#pragma region Macros #include #define rep(i, n) for(int(i) = 0; (i) < (n); (i)++) #define rrep(i, n) for(int(i) = (n)-1; (i) >= 0; (i)--) #define FOR(i, m, n) for(int(i) = (m); (i) < (n); (i)++) #define ROF(i, m, n) for(int(i) = (n)-1; (i) >= (m); (i)--) #define ALL(v) (v).begin(), (v).end() #define LLA(v) (v).rbegin(), (v).rend() #define SZ(v) (int)(v).size() #define INT(...) \ int __VA_ARGS__; \ read(__VA_ARGS__) #define LL(...) \ ll __VA_ARGS__; \ read(__VA_ARGS__) #define DOUBLE(...) \ double __VA_ARGS__; \ read(__VA_ARGS__) #define CHAR(...) \ char __VA_ARGS__; \ read(__VA_ARGS__) #define STRING(...) \ string __VA_ARGS__; \ read(__VA_ARGS__) #define VEC(type, name, size) \ vector name(size); \ read(name) #define VEC2(type, name, height, width) \ vector> name(height, vector(width)); \ read(name) #define DVEC(type, name1, name2, size) \ vector name1(size), name2(size); \ read(name1, name2) #define TVEC(type, name1, name2, name3, size) \ vector name1(size), name2(size), name3(size); \ read(name1, name2, name3) using namespace std; using ll = long long; using pii = pair; using pll = pair; const int INF = 1 << 30; const ll LINF = 1LL << 60; const int MOD = 1e9 + 7; const char newl = '\n'; const int dx[] = {1, 0, -1, 0}; const int dy[] = {0, 1, 0, -1}; template inline bool between(T x, T l, T r) { return l <= x && x < r; } template inline vector make_vec(size_t a, T val) { return vector(a, val); } template inline auto make_vec(size_t a, Ts... ts) { return vector(a, make_vec(ts...)); } void read() {} template inline void read(T &a) { cin >> a; } template inline void read(pair &p) { read(p.first), read(p.second); } template inline void read(vector &v) { for(auto &&a : v) read(a); } template inline void read(vector &a, vector &b) { for(int i = 0; i < a.size(); i++) { read(a[i]); read(b[i]); } } template inline void read(vector &a, vector &b, vector &c) { for(int i = 0; i < a.size(); i++) { read(a[i]); read(b[i]); read(c[i]); } } template inline void read(Head &head, Tail &...tail) { read(head), read(tail...); } template void _write(const T &a) { cout << a; } template void _write(const std::pair &a) { cout << a.first << ' ' << a.second; } template void write(const T &a) { _write(a); cout << newl; } template void write(const vector &a) { for(int i = 0; i < a.size(); i++) { _write(a[i]); cout << (i + 1 == a.size() ? newl : ' '); } } template void write(const Head &head, const Tail &...tail) { _write(head); cout << ' '; write(tail...); } template void writel(const T &a) { cout << a << '\n'; } template void writel(const vector &a) { for(int i = 0; i < a.size(); i++) { _write(a[i]); cout << newl; } } template void writel(const Head &head, const Tail &...tail) { _write(head); cout << newl; write(tail...); } template void _debug(const T &a) { cerr << a; } template void _debug(const std::pair &a) { cerr << a.first << ' ' << a.second; } template void debug(const T &a) { _debug(a); cerr << newl; } template void debug(const vector &a) { for(int i = 0; i < a.size(); i++) { _debug(a[i]); cerr << (i + 1 == a.size() ? newl : ' '); } } template void debug(const Head &head, const Tail &...tail) { _debug(head); cerr << ' '; debug(tail...); } template void debugl(const T &a) { cerr << a << '\n'; } template void debugl(const vector &a) { for(int i = 0; i < a.size(); i++) { _debug(a[i]); cerr << newl; } } template void debugl(const Head &head, const Tail &...tail) { _debug(head); cerr << newl; debug(tail...); } template auto sum(const vector &a) { return accumulate(ALL(a), T(0)); } template auto min(const vector &a) { return *min_element(ALL(a)); } template auto max(const vector &a) { return *max_element(ALL(a)); } template void msort(vector &a, vector &b) { assert(a.size() == b.size()); vector> ab(a.size()); for(int i = 0; i < a.size(); i++) ab[i] = {a[i], b[i]}; sort(ALL(ab)); for(int i = 0; i < a.size(); i++) { a[i] = ab[i].first; b[i] = ab[i].second; } } template void msort(vector &a, vector &b, vector &c) { assert(a.size() == b.size() && b.size() == c.size()); vector> abc(a.size()); for(int i = 0; i < a.size(); i++) abc[i] = {a[i], b[i], c[i]}; sort(ALL(abc)); for(int i = 0; i < a.size(); i++) { a[i] = get<0>(abc[i]); b[i] = get<1>(abc[i]); c[i] = get<2>(abc[i]); } } template inline bool chmax(T &a, U b) { if(a < b) { a = b; return 1; } return 0; } template inline bool chmin(T &a, U b) { if(a > b) { a = b; return 1; } return 0; } int digit(ll a) { ll ret = 0; while(a && ++ret) a /= 10; return ret; } int digit_sum(ll a) { ll ret = 0; while(a) { ret += a % 10; a /= 10; } return ret; } ll llpow(ll a, ll n) { ll ret = 1; rep(i, n) ret *= a; return ret; } inline int bsf(int v) { return __builtin_ctz(v); } // 最下位の1が下から何番目か inline int bsf(ll v) { return __builtin_ctzll(v); } inline int bsr(int v) { return 31 - __builtin_clz(v); } // 最上位の1が下から何番目か inline int bsr(ll v) { return 63 - __builtin_clzll(v); } inline int lsb(int v) { return v & -v; } // 最下位の1だけ残す inline ll lsb(ll v) { return v & -v; } inline int msb(int v) { return 1 << bsr(v); } // 最上位の1だけ残す inline ll msb(ll v) { return 1LL << bsr(v); } struct IO { IO() { ios::sync_with_stdio(false); cin.tie(nullptr); cout << fixed << setprecision(10); } } io; #pragma endregion /* ModInt */ template class ModInt { using u64 = uint_fast64_t; public: u64 val; ModInt(const u64 x = 0) : val((x + MOD) % MOD) {} constexpr u64 &value() { return val; } static const u64 get_mod() { return MOD; } constexpr ModInt operator-() { return val ? MOD - val : 0; } constexpr ModInt operator+(const ModInt &rhs) const { return ModInt(*this) += rhs; } constexpr ModInt operator-(const ModInt &rhs) const { return ModInt(*this) -= rhs; } constexpr ModInt operator*(const ModInt &rhs) const { return ModInt(*this) *= rhs; } constexpr ModInt operator/(const ModInt &rhs) const { return ModInt(*this) /= rhs; } constexpr ModInt &operator+=(const ModInt &rhs) { val += rhs.val; if(val >= MOD) { val -= MOD; } return *this; } constexpr ModInt &operator-=(const ModInt &rhs) { if(val < rhs.val) { val += MOD; } val -= rhs.val; return *this; } constexpr ModInt &operator*=(const ModInt &rhs) { val = val * rhs.val % MOD; return *this; } constexpr ModInt &operator/=(const ModInt &rhs) { *this *= rhs.inv(); return *this; } constexpr bool operator==(const ModInt &rhs) const { return this->val == rhs.val; } constexpr bool operator!=(const ModInt &rhs) const { return this->val != rhs.val; } friend constexpr ostream &operator<<(ostream &os, const ModInt &x) { return os << x.val; } friend constexpr istream &operator>>(istream &is, ModInt &x) { return is >> x.val; } constexpr ModInt inv() const { return ModInt(*this).pow(MOD - 2); } constexpr ModInt pow(long long e) const { u64 x = 1, p = val; while(e > 0) { if(e % 2 == 0) { p = (p * p) % MOD; e /= 2; } else { x = (x * p) % MOD; e--; } } return ModInt(x); } }; using mint = ModInt<1000000007UL>; // using mint = ModInt<998244353UL>; // 二項係数(nCk mod.p;1<=k<=n<=1e7,pは素数)for ModInt template struct CombinationMint { int N; vector fac, finv, inv; CombinationMint(const int n) : N(n + 1), fac(N), finv(N), inv(N) { fac[0] = fac[1] = 1; finv[0] = finv[1] = 1; inv[1] = 1; int mod = Mint::get_mod(); for(int i = 2; i < N; i++) { fac[i] = fac[i - 1] * i; inv[i] = -inv[mod % i] * (mod / i); finv[i] = finv[i - 1] * inv[i]; } } Mint comb(int n, int k) { assert(n < N); if(n < k) return 0; if(n < 0 || k < 0) return 0; return fac[n] * finv[k] * finv[n - k]; } }; // 長さn,1<=a[i]<=mで単調増加: comb(m, n) // 長さn,1<=a[i]<=mで広義単調増加: (b[i]:=a[i]+iとおいて↑に帰着) // 片方もしくは両端を固定するとき: comb(m + n - 1, (n - 1 or n - 2)), comb(m + n - 1, n); // 足してS,長さn: comb(S + n - 1, n) // 足してS以下,長さn: comb(S + n, n) // 二項係数(nCk mod.p;1<=k<=n<=1e7,pは素数)for long long struct CombinationLL { const int MOD = 1000000007; int N; vector fac, finv, inv; CombinationLL(const int n) : N(n + 1), fac(N), finv(N), inv(N) { fac[0] = fac[1] = 1; finv[0] = finv[1] = 1; inv[1] = 1; for(int i = 2; i < N; i++) { fac[i] = fac[i - 1] * i % MOD; inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD; finv[i] = finv[i - 1] * inv[i] % MOD; } } long long comb(int n, int k) { if(n < k) return 0; if(n < 0 || k < 0) return 0; assert(n < N); return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD; } }; // 二項係数(nCk mod.p;1<=k<=n<=2000,pは素数でなくともよい) const int MAX_C = 1000; long long Com[MAX_C][MAX_C]; void calc_com(int MOD) { memset(Com, 0, sizeof(Com)); Com[0][0] = 1; for(int i = 1; i < MAX_C; ++i) { Com[i][0] = 1; for(int j = 1; j < MAX_C; ++j) { Com[i][j] = (Com[i - 1][j - 1] + Com[i - 1][j]) % MOD; } } } // 二項係数 (nCk mod.p; p is prime, Lucasの定理) struct Lucas { vector> com; long long p; Lucas(long long p) : p(p) { init(p); } void init(long long p) { com.assign(p, vector(p)); com[0][0] = 1; for(int i = 1; i < p; i++) { com[i][0] = 1; for(int j = i; j > 0; j--) { com[i][j] = (com[i - 1][j - 1] + com[i - 1][j]) % p; } } } long long comb(long long n, long long k) { long long ret = 1; while(n > 0) { int ni = n % p; int ki = k % p; ret *= com[ni][ki]; ret %= p; n /= p; k /= p; } return ret; } }; // 二項係数 O(k) // nとkのどちらかが変化していくとき、O(変化量)ですべて求められる 多分 // 参考:https://perogram.hateblo.jp/entry/2020/07/08/120017 // https://yukicoder.me/submissions/520882 template T nCk(long long n, long long k, map, T> &mp) { auto key = {n, k}; if(mp.count(key)) return mp[key]; if(k == 0 || k == n) { T ret = 1; return ret; } if(k == 1 || k == n - 1) { T ret = n; return ret; } // return mp[key] = nCk(n, k - 1, mp) * (n - k + 1) / k; return mp[key] = nCk(n - 1, k, mp) * n / (n - k); } void solve() { INT(n); VEC(int, c, 9); CombinationMint C(n); mint power = (mint(10).pow(n) - 1) / 9; mint res = 0; rep(i, 9) { mint coef = 1; int m = n; rep(j, 9) { if(i == j) continue; coef *= C.comb(m, c[j]); m = m - c[j]; } res += coef * power * mint(i + 1) * mint(c[i]) / n; } write(res); } int main() { int t = 1; // cin >> t; while(t--) { solve(); } }