#886028 (C++23) No.2365 Present of good number

• 問題: No.2365 Present of good number
• ユーザー: ponjuice
• 提出日時: 2023-06-30 22:15:17
• 言語: C++23 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 30 ms / 2,000 ms
• コード長: 8,788 bytes
• コンパイル時間: 7,537 ms
• コンパイル使用メモリ: 329,636 KB
• 実行使用メモリ: 10,032 KB
• 最終ジャッジ日時: 2023-09-21 16:19:20
• 合計ジャッジ時間: 9,295 ms
• ジャッジサーバーID （参考情報）: judge14 / judge12

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	27 ms; 9,732 KB
testcase_01	AC	26 ms; 9,960 KB
testcase_02	AC	27 ms; 10,032 KB
testcase_03	AC	27 ms; 9,788 KB
testcase_04	AC	27 ms; 9,772 KB
testcase_05	AC	27 ms; 9,912 KB
testcase_06	AC	27 ms; 9,728 KB
testcase_07	AC	26 ms; 9,768 KB
testcase_08	AC	27 ms; 9,948 KB
testcase_09	AC	27 ms; 9,792 KB
testcase_10	AC	27 ms; 10,024 KB
testcase_11	AC	27 ms; 9,768 KB
testcase_12	AC	28 ms; 9,932 KB
testcase_13	AC	27 ms; 9,784 KB
testcase_14	AC	27 ms; 9,932 KB
testcase_15	AC	29 ms; 9,860 KB
testcase_16	AC	27 ms; 9,932 KB
testcase_17	AC	27 ms; 9,932 KB
testcase_18	AC	27 ms; 9,844 KB
testcase_19	AC	28 ms; 9,908 KB
testcase_20	AC	28 ms; 9,856 KB
testcase_21	AC	30 ms; 9,948 KB
testcase_22	AC	28 ms; 9,852 KB
testcase_23	AC	29 ms; 9,912 KB
testcase_24	AC	27 ms; 9,956 KB
testcase_25	AC	28 ms; 9,948 KB
testcase_26	AC	26 ms; 9,816 KB
testcase_27	AC	28 ms; 9,716 KB
testcase_28	AC	26 ms; 9,884 KB
testcase_29	AC	27 ms; 9,800 KB
testcase_30	AC	28 ms; 9,868 KB
testcase_31	AC	30 ms; 9,892 KB
testcase_32	AC	26 ms; 9,972 KB
testcase_33	AC	29 ms; 9,956 KB
testcase_34	AC	29 ms; 9,916 KB
testcase_35	AC	26 ms; 9,772 KB
testcase_36	AC	28 ms; 9,856 KB
testcase_37	AC	28 ms; 9,892 KB
testcase_38	AC	28 ms; 9,980 KB
testcase_39	AC	30 ms; 9,772 KB
testcase_40	AC	29 ms; 9,892 KB

ソースコード

#include <bits/stdc++.h>
using namespace std;
#include <atcoder/all>
using namespace atcoder;

//高速化 
struct ponjuice{ponjuice(){cin.tie(0);ios::sync_with_stdio(0);cout<<fixed<<setprecision(20);}}PonJuice;
//#define endl '\n' //インタラクティブ問題の時は消す

//型
using ll = long long;
using ld = long double;
using mint = modint1000000007;
template<class T>using vc = vector<T>; template<class T>using vvc = vc<vc<T>>; template<class T>using vvvc = vvc<vc<T>>;
using vi = vc<int>;  using vvi = vvc<int>;  using vvvi = vvvc<int>;
using vl = vc<ll>;   using vvl = vvc<ll>;   using vvvl = vvvc<ll>;
using pi = pair<int, int>;  using pl = pair<ll, ll>;
using ull = unsigned ll;
template<class T>using priq = priority_queue<T>;
template<class T>using priqg = priority_queue<T, vc<T>, greater<T>>;

// for文
#define overload4(a, b, c, d, e, ...) e
#define rep1(n)             for(ll i = 0; i < n; i++)
#define rep2(i, n)          for(ll i = 0; i < n; i++)
#define rep3(i, a, b)       for(ll i = a; i < b; i++)
#define rep4(i, a, b, step) for(ll i = a; i < b; i+= step)
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define per1(n)             for(ll i = n-1; i >= 0; i--)
#define per2(i, n)          for(ll i = n-1; i >= 0; i--)
#define per3(i, a, b)       for(ll i = b-1; i >= a; i--)
#define per4(i, a, b, step) for(ll i = b-1; i >= a; i-= step)
#define per(...) overload4(__VA_ARGS__, per4, per3, per2, per1)(__VA_ARGS__)
#define fore1(a)       for(auto&& i : a)	
#define fore2(i,a)     for(auto&& i : a)
#define fore3(x,y,a)   for(auto&& [x, y] : a)
#define fore4(x,y,z,a) for(auto&& [x, y, z] : a)
#define fore(...) overload4(__VA_ARGS__, fore4, fore3, fore2, fore1)(__VA_ARGS__)

//関数
#define mp make_pair
#define mt make_tuple
#define a first
#define b second
#define pb emplace_back
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define si(x) (ll)(x).size()
template<class S, class T>inline bool chmax(S& a, T b){return a < b && ( a = b , true);}
template<class S, class T>inline bool chmin(S& a, T b){return a > b && ( a = b , true);}
template<class T>void uniq(vc<T>&a){sort(all(a));a.erase(unique(all(a)),a.end());}
template<class T>vc<T> operator++(vc<T>&v,signed){auto res = v;fore(e,v)e++;return res;}
template<class T>vc<T> operator--(vc<T>&v,signed){auto res = v;fore(e,v)e--;return res;}
template<class T>vc<T> operator++(vc<T>&v){fore(e,v)e++;return v;}
template<class T>vc<T> operator--(vc<T>&v){fore(e,v)e--;return v;}

//入出力(operator)
template<int T>istream&operator>>(istream&is,static_modint<T>&a){ll v;is>>v;a=v;return is;}
istream&operator>>(istream&is,modint&a){ll v;cin>>v;a=v;return is;}
template<class S,class T>istream&operator>>(istream&is,pair<S,T>&a){is>>a.a>>a.b;return is;}
template<class T>istream&operator>>(istream&is,vc<T>&a){fore(e,a)is>>e;return is;}

template<int T>ostream&operator<<(ostream&os,static_modint<T>a){return os<<a.val();}
ostream&operator<<(ostream&os,modint a){return os<<a.val();}
template<class S,class T>ostream&operator<<(ostream&os,pair<S,T>&a){return os<<a.a<<" "<<a.b;}
template<class T>ostream&operator<<(ostream&os,set<T>&a){fore(it,a){os<<it<<" ";}return os;}
template<class T>ostream&operator<<(ostream&os,multiset<T>&a){fore(it,a){os<<it<<" ";}return os;}
template<class S,class T>ostream&operator<<(ostream&os,map<S,T>&a){fore(x,y,a){os<<x<<" "<<y<<"\n";}return os;}
template<class T>ostream&operator<<(ostream&os,unordered_set<T>&a){fore(it,a){os<<it<<" ";}return os;}
template<class S,class T>ostream&operator<<(ostream&os,unordered_map<S,T>&a){fore(x,y,a){os<<x<<" "<<y<<"\n";}return os;}
template<class T>ostream&operator<<(ostream&os,vc<T>&a){fore(e,a)os<<e<<" ";return os;}
template<class T>ostream&operator<<(ostream&os,vvc<T>&a){fore(e,a)os<<e<<"\n";return os;}

//入出力(関数)
vi readvi(ll n){vi a(n);cin>>a;return a;}
vl readvl(ll n){vl a(n);cin>>a;return a;}
vvi readg(ll n,ll m,bool bidirected=true){vvi g(n);rep(i,m){ll a,b;cin>>a>>b;a--;b--;g[a].pb(b);if(bidirected)g[b].pb(a);}return g;}
vvc<pi>readgc(ll n,ll m,bool bidirected=true){vvc<pi> g(n);rep(i,m){ll a,b,c;cin>>a>>b>>c;a--;b--;g[a].pb(b,c);if(bidirected)g[b].pb(a,c);}return g;}
vvi readt(ll n,bool bidirected=true){return readg(n,n-1,bidirected);}
vvc<pi> readtc(ll n,bool bidirected=true){return readgc(n,n-1,bidirected);}

inline void yes(){cout << "Yes\n";}
inline void no(){cout << "No\n";}
inline void yesno(bool y = true){if(y)yes();else no();}
inline void print(){cout<<endl;}
template<class T>inline void print(T a){cout<<a<<endl;}
template<class T,class... Ts>inline void print(T a,Ts ...b){cout<<a;(cout<<...<<(cout<<' ',b));cout<<endl;}

//定数
constexpr ll mod = 1000000007;
constexpr ll minf=-(1<<29);
constexpr ll inf=(1<<29);
constexpr ll MINF=-(1LL<<60);
constexpr ll INF=(1LL<<60);
constexpr ld EPS = 1e-8;
const ld PI = acosl(-1);
#define equals(a, b) (abs((a) - (b)) < EPS)
const int dx[4] ={-1, 0, 1, 0};
const int dy[4] ={ 0, 1, 0,-1};
const int dx8[8] ={-1,-1,-1, 0, 1, 1, 1, 0};
const int dy8[8] ={-1, 0, 1, 1, 1, 0,-1,-1};

void solve();
int main() {
	int t = 1;
    // cin >>t;
    while(t--)solve();
}

vvc<pi>ss(100'100);

ll md = mod-1;

struct mdint {
	ll val;
	mdint(int k = 0): val((k % md + md) % md) {}
	mdint operator*(const mdint other) {return val * other.val % md;}
	mdint& operator+=(const mdint other) {
        val = val + other.val >= md? val + other.val - md : val + other.val;
        return *this;
    }
};

template<class T>
struct Matrix {
    int _R , _C;
    vector<vector<T>> val;

    Matrix(int r, int c, T Val): val(r,vector<T>(c,Val)), _R(r), _C(c) {}
    Matrix(int r, int c): Matrix(r, c, 0) {}

    vector<T>& operator[](int i) {
        return val[i];
    }

    Matrix operator*(const Matrix& other) {
        assert(this->_C == other._R);
        Matrix result(this->_R, other._C);

        for (int i = 0; i < this->_R; i++) {
            for (int j = 0; j < other._C; j++) {
                for (int k = 0; k < this->_C; k++) {
                    result[i][j] += this->val[i][k] * other.val[k][j];
                }
            }
        }
        return result;
    }

};
Matrix<mdint> pow_mat(Matrix<mdint>a,ll n) {
    int si = a[0].size();
    Matrix<mdint> res(si,si);
    for (int i = 0; i < si; i++) res[i][i] = 1;

    while (n > 0) {
        if (n & 1) res = res * a;
        a = a * a;
        n >>= 1;
    }
    return res;
}

void solve(){

    rep(i,2,si(ss)){
        if(ss[i].size() == 0){
            ll res = 1;
            while(res*i < 100100){
                res*=i;
                for(int j = res; j < 100100; j += res){
                    if(ss[j].size() && ss[j].back().first == i){
                        ss[j].back().second++;
                    }else{
                        ss[j].emplace_back(i,1);
                    }
                }
            }
        }
    }

    ll n,k;
    cin >> n >> k;

    vc<pi> nw = ss[n];

    if(k < 50){
        rep(i,k){
            vc<pi>res,nx;
            rep(j,si(nw)){
                rep(k,si(ss[nw[j].first+1])){
                    res.emplace_back(ss[nw[j].first+1][k]);
                    res.back().second = res.back().second * nw[j].second % md;
                }
            }
            sort(all(res));
            rep(j,si(res)){
                if(nx.size() != 0 && nx.back().first == res[j].first){
                    nx.back().second += res[j].second;
                }else{
                    nx.emplace_back(res[j]);
                }
            }
            rep(j,nx.size()){
                nx[j].second %= md;
            }
            nw.swap(nx);
        }
        mint ans = 1;
        rep(i,si(nw)){
            ans *= mint(nw[i].first).pow(nw[i].second);
        }
        print(ans);
        return;
    }
    k-=50;
    rep(i,50){
        vc<pi>res,nx;
        rep(j,si(nw)){
            rep(k,si(ss[nw[j].first+1])){
                res.emplace_back(ss[nw[j].first+1][k]);
                res.back().second = res.back().second * nw[j].second % md;
            }
        }
        sort(all(res));
        rep(j,si(res)){
            if(nx.size() != 0 && nx.back().first == res[j].first){
                nx.back().second += res[j].second;
            }else{
                nx.emplace_back(res[j]);
            }
        }
        rep(j,nx.size()){
            nx[j].second %= md;
        }
        nw.swap(nx);
    }
    Matrix<mdint> dp(2,1,0);

    rep(i,si(nw)){
        if(nw[i].first == 2){
            dp[0][0] = nw[i].second;
        }else{
            dp[1][0] = nw[i].second;
        }
    }
    Matrix<mdint> mat(2,2,0);
    mat[0] = {0,2};
    mat[1] = {1,0};

    dp = pow_mat(mat,k) * dp;


    print(mint(2).pow(dp[0][0].val) * mint(3).pow(dp[1][0].val));
}