//#define _GLIBCXX_DEBUG //#pragma GCC target("avx2") //#pragma GCC optimize("O3") //#pragma GCC optimize("unroll-loops") #include using namespace std; #ifdef LOCAL #include #define OUT(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__) #else #define OUT(...) (static_cast(0)) #endif #define endl '\n' #define lfs cout<= (ll)(n); i--) namespace template_tute{ using ll = long long; using ld = long double; const ll MOD1 = 1e9+7; const ll MOD9 = 998244353; const ll INF = 1e18; using P = pair; template using PQ = priority_queue; template using QP = priority_queue,greater>; templatebool chmin(T1 &a,T2 b){if(a>b){a=b;return true;}else return false;} templatebool chmax(T1 &a,T2 b){if(a({a,b,c})-min({a,b,c});} void ans1(bool x){if(x) cout<<"Yes"<void ans(bool x,T1 y,T2 z){if(x)cout<void anss(T1 x,T2 y,T3 z){ans(x!=y,x,z);}; templatevoid debug(const T &v,ll h,ll w,string sv=" "){for(ll i=0;ivoid debug(const T &v,ll n,string sv=" "){if(n!=0)cout<void debug(const vector&v){debug(v,v.size());} templatevoid debug(const vector>&v){for(auto &vv:v)debug(vv,vv.size());} templatevoid debug(stack st){while(!st.empty()){cout<void debug(queue st){while(!st.empty()){cout<void debug(deque st){while(!st.empty()){cout<void debug(PQ st){while(!st.empty()){cout<void debug(QP st){while(!st.empty()){cout<void debug(const set&v){for(auto z:v)cout<void debug(const multiset&v){for(auto z:v)cout<void debug(const array &a){for(auto z:a)cout<void debug(const map&v){for(auto z:v)cout<<"["<vector>vec(ll x, ll y, T w){vector>v(x,vector(y,w));return v;} vectordx={1,-1,0,0,1,1,-1,-1};vectordy={0,0,1,-1,1,-1,1,-1}; templatevector make_v(size_t a,T b){return vector(a,b);} templateauto make_v(size_t a,Ts... ts){return vector(a,make_v(ts...));} templateostream &operator<<(ostream &os, const pair&p){return os << "(" << p.first << "," << p.second << ")";} templateostream &operator<<(ostream &os, const vector &v){os<<"[";for(auto &z:v)os << z << ",";os<<"]"; return os;} templatevoid rearrange(vector&ord, vector&v){ auto tmp = v; for(int i=0;ivoid rearrange(vector&ord,Head&& head, Tail&&... tail){ rearrange(ord, head); rearrange(ord, tail...); } template vector ascend(const vector&v){ vectorord(v.size());iota(ord.begin(),ord.end(),0); sort(ord.begin(),ord.end(),[&](int i,int j){return make_pair(v[i],i) vector descend(const vector&v){ vectorord(v.size());iota(ord.begin(),ord.end(),0); sort(ord.begin(),ord.end(),[&](int i,int j){return make_pair(v[i],-i)>make_pair(v[j],-j);}); return ord; } template vector inv_perm(const vector&ord){ vectorinv(ord.size()); for(int i=0;i0);return n>=0?n/div:(n-div+1)/div;} ll CEIL(ll n,ll div){assert(div>0);return n>=0?(n+div-1)/div:n/div;} ll digitsum(ll n){ll ret=0;while(n){ret+=n%10;n/=10;}return ret;} ll modulo(ll n,ll d){return (n%d+d)%d;}; templateT min(const vector&v){return *min_element(v.begin(),v.end());} templateT max(const vector&v){return *max_element(v.begin(),v.end());} templateT acc(const vector&v){return accumulate(v.begin(),v.end(),T(0));}; templateT reverse(const T &v){return T(v.rbegin(),v.rend());}; //mt19937 mt(chrono::steady_clock::now().time_since_epoch().count()); int popcount(ll x){return __builtin_popcountll(x);}; int poplow(ll x){return __builtin_ctzll(x);}; int pophigh(ll x){return 63 - __builtin_clzll(x);}; templateT poll(queue &q){auto ret=q.front();q.pop();return ret;}; templateT poll(priority_queue &q){auto ret=q.top();q.pop();return ret;}; templateT poll(QP &q){auto ret=q.top();q.pop();return ret;}; templateT poll(stack &s){auto ret=s.top();s.pop();return ret;}; ll MULT(ll x,ll y){if(LLONG_MAX/x<=y)return LLONG_MAX;return x*y;} ll POW2(ll x, ll k){ll ret=1,mul=x;while(k){if(mul==LLONG_MAX)return LLONG_MAX;if(k&1)ret=MULT(ret,mul);mul=MULT(mul,mul);k>>=1;}return ret;} ll POW(ll x, ll k){ll ret=1;for(int i=0;isputn(d, len) != len) { dest.setstate(std::ios_base::badbit); } } return dest; } namespace converter{ int dict[500]; const string lower="abcdefghijklmnopqrstuvwxyz"; const string upper="ABCDEFGHIJKLMNOPQRSTUVWXYZ"; const string digit="0123456789"; const string digit1="123456789"; void regi_str(const string &t){ for(int i=0;ito_int(const string &s,const string &t){ regi_str(t); vectorret(s.size()); for(int i=0;ito_int(const string &s){ auto t=s; sort(t.begin(),t.end()); t.erase(unique(t.begin(),t.end()),t.end()); return to_int(s,t); } vector>to_int(const vector&s,const string &t){ regi_str(t); vector>ret(s.size(),vector(s[0].size())); for(int i=0;i>to_int(const vector&s){ string t; for(int i=0;i&s,const string &t){ regi_int(t); string ret; for(auto z:s)ret+=dict[z]; return ret; } vector to_str(const vector>&s,const string &t){ regi_int(t); vectorret(s.size()); for(int i=0;i struct edge { int to; T cost; int id; edge():to(-1),id(-1){}; edge(int to, T cost = 1, int id = -1):to(to), cost(cost), id(id){} operator int() const { return to; } }; template using Graph = vector>>; template Graphrevgraph(const Graph &g){ Graphret(g.size()); for(int i=0;i Graph readGraph(int n,int m,int indexed=1,bool directed=false,bool weighted=false){ Graph ret(n); for(int es = 0; es < m; es++){ int u,v; T w=1; cin>>u>>v;u-=indexed,v-=indexed; if(weighted)cin>>w; ret[u].emplace_back(v,w,es); if(!directed)ret[v].emplace_back(u,w,es); } return ret; } template Graph readParent(int n,int indexed=1,bool directed=true){ Graphret(n); for(int i=1;i>p; p-=indexed; ret[p].emplace_back(i); if(!directed)ret[i].emplace_back(p); } return ret; } } using namespace template_tute; template< int mod > struct ModInt { int x; ModInt() : x(0) {} ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {} 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); } friend ModInt operator+(const ModInt& lhs, const ModInt& rhs) { return ModInt(lhs) += rhs; } friend ModInt operator-(const ModInt& lhs, const ModInt& rhs) { return ModInt(lhs) -= rhs; } friend ModInt operator*(const ModInt& lhs, const ModInt& rhs) { return ModInt(lhs) *= rhs; } friend ModInt operator/(const ModInt& lhs, const ModInt& rhs) { return ModInt(lhs) /= rhs; } 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; swap(a -= t * b, b); swap(u -= t * v, v); } return ModInt(u); } ModInt pow(int64_t n) const { ModInt ret(1), mul(x); while(n > 0) { if(n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } pairfrac(){ for(int j=1;j<=300;j++){ for(int i=-300;i<=300;i++){ if(ModInt(i)/j==*this){ return make_pair(i,j); } } } return make_pair(-1,-1); } friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; } friend istream &operator>>(istream &is, ModInt &a) { int64_t t; is >> t; a = ModInt< mod >(t); return (is); } static int get_mod() { return mod; } }; template< typename T > struct Combination { vector< T > _fact, _rfact, _inv; Combination(ll sz) : _fact(sz + 1), _rfact(sz + 1), _inv(sz + 1) { _fact[0] = _rfact[sz] = _inv[0] = 1; for(ll i = 1; i <= sz; i++) _fact[i] = _fact[i - 1] * i; _rfact[sz] /= _fact[sz]; for(ll i = sz - 1; i >= 0; i--) _rfact[i] = _rfact[i + 1] * (i + 1); for(ll i = 1; i <= sz; i++) _inv[i] = _rfact[i] * _fact[i - 1]; } inline T fact(ll k) const { return _fact[k]; } inline T rfact(ll k) const { return _rfact[k]; } inline T inv(ll k) const { return _inv[k]; } T P(ll n, ll r) const { if(r < 0 || n < r) return 0; return fact(n) * rfact(n - r); } T C(ll p, ll q) const { if(q < 0 || p < q) return 0; return fact(p) * rfact(q) * rfact(p - q); } T RC(ll p, ll q) const { if(q < 0 || p < q) return 0; return rfact(p) * fact(q) * fact(p - q); } T H(ll n, ll r) const { if(n < 0 || r < 0) return (0); return r == 0 ? 1 : C(n + r - 1, r); } //+1がm個、-1がn個で prefix sumが常にk以上 T catalan(ll m,ll n,ll k){ if(n>m-k)return 0; else return C(n+m,m)-C(n+m,n+k-1); } }; using modint = ModInt< MOD9 >;modint mpow(ll n, ll x){return modint(n).pow(x);}modint mpow(modint n, ll x){return n.pow(x);} //using modint=ld;modint mpow(ll n, ll x){return pow(n,x);}modint mpow(modint n, ll x){return pow(n,x);} using Comb=Combination; template< class T> struct Kitamasa { ll n; const T zero = 0;//addの単位元 const T iden = 1;//mulの単位元 using arr = vector; arr rec_f; const T add(T x, T y){ return x + y; } const T mul(T x, T y){ return x * y; } arr zeros(){ arr ret(n); for(ll i=0;i v):n(v.size()){ //an=sum(v0*a_(n-k)+v_1*a_(n-k+1)+... rec_f = zeros(); for(ll i=0;i a){//k項目を求める, a0...ak-1 vectorbit; while(k){ if(k&1)bit.push_back(1); else bit.push_back(0); k>>=1; } reverse(bit.begin(),bit.end()); arr now=zeros(); now[0]=iden; for(ll i=0;i struct Matrix { vector< vector< T > > A; Matrix() {} Matrix(size_t n, size_t m) : A(n, vector< T >(m, 0)) {} Matrix(size_t n) : A(n, vector< T >(n, 0)) {}; Matrix(vector>v):A(v){}; size_t height() const { return (A.size()); } size_t width() const { return (A[0].size()); } inline const vector< T > &operator[](int k) const { return (A.at(k)); } inline vector< T > &operator[](int k) { return (A.at(k)); } static Matrix I(size_t n) { Matrix mat(n); for(int i = 0; i < n; i++) mat[i][i] = 1; return (mat); } Matrix &operator+=(const Matrix &B) { size_t n = height(), m = width(); assert(n == B.height() && m == B.width()); for(int i = 0; i < n; i++) for(int j = 0; j < m; j++) (*this)[i][j] += B[i][j]; return (*this); } Matrix &operator-=(const Matrix &B) { size_t n = height(), m = width(); assert(n == B.height() && m == B.width()); for(int i = 0; i < n; i++) for(int j = 0; j < m; j++) (*this)[i][j] -= B[i][j]; return (*this); } Matrix &operator*=(const Matrix &B) { size_t n = height(), m = B.width(), p = width(); assert(p == B.height()); vector< vector< T > > C(n, vector< T >(m, 0)); for(int i = 0; i < n; i++) for(int j = 0; j < m; j++) for(int k = 0; k < p; k++) C[i][j] = (C[i][j] + (*this)[i][k] * B[k][j]); A.swap(C); return (*this); } Matrix &operator^=(long long k) { Matrix B = Matrix::I(height()); while(k > 0) { if(k & 1) B *= *this; *this *= *this; k >>= 1LL; } A.swap(B.A); return (*this); } Matrix operator+(const Matrix &B) const { return (Matrix(*this) += B); } Matrix operator-(const Matrix &B) const { return (Matrix(*this) -= B); } Matrix operator*(const Matrix &B) const { return (Matrix(*this) *= B); } Matrix operator^(const long long k) const { return (Matrix(*this) ^= k); } bool operator==(const Matrix &B)const{ return this->A == B.A; } bool operator!=(const Matrix &B)const{ return this->A != B.A; } friend ostream &operator<<(ostream &os, Matrix p) { size_t n = p.height(), m = p.width(); for(int i = 0; i < n; i++) { os << "["; for(int j = 0; j < m; j++) { os << p[i][j] << (j + 1 == m ? "]\n" : ","); } } return (os); } T determinant() { Matrix B(*this); assert(width() == height()); T ret = 1; for(int i = 0; i < width(); i++) { int idx = -1; for(int j = i; j < width(); j++) { if(B[j][i] != 0) idx = j; } if(idx == -1) return (0); if(i != idx) { ret *= -1; swap(B[i], B[idx]); } ret *= B[i][i]; T vv = B[i][i]; for(int j = 0; j < width(); j++) { B[i][j] /= vv; } for(int j = i + 1; j < width(); j++) { T a = B[j][i]; for(int k = 0; k < width(); k++) { B[j][k] -= B[i][k] * a; } } } return (ret); } }; void solve(){ ll res=0,buf=0; bool judge = true; ll n,m,k;cin>>n>>m>>k; vectorc(k); rep(i,0,k)cin>>c[i]; sort(ALL(c)); int sz=10; vectordp(sz+1);dp[0]=1; rep(i,0,sz)rep(j,1,7){ if(i+j<=sz)dp[i+j]+=dp[i]; } Kitamasa kit(vector{1,1,1,1,1,1}); vector tmp(6); rep(i,0,6)tmp[i]=dp[i]; //OUT(get(3)); rep(j,0,k){ mapmp; auto get=[&](ll d){ if(mp.count(d))return mp[d]; mp[d]=kit.calc(d,tmp); return mp[d]; }; Matrixmat(12,12); rep(i,0,6){ modint sum=0; if(i<=c[j])sum+=get(c[j]-i); rep(r,n-6,n){ modint add1=0; if(c[j]<=r)add1=sum*get(r-c[j]); modint add0=get(r-i)-add1; rep(p,1,7)if(r+p>=n){ int ir=r+p-n; mat[i][ir]+=add0; mat[i][ir+6]+=add1; mat[i+6][ir+6]+=add0+add1; } } } mat^=m; modint ret=0; rep(i,6,12)ret+=mat[0][i]; cout<>T; while(T--){ solve(); } return 0; }