#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using lint = long long int; long long int INF = 1001001001001001LL; int inf = 1000000007; long long int MOD = 1000000007LL; double PI = 3.1415926535897932; templateinline void chmin(T1 &a,const T2 &b){if(a>b) a=b;} templateinline void chmax(T1 &a,const T2 &b){if(a struct Mint{ T v; Mint():v(0){} Mint(signed v):v(v){} Mint(long long t){v=t%MOD;if(v<0) v+=MOD;} Mint pow(long long k){ Mint res(1),tmp(v); while(k){ if(k&1) res*=tmp; tmp*=tmp; k>>=1; } return res; } static Mint add_identity(){return Mint(0);} static Mint mul_identity(){return Mint(1);} Mint inv(){return pow(MOD-2);} Mint& operator+=(Mint a){v+=a.v;if(v>=MOD)v-=MOD;return *this;} Mint& operator-=(Mint a){v+=MOD-a.v;if(v>=MOD)v-=MOD;return *this;} Mint& operator*=(Mint a){v=1LL*v*a.v%MOD;return *this;} Mint& operator/=(Mint a){return (*this)*=a.inv();} Mint operator+(Mint a) const{return Mint(v)+=a;}; Mint operator-(Mint a) const{return Mint(v)-=a;}; Mint operator*(Mint a) const{return Mint(v)*=a;}; Mint operator/(Mint a) const{return Mint(v)/=a;}; Mint operator-() const{return v?Mint(MOD-v):Mint(v);} bool operator==(const Mint a)const{return v==a.v;} bool operator!=(const Mint a)const{return v!=a.v;} bool operator <(const Mint a)const{return v struct SquareMatrix{ vector> dat; size_t N; SquareMatrix() = default; SquareMatrix(size_t N, T val = T()):N(N){ dat = vector> (N, vector (N)); for(size_t i=0;i& operator[](size_t k){return dat[k];}; const vector& operator[](size_t k) const {return dat[k];}; SquareMatrix operator*(const SquareMatrix &B) const{ SquareMatrix res(N, 0); for(size_t i=0;i>=1; } return res; } }; using modint = Mint; modint culc_sub1(vector &a, lint w) { vector dp(w + 1, 0); dp[0] = modint(1); // 配る dp for(int i = 0; i < w; i++) { if(dp[0] == 0) continue; for(auto delta : a) { lint nxt = delta + i; if(nxt > w) continue; dp[nxt] += dp[i]; } } return dp[w]; } modint culc_sub2(vector &a, lint w) { vector dp(2 * w + 1, 0); dp[0] = 1; for(int i = 0; i < 2 * w; i++) { for(auto delta : a) { lint nxt = delta + i; if(nxt > 2 * w) continue; if(nxt == w) continue; dp[nxt] += dp[i]; } } return dp[2 * w]; } int main() { lint n, w, k; cin >> n >> w >> k; vector a(n); for(int i = 0; i < n; i++) cin >> a[i]; modint w1 = culc_sub1(a, w); // 次の島へ行く通り数 modint w2 = culc_sub2(a, w); // 次の島を踏まずに,次の次の島へ行く通り数. SquareMatrix mat(2); mat[0][0] = w1; mat[0][1] = w2; mat[1][0] = 1; mat[1][1] = 0; if(k == 1) { cout << w1.v << endl; return 0; } mat = mat.pow(k - 1); cout << (w1 * mat[0][0] + mat[0][1]).v << endl; return 0; }