import java.io.BufferedReader import java.io.InputStream import java.io.InputStreamReader import java.lang.AssertionError import java.util.* import kotlin.math.abs import kotlin.math.max import kotlin.math.min val MOD = 1_000_000_007 class Comb(n: Int, val mod: Int) { val F = LongArray(n + 1) val I = LongArray(n + 1) init { F[0] = 1 for (i in 1..n) { F[i] = F[i - 1] * i % mod } I[n] = powMod(F[n], (mod - 2).toLong(), mod) for (i in n - 1 downTo 0) { I[i] = I[i + 1] * (i + 1) % mod } } private fun powMod(a: Long, n: Long, mod: Int): Long { if (n == 0L) return 1 val res = powMod(a * a % mod, n / 2, mod) return if (n % 2 == 1L) res * a % mod else res } fun comb(n: Int, k: Int): Long { if (n < k) return 0L return F[n] * I[k] % mod * I[n - k] % mod } fun perm(n: Int, k: Int): Long { return F[n] * I[n - k] % mod } fun inv(x: Int): Long { return I[x] * F[x - 1] % mod } /** * nのグループからk回重複ありで選ぶ組み合わせ数 * n - 1のしきりとkの○で考える */ fun H(n: Int, k: Int) = comb(n + k - 1, k) } class Solver(stream: InputStream, private val out: java.io.PrintWriter) { private val reader = BufferedReader(InputStreamReader(stream), 32768) fun solve() { val (N, Mp, Mq, L) = na(4) val S = na(N) var cur = Array(N + 1){LongArray(Mq + 1)} var next = Array(N + 1){LongArray(Mq + 1)} cur[0][0] = 1 for (k in S) { for (i in 0 .. N) { cur[i].copyInto(next[i]) } for (i in 0 until N) { var sum = 0L // [q-1, q-k] のsum for (q in 0 .. Mq) { if (q - (k+1) >= 0) sum = (sum + MOD - cur[i][q - (k+1)]) % MOD // sum -= cur[i][q - (k+1)] next[i + 1][q] = (next[i + 1][q] + sum) % MOD sum = (sum + cur[i][q]) % MOD // q自身は加えない } } // debug{"next"} // debugDim(next) val tmp = cur cur = next next = tmp } debug{"DP"} debugDim(cur) val comb = Comb(Mp + N + 100, MOD) var ans = 0L for (i in 0 .. N) { for (q in 0 .. Mq) { val used = L*i - q if (used < 0) continue val remain = Mp - used if (remain < 0) continue debug{"$i:$q remain:$remain"} ans = (ans + comb.H(N, remain)*cur[i][q]%MOD) % MOD } } out.println(ans) } private val isDebug = try { // なんか本番でエラーでる System.getenv("MY_DEBUG") != null } catch (t: Throwable) { false } private var tokenizer: StringTokenizer? = null private fun next(): String { while (tokenizer == null || !tokenizer!!.hasMoreTokens()) { tokenizer = StringTokenizer(reader.readLine()) } return tokenizer!!.nextToken() } private fun ni() = next().toInt() private fun nl() = next().toLong() private fun ns() = next() private fun na(n: Int, offset: Int = 0): IntArray { return IntArray(n) { ni() + offset } } private fun nal(n: Int, offset: Int = 0): LongArray { val res = LongArray(n) for (i in 0 until n) { res[i] = nl() + offset } return res } private fun na2(n: Int, offset: Int = 0): Array { val a = Array(2){IntArray(n)} for (i in 0 until n) { for (e in a) { e[i] = ni() + offset } } return a } private inline fun debug(msg: () -> String) { if (isDebug) System.err.println(msg()) } /** * コーナーケースでエラー出たりするので、debug(dp[1])のように添え字付きの場合はdebug{}をつかうこと */ private inline fun debug(a: LongArray) { debug { a.joinToString(" ") } } private inline fun debug(a: IntArray) { debug { a.joinToString(" ") } } private inline fun debug(a: BooleanArray) { debug { toString(a) } } private inline fun toString(a: BooleanArray) = run{a.map { if (it) 1 else 0 }.joinToString("")} private inline fun debugDim(A: Array) { if (isDebug) { for (a in A) { debug(a) } } } private inline fun debugDim(A: Array) { if (isDebug) { for (a in A) { debug(a) } } } private inline fun debugDim(A: Array) { if (isDebug) { for (a in A) { debug(a) } } } /** * 勝手にimport消されるのを防ぎたい */ private fun hoge() { min(1, 2) max(1, 2) abs(-10) } private inline fun assert(b: Boolean) = run{if (!b) throw AssertionError()} private inline fun assert(b: Boolean, f: () -> String) = run{if (!b) throw AssertionError(f())} } fun main() { val out = java.io.PrintWriter(System.out) Solver(System.`in`, out).solve() out.flush() }