import std.stdio, std.string, std.conv, std.range; import std.algorithm, std.array, std.typecons, std.container; import std.math, std.numeric, std.random, core.bitop; enum inf = 1_001_001_001; enum infl = 1_001_001_001_001_001_001L; enum mod = 1_000_000_007L; void main() { int N, W; long K; scan(N, W, K); auto a = readln.split.to!(int[]); auto dp = new long[][](2*W + 1, 2); dp[0][0] = 1; foreach (i ; 0 .. 2*W + 1) { foreach (ai ; a) { foreach (j ; 0 .. 2) { if (i + ai <= 2*W) { (dp[i + ai][j | (i + ai == W)] += dp[i][j]) %= mod; } } } } auto x = dp[W][1], y = dp[2*W][0]; debug { writeln(dp); writefln("x: %s, y: %s", x, y); } auto A = new long[][](2, 2); A = [[x, y], [1L, 0L]]; auto res = mul(powMat(A, K), [[1L], [0L]]); debug { writeln(res); } auto ans = res[0][0]; writeln(ans); } long[][] powMat(long[][] A, long x) { if (x > 0) { auto res = square(powMat(A, x>>1)); if (x & 1) { res = mul(res, A); } return res; } else { auto res = new long[][](A.length, A.length); foreach (i ; 0 .. A.length) res[i][i] = 1; return res; } } long[][] square(long[][] A) { assert(A[0].length == A.length); auto B = new long[][](A.length, A.length); foreach (i ; 0 .. A.length) { foreach (j ; 0 .. A.length) { foreach (k ; 0 .. A.length) { B[i][j] += A[i][k] * A[k][j] % mod; B[i][j] %= mod; } } } return B; } auto mul(long[][] A, long[][] B) { assert(A[0].length == B.length); auto N = A.length; auto M = B[0].length; auto C = new long[][](N, M); foreach (i ; 0 .. N) { foreach (j ; 0 .. M) { foreach (k ; 0 .. A[i].length) { C[i][j] += A[i][k] * B[k][j] % mod; C[i][j] %= mod; } } } return C; } struct ModInt { long value = 0; long mod = 1_000_000_007L; this(long value, long mod = 1_000_000_007L) { this.mod = mod; this.value = (value % mod); if (this.value < 0) this.value += mod; } void opAssign(long x) { value = x % mod; if (value < 0) value += mod; } ModInt opBinary(string op)(const ModInt rhs){ static if (op == "+") { auto lhs = this; lhs.value += rhs.value; if (lhs.value >= mod) lhs.value -= mod; return lhs; } static if (op == "-") { auto lhs = this; lhs.value -= rhs.value; if (lhs.value < 0) lhs.value += mod; return lhs; } static if (op == "*") { auto lhs = this; (lhs.value *= rhs.value) %= mod; return lhs; } } ModInt opBinary(string op)(long rhs){ rhs %= mod; if (rhs < 0) rhs += mod; static if (op == "+") { auto lhs = this; lhs.value += rhs; if (lhs.value >= mod) lhs.value -= mod; return lhs; } static if (op == "-") { auto lhs = this; lhs.value -= rhs; if (lhs.value < 0) lhs.value += mod; return lhs; } static if (op == "*") { auto lhs = this; (lhs.value *= rhs) %= mod; return lhs; } } bool opEquals(ModInt a, ModInt b) { return a.value == b.value; } bool opEquals(T)(const T rhs) { long x = rhs % mod; if (x < 0) x += mod; return this.value == x; } void opOpAssign(string op)(const ModInt rhs) { static if (op == "+") { this.value += rhs.value; if (this.value >= mod) this.value -= mod; } static if (op == "-") { this.value -= rhs.value; if (this.value < 0) this.value += mod; } static if (op == "*") { (this.value *= rhs.value) %= mod; } } void opOpAssign(string op)(long rhs) { rhs %= mod; if (rhs < 0) rhs += mod; static if (op == "+") { this.value += rhs; if (this.value >= mod) this.value -= mod; } static if (op == "-") { this.value -= rhs; if (this.value < 0) this.value += mod; } static if (op == "*") { (this.value *= rhs) %= mod; } } string toString() { import std.conv : to; return value.to!string; } } unittest { enum mod = 1_000_000_007L; auto a = ModInt(2); auto b = ModInt(3); assert(a + b == 5); assert(a - b == mod - 1); assert(a * b == 6); assert(a + 8 == 10); assert(a - 1 == 1); assert(a * 7 == 14); ModInt c = 8; assert(c == 8); } void scan(T...)(ref T args) { import std.stdio : readln; import std.algorithm : splitter; import std.conv : to; import std.range.primitives; auto line = readln().splitter(); foreach (ref arg; args) { arg = line.front.to!(typeof(arg)); line.popFront(); } assert(line.empty); } void fillAll(R, T)(ref R arr, T value) { static if (is(typeof(arr[] = value))) { arr[] = value; } else { foreach (ref e; arr) { fillAll(e, value); } } } bool chmin(T, U...)(ref T x, U args) { bool isChanged; foreach (arg; args) { if (x > arg) { x = arg; isChanged = true; } } return isChanged; } bool chmax(T, U...)(ref T x, U args) { bool isChanged; foreach (arg; args) { if (x < arg) { x = arg; isChanged = true; } } return isChanged; }