#include using namespace std; using ll=long long; using ull=unsigned long long; using P=pair; templateusing minque=priority_queue,greater>; templatebool chmax(T &a,const T &b){return (abool chmin(T &a,const T &b){return (a>b?(a=b,true):false);} templateistream &operator>>(istream &is,pair&p){is>>p.first>>p.second;return is;} templateistream &operator>>(istream &is,tuple&a){is>>std::get<0>(a)>>std::get<1>(a)>>std::get<2>(a);return is;} templateistream &operator>>(istream &is,array&a){for(auto&i:a)is>>i;return is;} templateistream &operator>>(istream &is,vector &a){for(auto &i:a)is>>i;return is;} templatevoid operator++(pair&a,int n){a.first++,a.second++;} templatevoid operator--(pair&a,int n){a.first--,a.second--;} templatevoid operator++(vector&a,int n){for(auto &i:a)i++;} templatevoid operator--(vector&a,int n){for(auto &i:a)i--;} #define overload3(_1,_2,_3,name,...) name #define rep1(i,n) for(int i=0;i<(int)(n);i++) #define rep2(i,l,r) for(int i=(int)(l);i<(int)(r);i++) #define rep(...) overload3(__VA_ARGS__,rep2,rep1)(__VA_ARGS__) #define reps(i,l,r) rep2(i,l,r) #define all(x) x.begin(),x.end() #define pcnt(x) __builtin_popcountll(x) #define fin(x) return cout<<(x)<<'\n',static_cast(0) #define yn(x) cout<<((x)?"Yes\n":"No\n") #define uniq(x) sort(all(x)),x.erase(unique(all(x)),x.end()) template inline int fkey(vector&z,T key){return lower_bound(z.begin(),z.end(),key)-z.begin();} ll myceil(ll a,ll b){return (a+b-1)/b;} template auto vec(const int (&d)[n],const T &init=T()){ if constexpr (id(d,init)); else return init; } #ifdef LOCAL #include #define SWITCH(a,b) (a) #else #define debug(...) static_cast(0) #define debugg(...) static_cast(0) #define SWITCH(a,b) (b) templateostream &operator<<(ostream &os,const pair&p){os<>testcase; for(int i=0;i #include constexpr int carmichael_constexpr(int n){ if(n==998244353)return 998244352; if(n==1000000007)return 1000000006; if(n<=1)return n; int res=1; int t=0; while(n%2==0){ n/=2; t++; } if(t==2)res=2; else if(t>=3)res=1<<(t-2); for(int i=3;i*i<=n;i++)if(n%i==0){ int c=0; while(n%i==0){ n/=i; c++; } int prod=i-1; for(int j=0;j struct mod_int{ private: static constexpr unsigned int umod=static_cast(m); static constexpr unsigned int car=carmichael_constexpr(m); using uint=unsigned int; using mint=mod_int; uint v; static_assert(mval()<=1)return *this; if constexpr(m%8==1){ mint b=2; while(b.pow((m-1)/2).val()==1)b++; int m2=m-1,e=0; while(m2%2==0)m2>>=1,e++; mint x=this->pow((m2-1)/2); mint y=(*this)*x*x; x*=*this; mint z=b.pow(m2); while(y.val()!=1){ int j=0; mint t=y; while(t.val()!=1)t*=t,j++; z=z.pow(1<<(e-j-1)); x*=z; z*=z; y*=z;e=j; } return x; } else if constexpr(m%8==5){ mint ret=this->pow((m+3)/8); if((ret*ret).val()==this->val())return ret; else return ret*mint::raw(2).pow((m-1)/4); } else{ return this->pow((m+1)/4); } } public: using value_type=uint; mod_int():v(0){} template,std::nullptr_t> =nullptr> mod_int(T a){ a%=m; if(a<0)v=a+umod; else v=a; } template,std::nullptr_t> =nullptr> mod_int(T a):v(a%umod){} static constexpr mint raw(int a){ mint ret; ret.v=a; return ret; } inline uint val()const{return this->v;} static constexpr int mod(){return m;} inline mint &operator+=(const mint &b){ this->v+=b.v; if(this->v>=umod)this->v-=umod; return *this; } inline mint &operator-=(const mint &b){ this->v-=b.v; if(this->v>=umod)this->v+=umod; return *this; } inline mint &operator*=(const mint &b){ this->v=((unsigned long long)this->v*b.v)%umod; return *this; } inline mint &operator/=(const mint &b){ *this*=b.inv(); return *this; } inline mint operator+()const{return *this;} inline mint operator-()const{return mint()-*this;} friend inline mint operator+(const mint &a,const mint &b){return mint(a)+=b;} friend inline mint operator-(const mint &a,const mint &b){return mint(a)-=b;} friend inline mint operator*(const mint &a,const mint &b){return mint(a)*=b;} friend inline mint operator/(const mint &a,const mint &b){return mint(a)/=b;} friend inline bool operator==(const mint &a,const mint &b){return a.val()==b.val();} friend inline bool operator!=(const mint &a,const mint &b){return !(a==b);} friend inline bool operator<(const mint &a,const mint &b){return a.val()(const mint &a,const mint &b){return a.val()>b.val();} friend inline bool operator<=(const mint &a,const mint &b){return a.val()<=b.val();} friend inline bool operator>=(const mint &a,const mint &b){return a.val()>=b.val();} inline mint operator++(int){ mint ret=*this; *this+=mint::raw(1); return ret; } inline mint operator--(int){ mint ret=*this; *this-=mint::raw(1); return ret; } mint pow(long long n)const{ mint ret=mint::raw(1),a(*this); while(n){ if(n&1)ret*=a; a*=a; n>>=1; } return ret; } inline mint inv()const{ assert(this->v!=0); return pow(car-1); } std::optionalsqrt()const{ if(this->val()<=1||this->pow((m-1)/2)==1)return std::make_optional(this->sqrt_impl()); else return std::nullopt; } static constexpr unsigned int order(){return car;} friend std::istream &operator>>(std::istream &is,mint &b){ long long a; is>>a; b=mint(a); return is; } friend std::ostream &operator<<(std::ostream &os,const mint &b){ os< struct std::hash>{ std::size_t operator()(mod_intx)const{ return std::hash()(x.val()); } }; using mint998=mod_int<998244353>; using mint107=mod_int<1000000007>; #include template constexpr std::enable_if_t::digits<=32,int>msb(T n){return n==0?-1:31-__builtin_clz(n);} template constexpr std::enable_if_t<(std::numeric_limits::digits>32),int>msb(T n){return n==0?-1:63-__builtin_clzll(n);} template constexpr std::enable_if_t::digits<=32,int>lsb(T n){return n==0?-1:__builtin_ctz(n);} template constexpr std::enable_if_t<(std::numeric_limits::digits>32),int>lsb(T n){return n==0?-1:__builtin_ctzll(n);} template constexpr std::enable_if_t,T>floor_pow2(T n){return n==0?0:T(1)< constexpr std::enable_if_t,T>ceil_pow2(T n){return n<=1?1:T(1)<<(msb(n-1)+1);} template constexpr T safe_div(T a,T b){return a/b-(a%b&&(a^b)<0);} template constexpr T safe_ceil(T a,T b){return a/b+(a%b&&(a^b)>0);} struct is_modint_impl{ template static auto check(T&&x)->decltype(x.mod(),std::true_type{}); template static auto check(...)->std::false_type; }; template struct is_modint:public decltype(is_modint_impl::check(std::declval())){}; template inline constexpr bool is_modint_v=is_modint::value; struct is_dynamic_modint_impl{ template static auto check(T&&x)->decltype(x.set_mod((typename T::value_type)0),std::true_type{}); template static auto check(...)->std::false_type; }; template struct is_dynamic_modint:public decltype(is_dynamic_modint_impl::check(std::declval())){}; template inline constexpr bool is_dynamic_modint_v=is_dynamic_modint::value; template inline constexpr bool is_static_modint_v=is_modint_v&&!is_dynamic_modint_v; struct is_uso_modint_impl{ template static auto check(T&&x)->decltype(x.uso(),std::true_type{}); template static auto check(...)->std::false_type; }; template struct is_uso_modint:public decltype(is_uso_modint_impl::check(std::declval())){}; template inline constexpr bool is_uso_modint_v=is_uso_modint::value; template void hadamard(std::vector&f){ int n=f.size(); int log2n=msb(n); for(int i=0;i>i&1){ T x=f[j^(1< std::vectorxor_convolution(std::vectora,std::vectorb){ assert(a.size()==b.size()); int n=a.size(),log2n=msb(n); assert(floor_pow2(a.size())==a.size()); hadamard(a),hadamard(b); for(int i=0;i){ T inv2n=T::raw(2).pow(log2n).inv(); for(int i=0;i,2>,2>; void SOLVE(){ ll n; int k,x,y; cin>>n>>k>>x>>y; vectora(k); cin>>a; uniq(a); if(n==1){ int ans=0; rep(i,k)ans+=x<=a[i]&&a[i]<=y; fin(ans); } int z=ceil_pow2(max(y,*max_element(all(a)))+1); int lg=msb(z); vector>dp(4,vector(z)); dp[0][0]=1; rep(i,k)dp[1][a[i]]=1; auto mul=[&](Matrix lhs,Matrix rhs)->Matrix { Matrix res; rep(i,2)rep(j,2)res[i][j].resize(z); rep(i,2)rep(j,2)rep(k,2)rep(l,z)res[i][k][l]+=lhs[i][j][l]*rhs[j][k][l]; return res; }; auto E=[&]()->Matrix { Matrix res; rep(i,2)rep(j,2)res[i][j].resize(z); vectorf(z,1); res[0][0]=res[1][1]=f; return res; }; auto pow=[&](Matrix x,ll e)->Matrix { Matrix res=E(); while(e){ if(e&1)res=mul(res,x); x=mul(x,x); e>>=1; } return res; }; Matrix mat; vectorg(z); for(int x:a)g[x]++; { rep(i,2)rep(j,2)mat[i][j].resize(z); vectorf(z,1); mat[1][0]=f; auto g2(g); hadamard(g2); mat[0][0]=g2; vectorh(z,1-k); mat[0][1]=h; debug(mat); } mat=pow(mat,n-2); vectorf=xor_convolution(g,g); f[0]-=k; hadamard(f); hadamard(g); vectorh(z); rep(i,z)h[i]+=mat[0][0][i]*f[i]+mat[0][1][i]*g[i]; hadamard(h); // rep(i,2,4){ // rep(j,z){ // rep(l,k)dp[i][j]+=dp[i-1][j^a[l]]; // dp[i][j]-=dp[i-2][j]*(k-(i>2)); // } // } // debugg(dp); mint ans=0; rep(i,x,y+1)ans+=h[i]; ans/=z; cout<