結果

問題 No.890 移調の限られた旋法
ユーザー koyumeishikoyumeishi
提出日時 2019-09-20 22:58:05
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 180 ms / 2,000 ms
コード長 5,640 bytes
コンパイル時間 1,647 ms
コンパイル使用メモリ 140,200 KB
実行使用メモリ 34,696 KB
最終ジャッジ日時 2024-09-14 19:12:22
合計ジャッジ時間 8,767 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge3
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 168 ms
34,596 KB
testcase_01 AC 170 ms
34,620 KB
testcase_02 AC 169 ms
34,416 KB
testcase_03 AC 172 ms
34,600 KB
testcase_04 AC 155 ms
34,488 KB
testcase_05 AC 163 ms
34,696 KB
testcase_06 AC 160 ms
34,628 KB
testcase_07 AC 171 ms
34,420 KB
testcase_08 AC 169 ms
34,576 KB
testcase_09 AC 177 ms
34,564 KB
testcase_10 AC 164 ms
34,572 KB
testcase_11 AC 176 ms
34,464 KB
testcase_12 AC 174 ms
34,688 KB
testcase_13 AC 174 ms
34,548 KB
testcase_14 AC 165 ms
34,612 KB
testcase_15 AC 166 ms
34,584 KB
testcase_16 AC 165 ms
34,420 KB
testcase_17 AC 164 ms
34,532 KB
testcase_18 AC 157 ms
34,432 KB
testcase_19 AC 163 ms
34,472 KB
testcase_20 AC 157 ms
34,536 KB
testcase_21 AC 156 ms
34,644 KB
testcase_22 AC 158 ms
34,464 KB
testcase_23 AC 171 ms
34,588 KB
testcase_24 AC 174 ms
34,428 KB
testcase_25 AC 180 ms
34,604 KB
testcase_26 AC 179 ms
34,544 KB
testcase_27 AC 174 ms
34,424 KB
testcase_28 AC 174 ms
34,556 KB
testcase_29 AC 174 ms
34,592 KB
testcase_30 AC 164 ms
34,492 KB
testcase_31 AC 177 ms
34,628 KB
testcase_32 AC 170 ms
34,612 KB
testcase_33 AC 170 ms
34,612 KB
testcase_34 AC 166 ms
34,632 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <iostream>
#include <vector>
#include <cstdio>
#include <sstream>
#include <map>
#include <string>
#include <algorithm>
#include <queue>
#include <cmath>
#include <functional>
#include <set>
#include <ctime>
#include <random>
#include <chrono>
#include <cassert>
#include <tuple>
#include <utility>
using namespace std;

namespace {
  using Integer = long long; //__int128;
  template<class T, class S> istream& operator >> (istream& is, pair<T,S>& p){return is >> p.first >> p.second;}
  template<class T> istream& operator >> (istream& is, vector<T>& vec){for(T& val: vec) is >> val; return is;}
  template<class T> istream& operator ,  (istream& is, T& val){ return is >> val;}
  template<class T, class S> ostream& operator << (ostream& os, const pair<T,S>& p){return os << p.first << " " << p.second;}
  template<class T> ostream& operator << (ostream& os, const vector<T>& vec){for(size_t i=0; i<vec.size(); i++) os << vec[i] << (i==vec.size()-1?"":" "); return os;}
  template<class T> ostream& operator ,  (ostream& os, const T& val){ return os << " " << val;}

  template<class H> void print(const H& head){ cout << head; }
  template<class H, class ... T> void print(const H& head, const T& ... tail){ cout << head << " "; print(tail...); }
  template<class ... T> void println(const T& ... values){ print(values...); cout << endl; }

  template<class H> void eprint(const H& head){ cerr << head; }
  template<class H, class ... T> void eprint(const H& head, const T& ... tail){ cerr << head << " "; eprint(tail...); }
  template<class ... T> void eprintln(const T& ... values){ eprint(values...); cerr << endl; }

  class range{ Integer start_, end_, step_; public: struct range_iterator{ Integer val, step_; range_iterator(Integer v, Integer step) : val(v), step_(step) {} Integer operator * (){return val;} void operator ++ (){val += step_;} bool operator != (range_iterator& x){return step_ > 0 ? val < x.val : val > x.val;} }; range(Integer len) : start_(0), end_(len), step_(1) {} range(Integer start, Integer end) : start_(start), end_(end), step_(1) {} range(Integer start, Integer end, Integer step) : start_(start), end_(end), step_(step) {} range_iterator begin(){ return range_iterator(start_, step_); } range_iterator   end(){ return range_iterator(  end_, step_); } };

  inline string operator "" _s (const char* str, size_t size){ return move(string(str)); }
  constexpr Integer my_pow(Integer x, Integer k, Integer z=1){return k==0 ? z : k==1 ? z*x : (k&1) ? my_pow(x*x,k>>1,z*x) : my_pow(x*x,k>>1,z);}
  constexpr Integer my_pow_mod(Integer x, Integer k, Integer M, Integer z=1){return k==0 ? z%M : k==1 ? z*x%M : (k&1) ? my_pow_mod(x*x%M,k>>1,M,z*x%M) : my_pow_mod(x*x%M,k>>1,M,z);}
  constexpr unsigned long long operator "" _ten (unsigned long long value){ return my_pow(10,value); }

  inline int k_bit(Integer x, int k){return (x>>k)&1;} //0-indexed

  mt19937 mt(chrono::duration_cast<chrono::nanoseconds>(chrono::steady_clock::now().time_since_epoch()).count());

  template<class T> string join(const vector<T>& v, const string& sep){ stringstream ss; for(size_t i=0; i<v.size(); i++){ if(i>0) ss << sep; ss << v[i]; } return ss.str(); }

  inline string operator * (string s, int k){ string ret; while(k){ if(k&1) ret += s; s += s; k >>= 1; } return ret; }
}
constexpr long long mod = 9_ten + 7;

// nCk mod p, O(1)
// precomputation O(size)
class combination_mod{
  const long long mod;
  const long long size;
  
  vector<long long> fact; //n!
  vector<long long> fact_inv; // (n!)^-1

  void make_fact(){
    fact[0] = 1;
    for(long long i=1; i<size; i++){
      fact[i] = fact[i-1]*i % mod;
    }
  }

  void make_fact_inv(){
    fact_inv[0] = fact_inv[1] = 1;
    for(long long i=2; i<size; i++){
      fact_inv[i] = fact_inv[mod%i] * (mod - mod/i) % mod;  // x ^ -1
    }
    for(int i=2; i<size; i++){
      fact_inv[i] = fact_inv[i-1] * fact_inv[i] % mod;  // x! ^ -1
    }
  }

public:
  combination_mod(long long mod_, long long size_ = 2000000) : mod(mod_), size(size_+1){
    fact.resize(size);
    fact_inv.resize(size);
    make_fact();
    make_fact_inv();
  }

  //nCk mod p O(1)
  long long operator()(long long n, long long k){
    if(n<0 || k<0) return 0;
    if(k==0 || n==k) return 1;
    long long ret = fact[n] * fact_inv[k] % mod * fact_inv[n-k] % mod;
    return ret;
  }
};


vector<long long> divisors(long long N){
  if(N==1) return {1LL};
  
  vector<long long> ret;
  ret.push_back(1);
  ret.push_back(N);

  for(long long i=2; i*i<=N; i++){
    if(N%i==0){
      ret.push_back(i);
      if(i*i != N) ret.push_back(N/i);
    }
  }

  sort(ret.begin(), ret.end());
  return ret;
}

int main(){
  long long n,k;
  cin >> n,k;

  auto d = divisors(n);
  sort(d.begin(), d.end());

  combination_mod c(mod, 2000000);

  long long ans = 0;

  vector<pair<int, long long>> w;
  for(int cycle_size: d){
    int cycles = n / cycle_size;
    if(cycle_size == 1){
      w.emplace_back(cycle_size, 0);
      continue;
    }
    if(k % cycle_size != 0){
      w.emplace_back(cycle_size, 0);
      continue;
    }
    int x = k / cycle_size;
    if(cycles < x){
      w.emplace_back(cycle_size, 0);
      continue;
    }
    w.emplace_back(cycle_size, c(cycles, x));
  }

  sort(w.rbegin(), w.rend());
  // eprintln(join(w, "\n"));

  for(int i=0; i<w.size(); i++){
    for(int j=0; j<w.size(); j++){
      if(i==j) continue;
      if(w[i].first % w[j].first == 0){
        w[j].second += -w[i].second + mod;
        if(w[j].second >= mod)
          w[j].second -= mod;
      }
    }
  }
  println((mod - w.back().second) % mod);
  // eprintln(join(w, "\n"));

  return 0;
}
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