub; for (ll j = 0; j <= N - 1; j++){ if (j % 2 == 0){ minus_sub += comb(N - 1, j) * comb(M * K - y - (y + 1) * j + N - 2, N - 2); } else{ minus_sub -= comb(N - 1, j) * comb(M * K - y - (y + 1) * j + N - 2, N - 2); } } ans -= minus_sub; // debug_out(plus_sub.val(), minus_sub.val()); } cout << ans.val() << endl; }