#pragma GCC optimize("Ofast") //#pragma GCC optimize("unroll-loops") //#pragma GCC push_options //#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native") #include #include #include using namespace::std; __attribute__((constructor))void init(){cin.tie(0);ios::sync_with_stdio(false);cout< #include #include #include // #include // #include // namespace mp = boost::multiprecision; // typedef mp::number> cdouble; // typedef mp::cpp_int cint; templateusing pbds=__gnu_pbds::tree,__gnu_pbds::rb_tree_tag,__gnu_pbds::tree_order_statistics_node_update>; templateusing pbds_map=__gnu_pbds::tree,__gnu_pbds::rb_tree_tag,__gnu_pbds::tree_order_statistics_node_update>; templateusing hash_map=__gnu_pbds::gp_hash_table; templateusing pqueue =__gnu_pbds::priority_queue,__gnu_pbds::rc_binomial_heap_tag>; typedef long long lint; #define INF (1LL<<60) #define IINF (1<<30) #define EPS (1e-10) #define MOD 1000000007LL //#define MOD 998244353LL typedef vector vec; typedef vector> mat; typedef vector>> mat3; typedef vector svec; typedef vector> smat; templateinline void numout(T t){bool f=0;for(auto i:t){cout<<(f?" ":"")<inline void numout2(T t){for(auto i:t)numout(i);} templateinline void output(T t){bool f=0;for(auto i:t){cout<<(f?" ":"")<inline void output2(T t){for(auto i:t)output(i);} templateinline void _output(T t){bool f=0;for(lint i=0;iinline void _output2(T t){for(lint i=0;i=0;--i) #define rrepi(i,a,b) for(lint i=lint(b)-1;i>=lint(a);--i) #define irep(i) for(lint i=0;;++i) #define all(n) begin(n),end(n) #define dist(a,b,c,d) sqrt(pow(a-c,2)+pow(b-d,2)) inline lint gcd(lint A,lint B){return B?gcd(B,A%B):A;} inline lint lcm(lint A,lint B){return A/gcd(A,B)*B;} // inline cint cgcd(cint A,cint B){return B?cgcd(B,A%B):A;} // inline cint clcm(cint A,cint B){return A/cgcd(A,B)*B;} //inline bool chmin(auto& s,const auto& t){bool res=s>t;s=min(s,t);return res;} //inline bool chmax(auto& s,const auto& t){bool res=s dx={1,0,-1,0,1,1,-1,-1}; const vector dy={0,1,0,-1,1,-1,1,-1}; #define SUM(v) accumulate(all(v),0LL) //auto call=[&](auto f,auto... args){return f(f,args...);}; class mint { using u64 = std::uint_fast64_t; public: u64 a; constexpr mint(const long long x = 0)noexcept:a(x>=0?x%get_mod():get_mod()-(-x)%get_mod()){} constexpr u64 &value()noexcept{return a;} constexpr const u64 &value() const noexcept {return a;} constexpr mint operator+(const mint rhs)const noexcept{return mint(*this) += rhs;} constexpr mint operator-(const mint rhs)const noexcept{return mint(*this)-=rhs;} constexpr mint operator*(const mint rhs) const noexcept {return mint(*this) *= rhs;} constexpr mint operator/(const mint rhs) const noexcept {return mint(*this) /= rhs;} constexpr mint &operator+=(const mint rhs) noexcept { a += rhs.a; if (a >= get_mod())a -= get_mod(); return *this; } constexpr mint &operator-=(const mint rhs) noexcept { if (a= get_mod())a -= get_mod(); return *this; } constexpr mint operator--(int n) noexcept { if (a<1)a += get_mod(); a -= 1; return *this; } constexpr mint &operator/=(mint rhs) noexcept { u64 exp=get_mod()-2; while (exp) { if (exp % 2) { *this *= rhs; } rhs *= rhs; exp /= 2; } return *this; } constexpr bool operator==(mint x) noexcept { return a==x.a; } constexpr bool operator!=(mint x) noexcept { return a!=x.a; } constexpr static int root(){ mint root = 2; while(root.pow((get_mod()-1)>>1).a==1)root++; return root.a; } constexpr mint pow(long long n){ long long x=a; mint ret = 1; while(n>0) { if(n&1)(ret*=x); (x*=x)%=get_mod(); n>>=1; } return ret; } constexpr mint inv(){ return pow(get_mod()-2); } mint comb(lint b){ using lint=long long; static bool init=1; static lint fac[3000001],ifac[3000001]; if(init){ init=0; fac[0]=1; ifac[0]=1; auto mod_pow=[&](lint x,lint n){ lint ans = 1; while(n != 0){ if(n&1)ans=ans*x%get_mod(); x=x*x%get_mod(); n=n>>1; } return ans; }; for(int i=0;i<3000000;i++){ fac[i+1]=fac[i]*(i+1)%get_mod(); ifac[i+1]=ifac[i]*mod_pow(i+1, get_mod()-2)%get_mod(); } } if(a==0&&b==0)return 1; if((lint)a>(istream& lhs,mint& rhs) noexcept { lhs >> rhs.a; return lhs; } constexpr static u64 get_mod(){return MOD;} }; template vector> mul(const vector>& s,const vector>& t){ lint n=s.size(); vector> res(n,vector(n,0)); rep(i,n)rep(j,n)rep(k,n){ res[i][j]+=s[i][k]*t[k][j]; } return res; } template vector> mul(const vector>& s,const vector>& t){ lint n=s.size(); vector> res(n,vector(n,0)); rep(i,n)rep(j,n)rep(k,n){ res[i][j]+=s[i][k]*t[k][j]; } return res; } template vector> pow(const vector>& s,const lint& n){ if(n==0){ lint sz=s.size(); vector> res(sz,vector(sz,0)); rep(i,sz)res[i][i]=1; return res; } if(n==1)return s; if(n%2==0){ vector> tmp=pow(s,n/2); return mul(tmp,tmp); }else{ return mul(s,pow(s,n-1)); } } template vector conv(vector a,vector> b){ lint n=a.size(); vector res(n,0); rep(i,n)rep(j,n)res[i]+=a[j]*b[i][j]; return res; } int main(){ lint n,w,k; cin>>n>>w>>k; vec a(n); rep(i,n)cin>>a[i]; vector> dp(w*2+1,vector(2,0)); dp[0][0]=1; repi(i,1,2*w+1){ rep(j,n){ if(i-a[j]<0)continue; if(i%w==0){ dp[i][0]+=dp[i-a[j]][0]+dp[i-a[j]][1]; continue; } if((i-a[j])/w!=i/w){ dp[i][1]+=dp[i-a[j]][0]; }else{ dp[i][0]+=dp[i-a[j]][0]; dp[i][1]+=dp[i-a[j]][1]; } } } vector>v={{dp[w][0],dp[w*2][0]-dp[w][0]*dp[w][0]},{1,0}}; cout<({dp[w][0],1},pow(v,k))[1]<