#include using namespace std; #define incII(i, l, r) for(decay_t i = (l) ; i <= (r); i++) #define incIX(i, l, r) for(decay_t i = (l) ; i < (r); i++) #define incXI(i, l, r) for(decay_t i = (l) + 1; i <= (r); i++) #define incXX(i, l, r) for(decay_t i = (l) + 1; i < (r); i++) #define decII(i, l, r) for(decay_t i = (r) ; i >= (l); i--) #define decIX(i, l, r) for(decay_t i = (r) - 1; i >= (l); i--) #define decXI(i, l, r) for(decay_t i = (r) ; i > (l); i--) #define decXX(i, l, r) for(decay_t i = (r) - 1; i > (l); i--) #define inc(i, n) incIX(i, 0, n) #define dec(i, n) decIX(i, 0, n) #define inc1(i, n) incII(i, 1, n) #define dec1(i, n) decII(i, 1, n) auto inII = [](auto a, auto l, auto r) -> bool { return (l <= a && a <= r); }; auto inIX = [](auto a, auto l, auto r) -> bool { return (l <= a && a < r); }; auto inXI = [](auto a, auto l, auto r) -> bool { return (l < a && a <= r); }; auto inXX = [](auto a, auto l, auto r) -> bool { return (l < a && a < r); }; auto setmin = [](auto & a, auto b) -> bool { return (b < a ? a = b, true : false); }; auto setmax = [](auto & a, auto b) -> bool { return (b > a ? a = b, true : false); }; auto setmineq = [](auto & a, auto b) -> bool { return (b <= a ? a = b, true : false); }; auto setmaxeq = [](auto & a, auto b) -> bool { return (b >= a ? a = b, true : false); }; using LL = long long int; using LD = long double; #define PB push_back #define EB emplace_back #define MP make_pair #define MT make_tuple #define FI first #define SE second #define FR front() #define BA back() #define ALL(a) begin(a), end(a) #define RALL(a) rbegin(a), rend(a) #define RV(a) reverse(ALL(a)) #define ST(a) sort(ALL(a)) #define RST(a) sort(RALL(a)) #define SC static_cast #define SI(a) SC(a.size()) #define SL(a) SC(a.size()) #define RF(e, ...) for(auto && e: __VA_ARGS__) #define SF(a, ...) for(auto && [__VA_ARGS__]: a) #define until(e) while(not(e)) #define if_not(e) if(not(e)) #define ef else if #define UR assert(false) auto * IS = & cin; auto * OS = & cout; template void in(A & ... a) { (* IS >> ... >> a); } #define IN(...) __VA_ARGS__; in(__VA_ARGS__) struct OS_init { OS_init() { * OS << boolalpha << fixed << setprecision(20); } } os_init_; void out_([[maybe_unused]] string const & s) { } template void out_([[maybe_unused]] string const & s, A const & a) { * OS << a; } template void out_( string const & s, A const & a, B const & ... b) { * OS << a << s; out_(s, b ...); } auto outF = [](array const & s, auto const & ... a) { * OS << s[0]; out_(s[1], a ...); * OS << s[2] << flush; }; auto outN = [](auto const & ... a) { outF({ "", "" , "" }, a ...); }; auto outS = [](auto const & ... a) { outF({ "", " " , " " }, a ...); }; auto outL = [](auto const & ... a) { outF({ "", "\n", "\n" }, a ...); }; auto outSN = [](auto const & ... a) { outF({ "", " " , "" }, a ...); }; auto outNL = [](auto const & ... a) { outF({ "", "" , "\n" }, a ...); }; auto outSL = [](auto const & ... a) { outF({ "", " " , "\n" }, a ...); }; auto outD = [](auto const & ... a) { outF({ "[ ", " : " , " ]\n" }, a ...); }; auto out = outSL; template void disp_(A const & a) { * OS << a; } template void disp_(A const & a, string const & s, T const & ... t) { string ss; for(auto && e: a) { * OS << ss; ss = s; disp_(e, t ...); } } auto dispI = [](auto const & a, auto const & s, auto const & ... t) { disp_(a, t ...); * OS << s << flush; }; auto dispT = [](auto const & a, auto const & s, auto const & ... t) { for(auto && e: a) { disp_(e, t ...); * OS << s; } * OS << flush; }; auto dispL = [](auto const & a, auto const & ... t) { dispT(a, "\n", t ...); }; template istream & operator>>(istream & is, vector & v) { for(auto && e: v) { is >> e; } return is; } template ostream & operator<<(ostream & os, vector const & v) { string ss; for(auto && e: v) { os << ss << e; ss = " "; } return os; } template auto make_v(A a) { return a; } template auto make_v(A a, int n, M ... m) { return vector(n, make_v(a, m ...)); } template auto read_v(N ... n) { auto a = make_v(A { }, n ...); in(a); return a; } template istream & operator>>(istream & is, array & a) { for(auto && e: a) { is >> e; } return is; } template ostream & operator<<(ostream & os, array const & a) { string ss; for(auto && e: a) { os << ss << e; ss = " "; } return os; } template istream & operator>>(istream & is, pair & p) { return is >> p.first >> p.second; } template ostream & operator<<(ostream & os, pair const & p) { return os << p.first << " " << p.second; } template void tin_ (istream & is, T & t) { if constexpr(I < tuple_size::value) { is >> get(t); tin_(is, t); } } template void tout_(ostream & os, T const & t) { if constexpr(I < tuple_size::value) { if(I != 0) { os << " "; } os << get(t); tout_(os, t); } } template istream & operator>>(istream & is, tuple & t) { tin_ (is, t); return is; } template ostream & operator<<(ostream & os, tuple const & t) { tout_(os, t); return os; } // ---- ---- template struct Matrix_ { int h, w; vector> v; explicit Matrix_(int h = 1): h(h), w(h), v(h, vector(w, ZERO())) { } explicit Matrix_(int h, int w): h(h), w(w), v(h, vector(w, ZERO())) { } Matrix_(vector> const & v): h(SI(v)), w(SI(v[0])), v(v) { inc(i, h) { assert(SI(v[i]) == w); } } vector const & operator[](int i) const { return v.at(i); } vector & operator[](int i) { return v.at(i); } static Matrix_ unit(int n) { Matrix_ a(n); inc(i, n) { a[i][i] = UNIT(); } return a; } friend Matrix_ operator*(Matrix_ const & a, Matrix_ const & b) { assert(a.w == b.h); Matrix_ c(a.h, b.w); inc(i, a.h) { inc(j, b.w) { inc(k, a.w) { c[i][j] = PLUS(c[i][j], MULT(a[i][k], b[k][j])); } } } return c; } friend Matrix_ operator^(Matrix_ a, LL b) { assert(a.h == a.w); assert(b >= 0); auto p = Matrix_::unit(a.h); while(b) { if(b & 1) { p *= a; } a *= a; b >>= 1; } return p; } friend Matrix_ & operator*=(Matrix_ & a, Matrix_ const & b) { return (a = a * b); } friend Matrix_ & operator^=(Matrix_ & a, LL b) { return (a = a ^ b); } friend Matrix_ & operator*=(Matrix_ & a, T b) { inc(i, a.h) { inc(j, a.w) { a[i][j] = MULT(a[i][j], b); } } return a; } friend Matrix_ operator*(Matrix_ a, T b) { return (a *= b); } friend Matrix_ operator*(T b, Matrix_ a) { return (a *= b); } friend ostream & operator<<(ostream & s, Matrix_ const & a) { inc(i, a.h) { s << a[i] << endl; } return s; } }; template T PLUS(T a, T b) { return a + b; }; template T MULT(T a, T b) { return a * b; }; template T ZERO() { return 0; }; template T UNIT() { return 1; }; template using Matrix = Matrix_, MULT, ZERO, UNIT>; // ---- template class ModInt { private: LL v; pair ext_gcd(LL a, LL b) { if(b == 0) { assert(a == 1); return { 1, 0 }; } auto p = ext_gcd(b, a % b); return { p.SE, p.FI - (a / b) * p.SE }; } public: ModInt(LL vv = 0) { v = vv; if(abs(v) >= M) { v %= M; } if(v < 0) { v += M; } } LL val() { return v; } static LL mod() { return M; } ModInt inv() { return ext_gcd(M, v).SE; } ModInt exp(LL b) { ModInt p = 1, a = v; if(b < 0) { a = a.inv(); b = -b; } while(b) { if(b & 1) { p *= a; } a *= a; b >>= 1; } return p; } friend bool operator< (ModInt a, ModInt b) { return (a.v < b.v); } friend bool operator> (ModInt a, ModInt b) { return (a.v > b.v); } friend bool operator<=(ModInt a, ModInt b) { return (a.v <= b.v); } friend bool operator>=(ModInt a, ModInt b) { return (a.v >= b.v); } friend bool operator==(ModInt a, ModInt b) { return (a.v == b.v); } friend bool operator!=(ModInt a, ModInt b) { return (a.v != b.v); } friend ModInt operator+ (ModInt a ) { return ModInt(+a.v); } friend ModInt operator- (ModInt a ) { return ModInt(-a.v); } friend ModInt operator+ (ModInt a, ModInt b) { return ModInt(a.v + b.v); } friend ModInt operator- (ModInt a, ModInt b) { return ModInt(a.v - b.v); } friend ModInt operator* (ModInt a, ModInt b) { return ModInt(a.v * b.v); } friend ModInt operator/ (ModInt a, ModInt b) { return a * b.inv(); } friend ModInt operator^ (ModInt a, LL b) { return a.exp(b); } friend ModInt & operator+=(ModInt & a, ModInt b) { return (a = a + b); } friend ModInt & operator-=(ModInt & a, ModInt b) { return (a = a - b); } friend ModInt & operator*=(ModInt & a, ModInt b) { return (a = a * b); } friend ModInt & operator/=(ModInt & a, ModInt b) { return (a = a / b); } friend ModInt & operator^=(ModInt & a, LL b) { return (a = a ^ b); } friend istream & operator>>(istream & s, ModInt & b) { s >> b.v; b = ModInt(b.v); return s; } friend ostream & operator<<(ostream & s, ModInt b) { return (s << b.v); } }; using MI = ModInt<1'000'000'007>; // ---- int main() { LL IN(l, n); vector f(n + 1, false); { int IN(m); inc(i, m) { int IN(k); f[k] = true; } } auto id = [&](int i, int j) -> int { return i * (i + 3) / 2 + j; }; Matrix A(id(n + 1, 0), id(n + 1, 0)); A[id(0, 0)][id(0, 0)] = n; A[id(0, 0)][id(0, 1)] = 1; inc1(i, n) { incII(j, 0, i + 1) { if(i == j && f[i]) { A[id(i, j)][id(i, j + 1)] = 1; A[id(i, j)][id(0, 0)] = n - 1; A[id(i, j)][id(0, 1)] = 1; } else { inc1(k, n) { A[id(i, j)][k == i ? id(i, min(j + 1, i + 1)) : id(k, 1)] = 1; } } } } out((A ^ (l + 1))[id(1, 0)][id(0, 1)]); }