結果

問題 No.2365 Present of good number
ユーザー noya2
提出日時 2023-06-30 21:54:54
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 29 ms / 2,000 ms
コード長 11,171 bytes
コンパイル時間 4,798 ms
コンパイル使用メモリ 276,648 KB
最終ジャッジ日時 2025-02-15 03:49:24
ジャッジサーバーID
（参考情報） 		judge4 / judge1
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 2
other AC * 39
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ソースコード

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プレゼンテーションモードにする

#line 1 "c.cpp"
#include<bits/stdc++.h>
#include<atcoder/all>
#define rep(i,n) for (int i = 0; i < int(n); ++i)
#define repp(i,m,n) for (int i = m; i < int(n); ++i)
#define reb(i,n) for (int i = int(n)-1; i >= 0; --i)
#define all(v) v.begin(),v.end()
using namespace std;
using namespace atcoder;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using P = pair<int, int>;
using PL = pair<long long, long long>;
using pdd = pair<long double, long double>;
using pil = pair<int,ll>;
using pli = pair<ll,int>;
template<class T>istream &operator>>(istream &is,vector<T> &v){for(auto &e:v)is>>e;return is;}
template<typename T>bool range(T a,T b,T x){return (a<=x&&x<b);}
template<typename T>bool rrange(T a,T b,T c,T d,T x,T y){return (range(a,c,x)&&range(b,d,y));}
template<typename T> T rev(const T& str_or_vec){T res = str_or_vec; reverse(res.begin(),res.end()); return res; }
template<typename T>bool chmin(T &a,const T &b){if(a>b){a=b;return true;}return false;}
template<typename T>bool chmax(T &a,const T &b){if(a<b){a=b;return true;}return false;}
template<typename T>void uniq(vector<T> &v){sort(v.begin(),v.end());v.erase(unique(v.begin(),v.end()),v.end());}
template<typename T1, typename T2>void print(pair<T1,T2> a);
template<typename T>void print(vector<T> v);
template<typename T>void print(vector<vector<T>> v);
void print(){ putchar(' '); }
void print(bool a){ printf("%d", a); }
void print(int a){ printf("%d", a); }
void print(long a){ printf("%ld", a); }
void print(long long a){ printf("%lld", a); }
void print(char a){ printf("%c", a); }
void print(char a[]){ printf("%s", a); }
void print(const char a[]){ printf("%s", a); }
void print(long double a){ printf("%.15Lf", a); }
void print(const string& a){ for(auto&& i : a) print(i); }
void print(unsigned int a){ printf("%u", a); }
void print(unsigned long long a) { printf("%llu", a); }
template<class T> void print(const T& a){ cout << a; }
int out(){ putchar('\n'); return 0; }
template<class T> int out(const T& t){ print(t); putchar('\n'); return 0; }
template<class Head, class... Tail> int out(const Head& head, const Tail&... tail){ print(head); putchar(' '); out(tail...); return 0; }
template<typename T1,typename T2>void print(pair<T1,T2> a){print(a.first);print(),print(a.second);}
template<typename T>void print(vector<T> v){for(auto ite=v.begin();ite!=v.end();){print(*ite);if(++ite!=v.end())print();}}
template<typename T>void print(vector<vector<T>> v){for(auto ite=v.begin();ite!=v.end();){print(*ite);if(++ite!=v.end())out();}}
void yes(){out("Yes");}
void no (){out("No");}
void yn (bool t){if(t)yes();else no();}
void fast_io(){cin.tie(0); ios::sync_with_stdio(0); cout<<fixed<<setprecision(20);}
void o(){out("!?");}
int popc(ll n){ return __builtin_popcountll((ull)(n)); }
namespace noya2{
const int INF = 1001001007;
const long long mod1 = 998244353;
const long long mod2 = 1000000007;
const long long inf = 2e18;
const long double pi = 3.14159265358979323;
const long double eps = 1e-7;
const vector<int> dx = {0,1,0,-1,1,1,-1,-1};
const vector<int> dy = {1,0,-1,0,1,-1,-1,1};
const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const string alp = "abcdefghijklmnopqrstuvwxyz";
const string NUM = "0123456789";
} // namespace noya2
using namespace noya2;
//using mint = modint998244353;
using mint = modint1000000007;
//using mint = modint;
void out(mint a){out(a.val());}
void out(vector<mint> a){vector<ll> b(a.size()); rep(i,a.size()) b[i] = a[i].val(); out(b);}
void out(vector<vector<mint>> a){for (auto v : a) out(v);}
#line 2 "math.hpp"
#line 6 "math.hpp"
namespace noya2{
using namespace std;
using ll = long long;
template<typename T> T sqrt_safe(T x){ // floor(sqrt(x))
    assert(x >= T(0));
    if (x <= T(1)) return x;
    T tmp = (T)(sqrtl((long double)(x))) + T(2);
    while (tmp--){
        if (tmp * tmp <= x) break;
    }
    return tmp;
}
constexpr ll mod_safe(ll a, ll m){ // m >= 1, 0 <= mod_safe(a,m) < m, mod_safe(a,m) = a (mod m)
    ll res = a % m;
    if (res < 0) res += m;
    return res;
}
ll modpow(ll x, ll n, ll mod){
    x = mod_safe(x,mod);
    if (n == 0) return 1;
    ll res = modpow(x,n/2,mod);
    res = (res * res) % mod;
    if (n % 2 == 1) res = (res * x) % mod;
    return res;
}
ll naive_gcd(ll a, ll b){ return b ? naive_gcd(b, a % b) : a; }
// gcd(N >= 0, 0) = N, especialy gcd(0, 0) = 0
ll gcd_safe(ll a, ll b){ return naive_gcd(abs(a),abs(b)); }
ll lcm_safe(ll a, ll b){ return a / gcd_safe(a,b) * b; }
void ext_gcd1_plus(ll a, ll b, ll &x, ll &y){ // gcd(a,b) = 1, a >= 0, b >= 0, ax + by = 1
    if (b == 0){ // a = 1
        x = 1, y = 0;
        return ;
    }
    ext_gcd1_plus(b, a%b, y, x);
    x = mod_safe(x,b);
    y = (1 - a * x) / b;
}
void ext_gcd1_minus(ll a, ll b, ll &x, ll &y){ // gcd(a,b) = 1, a >= 0, b >= 0, ax - by = 1
    if (b == 0){ // a = 1
        x = 1, y = 0;
        return ;
    }
    ext_gcd1_plus(b, a%b, y, x);
    x = mod_safe(x,b);
    y = (a * x - 1) / b;
}
pair<ll,ll> ext_gcd(ll a, ll b, ll c){ // ax + by = c, |a|,|b|,|c| < 1e9, x <= max(|B|,|C|), y <= max(|A|,|C|)
    if (a < 0) return ext_gcd(-a,-b,-c);
    if (c < 0){
        pair<ll,ll> res = ext_gcd(a,b,-c);
        res.first = -res.first, res.second = -res.second;
        return res;
    }
    if (c == 0) return pair<ll,ll>(0,0);
    if (a == 0 && b == 0) return pair<ll,ll>(0,0); // answer not exist
    ll g = gcd_safe(a,b);
    if (c % g != 0) return pair<ll,ll>(0,0); // answer not exist
    a /= g, b /= g, c /= g;
    ll x, y;
    if (b == 0) return pair<ll,ll>(c,0);
    if (b > 0) ext_gcd1_plus(a,b,x,y);
    else ext_gcd1_minus(a,-b,x,y);
    x = mod_safe(x*c,abs(b));
    y = (c - a * x) / b;
    return pair<ll,ll>(x,y);
}
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
    if (m == 1) return 0;
    unsigned int _m = (unsigned int)(m);
    unsigned long long r = 1;
    unsigned long long y = mod_safe(x, m);
    while (n) {
        if (n & 1) r = (r * y) % _m;
        y = (y * y) % _m;
        n >>= 1;
    }
    return r;
}
constexpr int primitive_root_constexpr(int m) {
    if (m == 2) return 1;
    if (m == 167772161) return 3;
    if (m == 469762049) return 3;
    if (m == 754974721) return 11;
    if (m == 998244353) return 3;
    int divs[20] = {};
    divs[0] = 2;
    int cnt = 1;
    int x = (m - 1) / 2;
    while (x % 2 == 0) x /= 2;
    for (int i = 3; (long long)(i)*i <= x; i += 2) {
        if (x % i == 0) {
            divs[cnt++] = i;
            while (x % i == 0) {
                x /= i;
            }
        }
    }
    if (x > 1) {
        divs[cnt++] = x;
    }
    for (int g = 2;; g++) {
        bool ok = true;
        for (int i = 0; i < cnt; i++) {
            if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
                ok = false;
                break;
            }
        }
        if (ok) return g;
    }
}
template<typename T>
T ceil_safe(T p, T q);
template<typename T>
T floor_safe(T p, T q){
    if (q < T(0)) return floor_safe(-p,-q);
    if (p >= T(0)) return p / q;
    return -ceil_safe(-p,q);
}
template<typename T>
T ceil_safe(T p, T q){
    if (q < T(0)) return ceil_safe(-p,-q);
    if (p >= T(0)) return (p + q - 1) / q;
    return -floor_safe(-p,q);
}
struct Eratosthenes{
    static vector<int> table;
    Eratosthenes (int Nmax = -1) {init(Nmax);}
    static void init(int Nmax){
        if (!table.empty()) return ;
        table.resize(Nmax+1,0);
        table[0] = 1, table[1] = 1;
        for (int p = 2; p <= Nmax; p++){
            if (table[p] != 0) continue;
            for (int j = p; j <= Nmax; j += p){
                table[j] = p;
            }
        }
    }
};
vector<int>Eratosthenes::table = vector<int>(0);
void build_eratosthenes(const int Nmax){Eratosthenes::init(Nmax);}
vector<pair<int,int>> fast_prime_factorization(int N){
    int pre = -1, cnt = 0;
    vector<pair<int,int>> res;
    while(true) {
        if (N == 1){
            if (cnt > 0) res.emplace_back(pre,cnt);
            break;
        }
        int div = Eratosthenes::table[N];
        if (pre != div){
            if (cnt > 0) res.emplace_back(pre,cnt);
            pre = div, cnt = 1;
        }
        else cnt++;
        N /= div;
    }
    return res;
}
vector<int> fast_divisor_enumeration(int N){
    auto pes = fast_prime_factorization(N);
    vector<int> res = {1};
    for (auto pe : pes){
        vector<int> nres;
        for (auto x : res){
            for (int _t = 0; _t <= pe.second; _t++){
                nres.emplace_back(x);
                x *= pe.first;
            }
        }
        swap(res,nres);
    }
    return res;
}
bool fast_is_prime(int N){
    if (N <= 1) return false;
    return Eratosthenes::table[N] == N;
}
vector<int> mobius(int N){
    vector<int> res(N+1,0);
    res[1] = 1;
    for (int p = 2; p <= N; p++){
        if (fast_is_prime(p)){
            for (int i = N/p; i > 0; i--){
                res[i*p] = -res[i];
            }
        }
    }
    return res;
};
vector<pair<ll,int>> prime_factorization(ll N){
    vector<pair<ll,int>> res;
    ll iN = N;
    for (ll d = 2; d * d <= N; d++){
        if (iN % d != 0) continue;
        if (iN == 1) break;
        int ie = 0;
        while (iN % d == 0) iN /= d, ie++;
        res.emplace_back(d,ie);
    }
    if (iN != 1) res.emplace_back(iN,1);
    return res;
}
vector<ll> divisor_enumeration(ll N){
    vector<ll> res;
    for (ll d = 1; d * d <= N; d++){
        if (N % d != 0) continue;
        res.emplace_back(d);
        if (d * d != N) res.emplace_back(N/d);
    }
    return res;
}
bool is_prime(ll N){
    if (N <= 1) return false;
    if (N <= 3) return true;
    if (N % 2 == 0) return false;
    for (ll d = 3; d * d <= N; d += 2){
        if (N % d == 0) return false;
    }
    return true;
}
}// namespace noya2
#line 78 "c.cpp"
void solve(){
    const int mx = 100001;
    build_eratosthenes(mx);
    int n; cin >> n;
    ll k; cin >> k;
    map<int,ll> pe;
    for (auto [p, e] : fast_prime_factorization(n)){
        pe[p] = e;
    }
    while (k > 0){ k--;
        map<int,ll> mp;
        for (auto [p, e] : pe){
            auto qe = fast_prime_factorization(p+1);
            for (auto [q, f] : qe){
                mp[q] += f*e;
            }
        }
        swap(pe,mp);
        int siz = pe.size();
        if (pe.find(2) != pe.end()) siz--;
        if (pe.find(3) != pe.end()) siz--;
        if (siz == 0) break;
    }
    if (k == 0){
        mint ans = 1;
        for (auto [p, e] : pe){
            ans *= mint(p).pow(e);
        }
        out(ans);
        return ;
    }
    auto get = [&](int p){
        if (pe.find(p) == pe.end()) return 0LL;
        return pe[p];
    };
    ll s = modpow(2,k/2,mint::mod()-1);
    if (k % 2 == 0){
        ll a = s * get(2) % (mod2-1);
        ll b = s * get(3) % (mod2-1);
        mint ans = mint(2).pow(a) * mint(3).pow(b);
        out(ans);
    }
    else {
        ll a = s * get(3) * 2 % (mod2-1);
        ll b = s * get(2) % (mod2-1);
        mint ans = mint(2).pow(a) * mint(3).pow(b);
        out(ans);
    }
}
int main(){
    fast_io();
    int t = 1; //cin >> t;
    while(t--) solve();
}
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