#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; typedef long long ll; typedef unsigned int ui; const ll mod = 1000000007; const ll INF = (ll)1000000007 * 1000000007; typedef pair P; #define stop char nyaa;cin>>nyaa; #define rep(i,n) for(int i=0;i=0;i--) #define Rep(i,sta,n) for(int i=sta;i=sta;i--) #define rep1(i,n) for(int i=1;i<=n;i++) #define per1(i,n) for(int i=n;i>=1;i--) #define Rep1(i,sta,n) for(int i=sta;i<=n;i++) typedef long double ld; typedef complex Point; const ld eps = 1e-8; const ld pi = acos(-1.0); typedef pair LP; template struct ModInt { long long x; ModInt() : x(0) {} ModInt(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {} explicit operator int() const {return x;} ModInt &operator+=(const ModInt &p) { if((x += p.x) >= mod) x -= mod; return *this; } ModInt &operator-=(const ModInt &p) { if((x += mod - p.x) >= mod) x -= mod; return *this; } ModInt &operator*=(const ModInt &p) { x = (int)(1LL * x * p.x % mod); return *this; } ModInt &operator/=(const ModInt &p) { *this *= p.inverse(); return *this; } ModInt operator-() const { return ModInt(-x); } ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; } ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; } ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; } ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; } bool operator==(const ModInt &p) const { return x == p.x; } bool operator!=(const ModInt &p) const { return x != p.x; } ModInt inverse() const{ int a = x, b = mod, u = 1, v = 0, t; while(b > 0) { t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } return ModInt(u); } ModInt power(long long p) const{ int a = x; if (p==0) return 1; if (p==1) return ModInt(a); if (p%2==1) return (ModInt(a)*ModInt(a)).power(p/2)*ModInt(a); else return (ModInt(a)*ModInt(a)).power(p/2); } ModInt power(const ModInt p) const{ return ((ModInt)x).power(p.x); } friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; } friend istream &operator>>(istream &is, ModInt &a) { long long x; is >> x; a = ModInt(x); return (is); } }; using modint = ModInt; int n,w,a[45]; ll k; template struct Matrix{ vector> val; Matrix(int n,int m,T x=0):val(n,vector(m,x)){} size_t size() const {return val.size();} inline vector& operator [] (int i) {return val[i];} Matrix &operator=(const vector> &A) { int n=A.size(),m=A[0].size(); val=A; return *this; } Matrix &operator+=(const Matrix &A) { for (int i=0;i &operator*=(const Matrix &A) { Matrix R(val.size(),A.val[0].size()); for (int i = 0; i < val.size(); ++i) for (int j = 0; j < A.val[0].size(); ++j) for (int k = 0; k < A.size(); ++k) R[i][j] = R[i][j] + (val[i][k] * A.val[k][j]); for (int i=0;i operator+(const Matrix &p) const { return Matrix(*this) += p; } Matrix operator*(const Matrix &p) const { return Matrix(*this) *= p; } bool operator==(const Matrix &p) const { return val == p.val; } bool operator!=(const Matrix &p) const { return val != p.val; } Matrix pow(long long n) { Matrix A=*this; Matrix R(A.size(), A.size()); for (int i = 0; i < A.size(); ++i) R[i][i] = 1; while (n > 0) { if (n & 1) R = R * A; A = A * A; n >>= 1; } return R; } }; modint dp(int m){ vector v(m+1,0); v[0]=1; Rep(i,1,m+1){ rep(k,n){ if(i>=a[k]){ v[i]+=v[i-a[k]]; } } } return v[m]; } void solve(){ cin >> n >> w >> k; rep(i,n){ cin >> a[i]; } modint p=dp(w),q=dp(2*w)-p*p; Matrix A(2,2),b(2,1); A={{p,q},{1,0}};b={{p},{1}}; Matrix R=A.pow(k-1); Matrix ans=R*b; cout << ans[0][0] << endl; } int main(){ ios::sync_with_stdio(false); cin.tie(0); cout << fixed << setprecision(50); solve(); }