#164838 (C++14) No.503 配列コレクション

• 問題: No.503 配列コレクション
• ユーザー: koyumeishi
• 提出日時: 2017-04-08 00:35:24
• 言語: C++14 (gcc 13.3.0 + boost 1.87.0)
• 結果: CE (最新)
  AC
  (最初)
• 実行時間: -
• コード長: 7,840 bytes
• コンパイル時間: 1,207 ms
• コンパイル使用メモリ: 94,356 KB
• 最終ジャッジ日時: 2024-11-14 20:00:03
• 合計ジャッジ時間: 1,778 ms
• ジャッジサーバーID （参考情報）: judge3 / judge2

コンパイルメッセージ

main.cpp:115:22: error: aggregate 'std::array<Montgomery::M_Int<1000000007>, 2000000> fact' has incomplete type and cannot be defined
  115 | array<mint, 2000000> fact;  //n!
      |                      ^~~~
main.cpp:116:22: error: aggregate 'std::array<Montgomery::M_Int<1000000007>, 2000000> fact_inv' has incomplete type and cannot be defined
  116 | array<mint, 2000000> fact_inv;  // (n!)^-1
      |                      ^~~~~~~~

ソースコード

#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;

namespace Montgomery{
  template<long long MOD>
  constexpr long long PRE_COMP(long long r, long long res=0, long long t=0, long long i = 1){
    return (r>1) ? ( PRE_COMP<MOD>(r/2, res + (t%2==0?i:0), (t%2==0?(t+MOD):t) / 2, i*2) ):( res );
  }

  template<long long MOD>
  class Values{
  public:
    static constexpr long long R = 1LL<<30; // R>MOD && gcd(R,MOD)==1
    static constexpr long long mask = (1LL<<30)-1;
    static constexpr long long R2 = (R*R)%MOD;
    static constexpr long long Ninv = PRE_COMP<MOD>(1<<30); // N*Ninv = R-1 mod R
    static long long Reduction(long long x){
      long long s = ((x & mask) * Ninv) & mask;
      long long ret = (x + s*MOD ) >> 30;
      if(ret>=MOD) ret -= MOD;
      return ret;
    }
  };

  template<long long MOD> struct M_Int{
    long long value;
    M_Int() : value(0) {}
    M_Int(long long val, bool convert=true) : value(convert ? Values<MOD>::Reduction(val * Values<MOD>::R2) : val){} //convert==true : int -> M_Int, false : M_Int::value -> M_Int
    M_Int(const M_Int& x) : value( x.value ){} //M_Int -> M_Int
    M_Int& operator = (const M_Int& x){ value = x.value; return *this; }
    M_Int& operator = (const long long& x){ value = Values<MOD>::Reduction(x * Values<MOD>::R2); return *this; }

    M_Int operator * (const M_Int& x)    { return M_Int( Values<MOD>::Reduction(value * x.value) , false ); }
    M_Int operator * (const long long& x){ return (*this) * M_Int(x); }
    template<class T> M_Int& operator *= (const T& x){ return (*this) = (*this)*x; }

    M_Int operator + (const M_Int& x)    { long long tmp = value + x.value; if(tmp >= MOD) tmp -= MOD; return M_Int(tmp, false); }
    M_Int operator + (const long long& x){ return (*this)+M_Int(x); }
    template<class T> M_Int& operator += (const T& x)    { return (*this) = (*this) + x; }

    M_Int operator - (const M_Int& x)    { long long tmp = value - x.value; if(tmp < 0  ) tmp += MOD; return M_Int(tmp, false); }
    M_Int operator - (const long long& x){ return (*this)-M_Int(x); }
    template<class T> M_Int& operator -= (const T& x)    { return (*this) = (*this) - x; }

    bool operator == (const M_Int& x){ return value == x.value; }
    bool operator == (const long long& x){ M_Int tmp(x); return (*this)==tmp; }
    long long to_i () { // M_int -> int
      return Values<MOD>::Reduction(value);
    }
    operator long long () { // M_int -> int
      return Values<MOD>::Reduction(value);
    }
  };

  template<long long MOD> istream& operator>>(istream& is, M_Int<MOD>& v){ long long tmp; is >> tmp; v=tmp; return is; }
  template<long long MOD> ostream& operator<<(ostream& os, M_Int<MOD> v){ return os << v.to_i(); }
  
  template<long long MOD> M_Int<MOD> operator + (long long l, M_Int<MOD> r){ return r+l; }
  template<long long MOD> M_Int<MOD> operator - (long long l, M_Int<MOD> r){ return r-l; }
  template<long long MOD> M_Int<MOD> operator * (long long l, M_Int<MOD> r){ return r*l; }
}

using mint = Montgomery::M_Int<mod>;

array<mint, 2000000> fact;  //n!
array<mint, 2000000> fact_inv;  // (n!)^-1

#include <array>
// nCk mod p, O(1)
// precomputation O(size)
template<long long MOD, size_t size>
class combination_mod{

  //const long long size;
  // vector<mint> fact;  //n!
  // vector<mint> fact_inv;  // (n!)^-1

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

  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);  // x ^ -1
    }
    for(int i=2; i<size; i++){
      fact_inv[i] = fact_inv[i-1] * fact_inv[i];  // x! ^ -1
    }
  }

public:
  combination_mod(){
    // fact.resize(size);
    // fact_inv.resize(size);
    make_fact();
    make_fact_inv();
  }

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

combination_mod<mod, 2000000> c;

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

  long long len = n;
  int t = 0;
  while( len >= k ){
    len -= k-1;
    t++;
  }

  if( d == 1 ){
    println(len);
    return 0;
  }
  if(len == 1){
    println( my_pow_mod(d, t, mod) );
    return 0;
  }


  mint ans = 0;
  mint dd(1);
  mint d_(d);
  for(int x=0; x<=t; x++){
    int rem = t-x;
    //ans += dd * c(rem+len-2, rem) % mod * (len) % mod;
    ans += dd * c(rem+len-2, rem);

    dd *= d_;
  }

  println( ans.to_i() * len % mod );

  return 0;
}