/** * author: otera * created: 18.02.2022 22:01:18 **/ #include #include std::ostream& operator<<(std::ostream& out, const atcoder::modint1000000007 &e) { out << e.val(); return out; } std::ostream& operator<<(std::ostream& out, const atcoder::modint998244353 &e) { out << e.val(); return out; } std::ostream& operator<<(std::ostream& out, const atcoder::modint &e) { out << e.val(); return out; } using namespace std; using ll = long long; using ld = long double; using ull = unsigned long long; using uint = unsigned; #define repa(i, n) for(int i = 0; i < n; ++ i) #define repb(i, a, b) for(int i = a; i < b; ++ i) #define repc(i, a, b, c) for(int i = a; i < b; i += c) #define overload4(a, b, c, d, e, ...) e #define rep(...) overload4(__VA_ARGS__, repc, repb, repa)(__VA_ARGS__) #define rep1a(i, n) for(int i = 0; i <= n; ++ i) #define rep1b(i, a, b) for(int i = a; i <= b; ++ i) #define rep1c(i, a, b, c) for(int i = a; i <= b; i += c) #define rep1(...) overload4(__VA_ARGS__, rep1c, rep1b, rep1a)(__VA_ARGS__) #define per(i,n) for(int i=n-1;i>=0;i--) #define per1(i,n) for(int i=n;i>=1;i--) typedef pair P; typedef pair LP; #define pb push_back #define eb emplace_back #define fr first #define sc second #define all(c) c.begin(),c.end() #define lb(c, x) distance((c).begin(), lower_bound(all(c), (x))) #define ub(c, x) distance((c).begin(), upper_bound(all(c), (x))) #define Sort(a) sort(all(a)) #define Rev(a) reverse(all(a)) #define Uniq(a) sort(all(a));a.erase(unique(all(a)),end(a)) #define si(c) (int)(c).size() inline ll popcnt(ull a){ return __builtin_popcountll(a); } #define tpow(n) (1LL<<(n)) #define unless(A) if(!(A)) ll intpow(ll a, ll b){ ll ans = 1; while(b){ if(b & 1) ans *= a; a *= a; b /= 2; } return ans; } ll intpow(ll a, ll b, ll m) {ll ans = 1; while(b){ if(b & 1) (ans *= a) %= m; (a *= a) %= m; b /= 2; } return ans; } template inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; } template inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; } #define INT(...) int __VA_ARGS__;in(__VA_ARGS__) #define LL(...) ll __VA_ARGS__;in(__VA_ARGS__) #define ULL(...) ull __VA_ARGS__;in(__VA_ARGS__) #define STR(...) string __VA_ARGS__;in(__VA_ARGS__) #define CHR(...) char __VA_ARGS__;in(__VA_ARGS__) #define DBL(...) double __VA_ARGS__;in(__VA_ARGS__) #define LD(...) ld __VA_ARGS__;in(__VA_ARGS__) #define vec(type,name,...) vectorname(__VA_ARGS__) #define VEC(type,name,size) vectorname(size);in(name) #define vv(type,name,h,...) vector>name(h,vector(__VA_ARGS__)) #define VV(type,name,h,w) vector>name(h,vector(w));in(name) #define vvv(type,name,h,w,...) vector>>name(h,vector>(w,vector(__VA_ARGS__))) // template using vc = vector; // template using vvc = vector>; // template using vvvc = vector>; // template using vvvvc = vector>; template using pq = priority_queue; template using pqg = priority_queue, greater>; template void scan(T& a){ cin >> a; } template void scan(vector& a){ for(auto&& i : a) scan(i); } void in(){} template void in(Head& head, Tail&... tail){ scan(head); in(tail...); } void print(){ cout << ' '; } template void print(const T& a){ cout << a; } template void print(const vector& a){ if(a.empty()) return; print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ cout << ' '; print(*i); } } int out(){ cout << '\n'; return 0; } template int out(const T& t){ print(t); cout << '\n'; return 0; } template int out(const Head& head, const Tail&... tail){ print(head); cout << ' '; out(tail...); return 0; } #define CHOOSE(a) CHOOSE2 a #define CHOOSE2(a0,a1,a2,a3,a4,x,...) x #define debug_1(x1) cout<<#x1<<": "< vc; typedef vector mat; mat mul(mat& A, mat& B) { mat C(A.size(), vc(B[0].size(), 0)); for(int i = 0; i < A.size(); ++i) { for(int j = 0; j < B[0].size(); ++j) { for(int k = 0; k < B.size(); ++k) { C[i][j] += A[i][k] * B[k][j]; } } } return C; } mat pow(mat A, ll n) { mat B(A.size(), vc(A.size(), 0)); for(int i = 0; i < A.size(); ++i) { B[i][i] = 1; } while(n > 0) { if(n & 1) B = mul(B, A); A = mul(A, A); n >>= 1; } return B; } void solve() { LL(l); INT(n, m); VEC(int, k, m); rep(i, m) -- k[i]; int N = (n + 2) * n; mat A(N, vc(N, 0)); rep(x, n + 2) { rep(y, n) { rep(nxt, n) { bool check = false; if(y != nxt) { rep(i, m) { if(k[i] == y and k[i] + 1 == x) { check = true; } } } if(!check) { int nx = (x == n + 1 and y == nxt ? n + 1 : y == nxt ? x + 1 : 1); A[nx * n + nxt][x * n + y] += 1; } } } } A = pow(A, l - 1); mint ans = mint(n).pow(l); rep(x, n + 2) { rep(y, n) { bool check = false; rep(i, m) { if(k[i] == y and k[i] + 1 == x) { check = true; } } if(check) continue; rep(st, n) { ans -= A[x * n + y][1 * n + st]; } } } out(ans); } signed main() { ios::sync_with_stdio(false); cin.tie(0); // cout << fixed << setprecision(20); // INT(t); rep(i, t)solve(); solve(); return 0; }