#687919 (C++17) No.1632 Sorting Integers (GCD of M)

• 問題: No.1632 Sorting Integers (GCD of M)
• ユーザー: 👑 emthrm
• 提出日時: 2021-08-10 22:21:29
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 2 ms / 2,000 ms
• コード長: 5,495 bytes
• コンパイル時間: 2,265 ms
• コンパイル使用メモリ: 206,936 KB
• 実行使用メモリ: 4,348 KB
• 最終ジャッジ日時: 2023-10-24 08:55:47
• 合計ジャッジ時間: 5,067 ms
• ジャッジサーバーID （参考情報）: judge11 / judge15

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 4,348 KB
testcase_01	AC	2 ms; 4,348 KB
testcase_02	AC	2 ms; 4,348 KB
testcase_03	AC	2 ms; 4,348 KB
testcase_04	AC	2 ms; 4,348 KB
testcase_05	AC	2 ms; 4,348 KB
testcase_06	AC	2 ms; 4,348 KB
testcase_07	AC	2 ms; 4,348 KB
testcase_08	AC	2 ms; 4,348 KB
testcase_09	AC	2 ms; 4,348 KB
testcase_10	AC	2 ms; 4,348 KB
testcase_11	AC	2 ms; 4,348 KB
testcase_12	AC	2 ms; 4,348 KB
testcase_13	AC	1 ms; 4,348 KB
testcase_14	AC	2 ms; 4,348 KB
testcase_15	AC	2 ms; 4,348 KB
testcase_16	AC	2 ms; 4,348 KB
testcase_17	AC	2 ms; 4,348 KB
testcase_18	AC	2 ms; 4,348 KB
testcase_19	AC	2 ms; 4,348 KB
testcase_20	AC	2 ms; 4,348 KB
testcase_21	AC	2 ms; 4,348 KB
testcase_22	AC	1 ms; 4,348 KB
testcase_23	AC	2 ms; 4,348 KB
testcase_24	AC	2 ms; 4,348 KB
testcase_25	AC	2 ms; 4,348 KB
testcase_26	AC	2 ms; 4,348 KB
testcase_27	AC	2 ms; 4,348 KB
testcase_28	AC	2 ms; 4,348 KB
testcase_29	AC	2 ms; 4,348 KB
testcase_30	AC	2 ms; 4,348 KB
testcase_31	AC	2 ms; 4,348 KB
testcase_32	AC	2 ms; 4,348 KB
testcase_33	AC	2 ms; 4,348 KB
testcase_34	AC	2 ms; 4,348 KB
testcase_35	AC	2 ms; 4,348 KB
testcase_36	AC	1 ms; 4,348 KB
testcase_37	AC	2 ms; 4,348 KB
testcase_38	AC	2 ms; 4,348 KB
testcase_39	AC	1 ms; 4,348 KB
testcase_40	AC	2 ms; 4,348 KB
testcase_41	AC	2 ms; 4,348 KB
testcase_42	AC	2 ms; 4,348 KB
testcase_43	AC	2 ms; 4,348 KB
testcase_44	AC	2 ms; 4,348 KB
testcase_45	AC	2 ms; 4,348 KB
testcase_46	AC	2 ms; 4,348 KB
testcase_47	AC	2 ms; 4,348 KB
testcase_48	AC	2 ms; 4,348 KB
testcase_49	AC	1 ms; 4,348 KB
testcase_50	AC	2 ms; 4,348 KB
testcase_51	AC	2 ms; 4,348 KB
testcase_52	AC	2 ms; 4,348 KB
testcase_53	AC	2 ms; 4,348 KB
testcase_54	AC	2 ms; 4,348 KB
testcase_55	AC	2 ms; 4,348 KB
testcase_56	AC	2 ms; 4,348 KB
testcase_57	AC	2 ms; 4,348 KB
testcase_58	AC	2 ms; 4,348 KB
testcase_59	AC	2 ms; 4,348 KB
testcase_60	AC	1 ms; 4,348 KB
testcase_61	AC	2 ms; 4,348 KB
testcase_62	AC	2 ms; 4,348 KB

ソースコード

#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;
#define FOR(i,m,n) for(int i=(m);i<(n);++i)
#define REP(i,n) FOR(i,0,n)
#define ALL(v) (v).begin(),(v).end()
using ll = long long;
constexpr int INF = 0x3f3f3f3f;
constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL;
constexpr double EPS = 1e-8;
constexpr int MOD = 1000000007;
// constexpr int MOD = 998244353;
constexpr int dy[] = {1, 0, -1, 0}, dx[] = {0, -1, 0, 1};
constexpr int dy8[] = {1, 1, 0, -1, -1, -1, 0, 1}, dx8[] = {0, -1, -1, -1, 0, 1, 1, 1};
template <typename T, typename U> inline bool chmax(T &a, U b) { return a < b ? (a = b, true) : false; }
template <typename T, typename U> inline bool chmin(T &a, U b) { return a > b ? (a = b, true) : false; }
struct IOSetup {
  IOSetup() {
    std::cin.tie(nullptr);
    std::ios_base::sync_with_stdio(false);
    std::cout << fixed << setprecision(20);
  }
} iosetup;

template <int M>
struct MInt {
  unsigned int val;
  MInt(): val(0) {}
  MInt(long long x) : val(x >= 0 ? x % M : x % M + M) {}
  static constexpr int get_mod() { return M; }
  static void set_mod(int divisor) { assert(divisor == M); }
  static void init(int x = 10000000) { inv(x, true); fact(x); fact_inv(x); }
  static MInt inv(int x, bool init = false) {
    // assert(0 <= x && x < M && std::__gcd(x, M) == 1);
    static std::vector<MInt> inverse{0, 1};
    int prev = inverse.size();
    if (init && x >= prev) {
      // "x!" and "M" must be disjoint.
      inverse.resize(x + 1);
      for (int i = prev; i <= x; ++i) inverse[i] = -inverse[M % i] * (M / i);
    }
    if (x < inverse.size()) return inverse[x];
    unsigned int a = x, b = M; int u = 1, v = 0;
    while (b) {
      unsigned int q = a / b;
      std::swap(a -= q * b, b);
      std::swap(u -= q * v, v);
    }
    return u;
  }
  static MInt fact(int x) {
    static std::vector<MInt> f{1};
    int prev = f.size();
    if (x >= prev) {
      f.resize(x + 1);
      for (int i = prev; i <= x; ++i) f[i] = f[i - 1] * i;
    }
    return f[x];
  }
  static MInt fact_inv(int x) {
    static std::vector<MInt> finv{1};
    int prev = finv.size();
    if (x >= prev) {
      finv.resize(x + 1);
      finv[x] = inv(fact(x).val);
      for (int i = x; i > prev; --i) finv[i - 1] = finv[i] * i;
    }
    return finv[x];
  }
  static MInt nCk(int n, int k) {
    if (n < 0 || n < k || k < 0) return 0;
    if (n - k > k) k = n - k;
    return fact(n) * fact_inv(k) * fact_inv(n - k);
  }
  static MInt nPk(int n, int k) { return n < 0 || n < k || k < 0 ? 0 : fact(n) * fact_inv(n - k); }
  static MInt nHk(int n, int k) { return n < 0 || k < 0 ? 0 : (k == 0 ? 1 : nCk(n + k - 1, k)); }
  static MInt large_nCk(long long n, int k) {
    if (n < 0 || n < k || k < 0) return 0;
    inv(k, true);
    MInt res = 1;
    for (int i = 1; i <= k; ++i) res *= inv(i) * n--;
    return res;
  }
  MInt pow(long long exponent) const {
    MInt tmp = *this, res = 1;
    while (exponent > 0) {
      if (exponent & 1) res *= tmp;
      tmp *= tmp;
      exponent >>= 1;
    }
    return res;
  }
  MInt &operator+=(const MInt &x) { if((val += x.val) >= M) val -= M; return *this; }
  MInt &operator-=(const MInt &x) { if((val += M - x.val) >= M) val -= M; return *this; }
  MInt &operator*=(const MInt &x) { val = static_cast<unsigned long long>(val) * x.val % M; return *this; }
  MInt &operator/=(const MInt &x) { return *this *= inv(x.val); }
  bool operator==(const MInt &x) const { return val == x.val; }
  bool operator!=(const MInt &x) const { return val != x.val; }
  bool operator<(const MInt &x) const { return val < x.val; }
  bool operator<=(const MInt &x) const { return val <= x.val; }
  bool operator>(const MInt &x) const { return val > x.val; }
  bool operator>=(const MInt &x) const { return val >= x.val; }
  MInt &operator++() { if (++val == M) val = 0; return *this; }
  MInt operator++(int) { MInt res = *this; ++*this; return res; }
  MInt &operator--() { val = (val == 0 ? M : val) - 1; return *this; }
  MInt operator--(int) { MInt res = *this; --*this; return res; }
  MInt operator+() const { return *this; }
  MInt operator-() const { return MInt(val ? M - val : 0); }
  MInt operator+(const MInt &x) const { return MInt(*this) += x; }
  MInt operator-(const MInt &x) const { return MInt(*this) -= x; }
  MInt operator*(const MInt &x) const { return MInt(*this) *= x; }
  MInt operator/(const MInt &x) const { return MInt(*this) /= x; }
  friend std::ostream &operator<<(std::ostream &os, const MInt &x) { return os << x.val; }
  friend std::istream &operator>>(std::istream &is, MInt &x) { long long val; is >> val; x = MInt(val); return is; }
};
namespace std { template <int M> MInt<M> abs(const MInt<M> &x) { return x; } }
using ModInt = MInt<MOD>;

long long mod_pow(long long base, long long exponent, int mod) {
  base %= mod;
  long long res = 1;
  while (exponent > 0) {
    if (exponent & 1) (res *= base) %= mod;
    (base *= base) %= mod;
    exponent >>= 1;
  }
  return res;
}

int main() {
  constexpr int D = 10;
  int n; cin >> n;
  int c[D]{}; FOR(i, 1, D) cin >> c[i];
  REP(d, D) {
    if (c[d] == n) {
      cout << (ModInt(10).pow(n) - 1) * d / 9 << '\n';
      return 0;
    }
  }
  int g = 0;
  REP(i, D) FOR(j, i + 1, D) {
    if (c[i] > 0 && c[j] > 0) g = gcd(g, j - i);
  }
  int m = 0;
  REP(d, D) {
    m = m * mod_pow(10, c[d], 9 * g) % (9 * g);
    m = (m + (d * (mod_pow(10, c[d], 81 * g) + 81 * g - 1) % (81 * g) / 9)) % (9 * g);
  }
  cout << gcd(m, 9 * g) << '\n';
  return 0;
}