#include #include using namespace std; using namespace atcoder; #define rep(i,n)for (int i = 0; i < int(n); ++i) #define rrep(i,n)for (int i = int(n)-1; i >= 0; --i) #define all(x) (x).begin(), (x).end() #define rall(x) (x).rbegin(), (x).rend() template void chmax(T& a, const T& b) {a = max(a, b);} template void chmin(T& a, const T& b) {a = min(a, b);} using ll = long long; using P = pair; using VI = vector; using VVI = vector; using VL = vector; using VVL = vector; using mint = modint1000000007; constexpr int FACT_SIZE = 1000000; mint Fact[FACT_SIZE + 1]; mint iFact[FACT_SIZE + 1]; const auto fact_init = [] { Fact[0] = mint::raw(1); for(int i = 1; i <= FACT_SIZE; ++i) { Fact[i] = Fact[i-1] * i; } iFact[FACT_SIZE] = Fact[FACT_SIZE].inv(); for(int i = FACT_SIZE; i; --i) { iFact[i-1] = iFact[i] * i; } return false; }(); mint comb(int n, int k) { if (k == 0) return mint::raw(1); assert(n >= 0 && k >= 0); if (k > n) return mint::raw(0); return Fact[n] * iFact[n - k] * iFact[k]; } mint fact(int n) {return Fact[n];} mint perm(int n, int k) { assert(0 <= n); return Fact[n] * iFact[n - k]; } int main() { ios::sync_with_stdio(false); cin.tie(0); int N, P, Q, L; cin >> N >> P >> Q >> L; // gave to j persons, k qs used vector> dp(N + 1, vector(Q + 1)); vector> ndp(N + 1, vector(Q + 1)); dp[0][0] = 1; rep(i, N) { rep(j, N + 1) rep(k, Q + 1) ndp[j][k] = mint::raw(0); int s; cin >> s; rep(j, N + 1) rep(k, Q + 1) if (dp[j][k].val() != 0) { const mint v = dp[j][k]; int p_rest = P - (j * L - k); int q_rest = Q - k; int nq_min = max(L - p_rest, 1); int nq_max = min(q_rest, s); if (nq_min <= nq_max) { int nk1 = k + nq_min; int nk2 = k + nq_max; if (nk1 < Q + 1) ndp[j+1][nk1] += v; if (nk2 + 1 < Q + 1) ndp[j+1][nk2 + 1] -= v; } { int nk1 = k; int nk2 = k; if (nk1 < Q + 1) ndp[j][nk1] += v; if (nk2 + 1 < Q + 1) ndp[j][nk2 + 1] -= v; } } rep(j, N + 1) { mint now; rep(k, Q + 1) { now += ndp[j][k]; ndp[j][k] = now; } } swap(dp, ndp); } mint ans; rep(j, N + 1) rep(k, Q + 1) if (dp[j][k].val() != 0) { const mint v = dp[j][k]; int p_rest = P - (j * L - k); ans += comb(p_rest + N - 1, N - 1) * v; } cout << ans.val() << '\n'; }