/* #pragma GCC target("avx2") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") //*/ #include // #include using namespace std; // using namespace atcoder; #define DEBUG(x) cerr<<#x<<": "< #define vl vector #define vii vector< vector > #define vll vector< vector > #define vs vector #define pii pair #define pis pair #define psi pair #define pll pair template pair operator+(const pair &s, const pair &t) { return pair(s.first + t.first, s.second + t.second); } template pair operator-(const pair &s, const pair &t) { return pair(s.first - t.first, s.second - t.second); } template ostream& operator<<(ostream& os, pair p) { os << "(" << p.first << ", " << p.second << ")"; return os; } #define X first #define Y second #define rep(i,n) for(int i=0;i<(int)(n);i++) #define rep1(i,n) for(int i=1;i<=(int)(n);i++) #define rrep(i,n) for(int i=(int)(n)-1;i>=0;i--) #define rrep1(i,n) for(int i=(int)(n);i>0;i--) #define REP(i,a,b) for(int i=a;i bool chmax(T &a, const T &b) { if (a bool chmin(T &a, const T &b) { if (a>b) { a = b; return 1; } return 0; } #define UNIQUE(v) v.erase(std::unique(v.begin(), v.end()), v.end()); const ll inf = 1000000001; const ll INF = (ll)1e18 + 1; const long double pi = 3.1415926535897932384626433832795028841971L; int popcount(ll t) { return __builtin_popcountll(t); } // int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1}; // int dx2[8] = { 1,1,0,-1,-1,-1,0,1 }, dy2[8] = { 0,1,1,1,0,-1,-1,-1 }; vi dx = {0, 1, 0, -1}, dy = {-1, 0, 1, 0}; // vi dx2 = { 1,1,0,-1,-1,-1,0,1 }, dy2 = { 0,1,1,1,0,-1,-1,-1 }; struct Setup_io { Setup_io() { ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0); cout << fixed << setprecision(25); } } setup_io; const ll MOD = 1000000007; // const ll MOD = 998244353; // #define mp make_pair //#define endl '\n' const int MAXN = 555555; vl fact(MAXN); vl rfact(MAXN); ll mod_pow(ll x, ll p, ll M = MOD) { if (p < 0) { x = mod_pow(x, M - 2, M); p = -p; } ll a = 1; while (p) { if (p % 2) a = a*x%M; x = x*x%M; p /= 2; } return a; } ll mod_inverse(ll a, ll M = MOD) { return mod_pow(a, M - 2, M); } void set_fact(ll n, ll M = MOD) { fact[0] = 1; for (ll i = 1; i <= n; i++) { fact[i] = i * fact[i - 1] % M; } rfact[n] = mod_inverse(fact[n], M); for (ll i = n - 1; i >= 0; i--) { rfact[i] = (i + 1) * rfact[i + 1] % M; } } //http://drken1215.hatenablog.com/entry/2018/06/08/210000 //n���傫��fact���v�Z�ł��Ȃ��Ƃ��̂ق��̌v�Z���@�ɂ‚��ď����Ă��� ll nCr(ll n, ll r, ll M = MOD) { if (r > n) return 0; assert(fact[2] == 2); ll ret = fact[n]; if (rfact[r] == 0) { rfact[r] = mod_inverse(fact[r], M); } ret = (ret*rfact[r]) % M; if (rfact[n - r] == 0) { rfact[n - r] = mod_inverse(fact[n - r], M); } ret = (ret*rfact[n - r]) % M; return ret; } ll nHr(ll n, ll r) { return nCr(n+r-1, r); } signed main() { int n, mp, mq, l; cin >> n >> mp >> mq >> l; vi s(n); rep (i, n) cin >> s[i]; vll dp1(n + 1, vl(mq + 1)), dp2(n + 1, vl(mq + 1)); dp1[0][0] = 1; rep (i, n) { rep (j, n + 1) rep (k, mq + 1) dp2[j][k] = 0; rep (j, n + 1) { rep (k, mq + 1) { if (dp1[j][k] == 0) continue; (dp2[j][k] += dp1[j][k]) %= MOD; if (k + 1 <= mq) { (dp2[j][k + 1] -= dp1[j][k]) %= MOD; } if (k + 1 <= mq) { (dp2[j + 1][k + 1] += dp1[j][k]) %= MOD; } if (k + s[i] + 1 <= mq) { (dp2[j + 1][k + s[i] + 1] -= dp1[j][k]) %= MOD; } } } rep (j, n + 1) { rep (k, mq) { (dp2[j][k + 1] += dp2[j][k]) %= MOD; } } // DEBUG_MAT(dp2); swap(dp1, dp2); } set_fact(mp + mq + n + 10); ll ans = 0; rep (i, n + 1) rep (k, mq + 1) { ll need = l * i; need -= k; if (need > mp) continue; ll use = mp - need; ans += dp1[i][k] * nCr(use + n - 1, n - 1); ans %= MOD; } ans = (ans + MOD) % MOD; cout << ans << endl; }