/* Code for problem F by cookiedoth Generated 09 Apr 2021 at 04.37 PM ▅███████ ]▄▄▄▄▄▄▄ █████████▅▄▃ Il████████████████] ◥⊙▲⊙▲⊙▲⊙▲⊙▲⊙▲⊙◤ >_< o_O ^_^ */ #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #define ll long long #define ld long double #define null NULL #define all(a) a.begin(), a.end() #define rall(a) a.rbegin(), a.rend() #define debug(a) cerr << #a << " = " << a << endl #define forn(i, n) for (int i = 0; i < n; ++i) #define length(a) (int)a.size() using namespace std; template int chkmax(T &a, T b) { if (b > a) { a = b; return 1; } return 0; } template int chkmin(T &a, T b) { if (b < a) { a = b; return 1; } return 0; } template void output(iterator begin, iterator end, ostream& out = cerr) { while (begin != end) { out << (*begin) << " "; begin++; } out << endl; } template void output(T x, ostream& out = cerr) { output(x.begin(), x.end(), out); } void fast_io() { ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); } const int MOD = 1e9 + 7; int mul(int a, int b) { return (1LL * a * b) % MOD; } int diff(int a, int b) { a -= b; if (a < 0) { a += MOD; } return a; } void subt(int &a, const int &b) { a -= b; if (a < 0) { a += MOD; } } int sum(int a, int b) { a += b; if (a >= MOD) { a -= MOD; } return a; } void add(int &a, const int &b) { a += b; if (a >= MOD) { a -= MOD; } } int power(int a, int deg) { int res = 1; for (; deg; a = mul(a, a), deg >>= 1) { if (deg & 1) { res = mul(res, a); } } return res; } int inverse(int a) { return power(a, MOD - 2); } int divide(int a, int b) { return mul(a, inverse(b)); } const int MAX_N = 42; const int C = 2e4 + 228; int n, M_p, M_q, L; int dp[MAX_N][C], _dp[MAX_N][C]; void recalcDP(int s) { for (int i = 0; i <= n; ++i) { copy(dp[i], dp[i] + M_q + 1, _dp[i]); for (int j = 1; j <= M_q; ++j) { add(dp[i][j], dp[i][j - 1]); } if (i) { for (int j = 1; j <= M_q; ++j) { int ps = j - 1 - s; add(_dp[i][j], dp[i - 1][j - 1]); if (ps >= 0) { subt(_dp[i][j], dp[i - 1][ps]); } } } } swap(dp, _dp); } const int mx = 1e5; int fact[mx], _fact[mx]; void init_binom() { fact[0] = _fact[0] = 1; for (int i = 1; i < mx; ++i) { fact[i] = mul(fact[i - 1], i); _fact[i] = inverse(fact[i]); } } int binom(int n, int k) { return k > n ? 0 : mul(fact[n], mul(_fact[k], _fact[n - k])); } void calc_ans() { int ans = 0; for (int q1 = 0; q1 <= n; ++q1) { for (int cov = 0; cov <= M_q; ++cov) { int remP = M_p - (L * q1 - cov); if (remP < 0 || dp[q1][cov] == 0) { continue; } // cerr << "q1 = " << q1 << ", cov = " << cov << '\n'; // cerr << "opa " << remP << ' ' << dp[q1][cov] << '\n'; add(ans, mul(binom(remP + n - 1, n - 1), dp[q1][cov])); // cerr << "ans = " << ans << '\n'; } } cout << ans << '\n'; } signed main() { fast_io(); cin >> n >> M_p >> M_q >> L; dp[0][0] = 1; for (int i = 0; i < n; ++i) { int s; cin >> s; recalcDP(s); } init_binom(); calc_ans(); }