#include using namespace std; using LL = long long int; #define incID(i, l, r) for(int i = (l) ; i < (r); ++i) #define decID(i, l, r) for(int i = (r) - 1; i >= (l); --i) #define incII(i, l, r) for(int i = (l) ; i <= (r); ++i) #define decII(i, l, r) for(int i = (r) ; i >= (l); --i) #define inc(i, n) incID(i, 0, n) #define dec(i, n) decID(i, 0, n) #define inc1(i, n) incII(i, 1, n) #define dec1(i, n) decII(i, 1, n) #define inID(v, l, r) ((l) <= (v) && (v) < (r)) #define inII(v, l, r) ((l) <= (v) && (v) <= (r)) #define PB push_back #define EB emplace_back #define MP make_pair #define FI first #define SE second #define FR front() #define BA back() #define ALL(v) v.begin(), v.end() #define RALL(v) v.rbegin(), v.rend() auto setmin = [](auto & a, auto b) { return (b < a ? a = b, true : false); }; auto setmax = [](auto & a, auto b) { return (b > a ? a = b, true : false); }; auto setmineq = [](auto & a, auto b) { return (b <= a ? a = b, true : false); }; auto setmaxeq = [](auto & a, auto b) { return (b >= a ? a = b, true : false); }; #define SI(v) static_cast(v.size()) #define RF(e, v) for(auto & e: v) #define until(e) while(! (e)) #define if_not(e) if(! (e)) #define ef else if #define UR assert(false) #define IN(T, ...) T __VA_ARGS__; IN_(__VA_ARGS__); void IN_() { }; template void IN_(T & a, U & ... b) { cin >> a; IN_(b ...); }; template void OUT(T && a) { cout << a << endl; } template void OUT(T && a, U && ... b) { cout << a << " "; OUT(b ...); } // ---- ---- template struct Matrix { vector> v; Matrix(T t) { init(); inc(i, N) { v[i][i] = t; } } Matrix(vector> const & w = { }) { init(w); } void init(vector> const & w = { }) { v = vector>(N, vector(N, 0)); assert(w.size() <= N); inc(i, w.size()) { assert(w[i].size() <= N); inc(j, w[i].size()) { v[i][j] = w[i][j]; } } } vector const & operator[](int i) const { return v[i]; } vector & operator[](int i) { return v[i]; } friend Matrix operator+(Matrix const & a, Matrix const & b) { Matrix c; inc(i, N) { inc(j, N) { c[i][j] = a[i][j] + b[i][j]; } } return c; } friend Matrix operator-(Matrix const & a, Matrix const & b) { Matrix c; inc(i, N) { inc(j, N) { c[i][j] = a[i][j] - b[i][j]; } } return c; } friend Matrix operator*(Matrix const & a, Matrix const & b) { Matrix c; inc(i, N) { inc(j, N) { inc(k, N) { c[i][j] += a[i][k] * b[k][j]; } } } return c; } friend Matrix operator^(Matrix const & a, LL b) { Matrix c(1), e = a; assert(b >= 0); while(b) { if(b & 1) { c *= e; } e *= e; b >>= 1; } return c; } friend Matrix & operator+=(Matrix & a, Matrix const & b) { return (a = a + b); } friend Matrix & operator-=(Matrix & a, Matrix const & b) { return (a = a - b); } friend Matrix & operator*=(Matrix & a, Matrix const & b) { return (a = a * b); } friend Matrix & operator^=(Matrix & a, LL b) { return (a = a ^ b); } friend ostream & operator<<(ostream & os, Matrix const & m) { inc(i, N) { inc(j, N) { os << m[i][j] << " "; } os << endl; } return os; } }; // ---- template class ModInt { private: LL v; pair ext_gcd(LL a, LL b) { if(b == 0) { assert(a == 1); return { 1, 0 }; } auto p = ext_gcd(b, a % b); return { p.SE, p.FI - (a / b) * p.SE }; } public: ModInt(LL vv = 0) { v = vv; if(abs(v) >= M) { v %= M; } if(v < 0) { v += M; } } LL get_v() { return v; } ModInt inv() { return ext_gcd(M, v).SE; } ModInt exp(LL b) { ModInt p = 1, a = v; if(b < 0) { a = a.inv(); b = -b; } while(b) { if(b & 1) { p *= a; } a *= a; b >>= 1; } return p; } friend bool operator< (ModInt a, ModInt b) { return (a.v < b.v); } friend bool operator> (ModInt a, ModInt b) { return (a.v > b.v); } friend bool operator<=(ModInt a, ModInt b) { return (a.v <= b.v); } friend bool operator>=(ModInt a, ModInt b) { return (a.v >= b.v); } friend bool operator==(ModInt a, ModInt b) { return (a.v == b.v); } friend bool operator!=(ModInt a, ModInt b) { return (a.v != b.v); } friend ModInt operator+ (ModInt a ) { return ModInt(+a.v); } friend ModInt operator- (ModInt a ) { return ModInt(-a.v); } friend ModInt operator+ (ModInt a, ModInt b) { return ModInt(a.v + b.v); } friend ModInt operator- (ModInt a, ModInt b) { return ModInt(a.v - b.v); } friend ModInt operator* (ModInt a, ModInt b) { return ModInt(a.v * b.v); } friend ModInt operator/ (ModInt a, ModInt b) { return a * b.inv(); } friend ModInt operator^ (ModInt a, LL b) { return a.exp(b); } friend ModInt & operator+=(ModInt & a, ModInt b) { return (a = a + b); } friend ModInt & operator-=(ModInt & a, ModInt b) { return (a = a - b); } friend ModInt & operator*=(ModInt & a, ModInt b) { return (a = a * b); } friend ModInt & operator/=(ModInt & a, ModInt b) { return (a = a / b); } friend ModInt & operator^=(ModInt & a, LL b) { return (a = a ^ b); } friend istream & operator>>(istream & s, ModInt & b) { s >> b.v; b = ModInt(b.v); return s; } friend ostream & operator<<(ostream & s, ModInt b) { return (s << b.v); } }; // ---- using MI = ModInt< 1'000'000'007 >; template istream & operator>>(istream & s, vector & v) { RF(e, v) { s >> e; } return s; } template ostream & operator<<(ostream & s, vector const & v) { inc(i, SI(v)) { s << (i == 0 ? "" : " ") << v[i]; } return s; } #define inCD(v, l, r) ((l) < (v) && (v) < (r)) int main() { IN(LL, n, w, k); vector a(n); cin >> a; sort(ALL(a)); auto id = [&](int f, int p) { assert(inII(f, 0, 1)); assert(inII(p, 0, 2 * w)); return (2 * w + 1) * f + p; }; const int M = 40; Matrix A, v; inc(f, 2) { inc(p, w) { RF(e, a) { if(p + e <= (1 - f) * w + w) { int x = p + e + (f * w); int ff = (inCD(x, w, 2 * w) ? 1 : 0); A[id(f, p)][id(ff, p + e)] = 1; } } } } inc(f, 2) { incII(p, w, 2 * w) { A[id(f, p)][id(f, p)] = 1; } } A ^= w; inc(f, 2) { inc(g, 2) { incII(i, 0, 2 * w) { incII(j, w, 2 * w) { A[id(f, i)][id(g, j - w)] = exchange(A[id(f, i)][id(g, j)], 0); } } } } v[0][id(0, 0)] = 1; A ^= k; v *= A; OUT(v[0][id(0, 0)]); }