#527738 (C++14) No.181 A↑↑N mod M

提出ソース

結果

問題	No.181 A↑↑N mod M
ユーザー	heno239
提出日時	2020-08-10 20:41:54
言語	C++14 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	14 ms / 5,000 ms
コード長	4,589 bytes
コンパイル時間	1,480 ms
コンパイル使用メモリ	117,520 KB
実行使用メモリ	20,044 KB
最終ジャッジ日時	2024-10-08 13:43:21
合計ジャッジ時間	3,214 ms
ジャッジサーバーID （参考情報）	judge3 / judge5

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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	13 ms 19,912 KB
testcase_01	AC	13 ms 19,912 KB
testcase_02	AC	13 ms 19,912 KB
testcase_03	AC	13 ms 19,916 KB
testcase_04	AC	13 ms 19,908 KB
testcase_05	AC	13 ms 19,908 KB
testcase_06	AC	13 ms 20,040 KB
testcase_07	AC	13 ms 19,912 KB
testcase_08	AC	13 ms 20,036 KB
testcase_09	AC	13 ms 19,912 KB
testcase_10	AC	13 ms 19,912 KB
testcase_11	AC	13 ms 20,036 KB
testcase_12	AC	13 ms 20,044 KB
testcase_13	AC	13 ms 19,912 KB
testcase_14	AC	13 ms 19,912 KB
testcase_15	AC	13 ms 19,912 KB
testcase_16	AC	14 ms 20,040 KB
testcase_17	AC	13 ms 20,040 KB
testcase_18	AC	13 ms 19,916 KB
testcase_19	AC	12 ms 19,912 KB
testcase_20	AC	13 ms 20,040 KB
testcase_21	AC	13 ms 19,912 KB
testcase_22	AC	13 ms 20,040 KB
testcase_23	AC	13 ms 19,912 KB
testcase_24	AC	12 ms 19,912 KB
testcase_25	AC	13 ms 19,916 KB
testcase_26	AC	13 ms 20,040 KB
testcase_27	AC	14 ms 20,040 KB
testcase_28	AC	13 ms 19,916 KB
testcase_29	AC	13 ms 19,916 KB
testcase_30	AC	13 ms 19,912 KB
testcase_31	AC	13 ms 20,036 KB
testcase_32	AC	12 ms 19,908 KB
testcase_33	AC	13 ms 19,908 KB
testcase_34	AC	13 ms 19,912 KB
testcase_35	AC	13 ms 20,040 KB
testcase_36	AC	13 ms 19,912 KB
testcase_37	AC	13 ms 20,044 KB
testcase_38	AC	13 ms 20,040 KB
testcase_39	AC	13 ms 19,916 KB
testcase_40	AC	13 ms 19,908 KB
testcase_41	AC	12 ms 19,808 KB
testcase_42	AC	13 ms 19,912 KB

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ソースコード

raw source code

#include<iostream>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<utility>
#include<cassert>
#include<complex>
#include<numeric>
using namespace std;

//#define int long long
typedef long long ll;

typedef unsigned long long ul;
typedef unsigned int ui;
constexpr ll mod = 998244353;
const ll INF = mod * mod;
typedef pair<int, int>P;
#define stop char nyaa;cin>>nyaa;
#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
#define all(v) (v).begin(),(v).end()
typedef pair<ll, ll> LP;
typedef double ld;
typedef pair<ld, ld> LDP;
const ld eps = 1e-12;
const ld pi = acos(-1.0);

ll mod_pow(ll x, ll n, ll m=mod) {
	ll res = 1;
	while (n) {
		if (n & 1)res = res * x % m;
		x = x * x % m; n >>= 1;
	}
	return res;
}
struct modint {
	ll n;
	modint() :n(0) { ; }
	modint(ll m) :n(m) {
		if (n >= mod)n %= mod;
		else if (n < 0)n = (n % mod + mod) % mod;
	}
	operator int() { return n; }
};
bool operator==(modint a, modint b) { return a.n == b.n; }
modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= mod; return a; }
modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += mod; return a; }
modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; }
modint operator+(modint a, modint b) { return a += b; }
modint operator-(modint a, modint b) { return a -= b; }
modint operator*(modint a, modint b) { return a *= b; }
modint operator^(modint a, ll n) {
	if (n == 0)return modint(1);
	modint res = (a * a) ^ (n / 2);
	if (n % 2)res = res * a;
	return res;
}

ll inv(ll a, ll p) {
	return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p);
}
modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); }

const int max_n = 1 << 20;
modint fact[max_n], factinv[max_n];
void init_f() {
	fact[0] = modint(1);
	for (int i = 0; i < max_n - 1; i++) {
		fact[i + 1] = fact[i] * modint(i + 1);
	}
	factinv[max_n - 1] = modint(1) / fact[max_n - 1];
	for (int i = max_n - 2; i >= 0; i--) {
		factinv[i] = factinv[i + 1] * modint(i + 1);
	}
}
modint comb(int a, int b) {
	if (a < 0 || b < 0 || a < b)return 0;
	return fact[a] * factinv[b] * factinv[a - b];
}

ll gcd(ll a, ll b) {
	if (a < b)swap(a, b);
	while (b) {
		ll r = a % b; a = b; b = r;
	}
	return a;
}

//x,yがax+by=gcd(a,b)の解になる
ll extgcd(ll a, ll b, ll& x, ll& y) {
	ll d = a;
	if (b != 0) {
		d = extgcd(b, a % b, y, x);
		y -= (a / b) * x;
	}
	else {
		x = 1; y = 0;
	}
	return d;
}
//aのmod mでの逆元を求める
ll mod_inverse(ll a, ll m) {
	ll x, y;
	extgcd(a, m, x, y);
	return (m + x % m) % m;
}

int cnte[2001];
vector<P> ps[2001];

void init() {
	rep1(n, 2000) {
		rep1(j, n - 1) {
			if (gcd(n, j) == 0)cnte[n]++;
		}
		int cop = n;
		for (int j = 2; j <= n; j++) {
			if (cop % j == 0) {
				int cnt = 0;
				while (cop % j == 0) {
					cop /= j; cnt++;
				}
				ps[n].push_back({ j,cnt });
			}
		}
	}
}
ll num(ll a, ll n) {
	if (n == 0)return 1;
	else if (n >= 3) {
		return 16;
	}
	else if (n == 1)return min(a, (ll)16);
	else {
		if (a == 2)return 4;
		else return 16;
	}
}
ll rem(ll r0, ll m0, ll r1, ll m1) {
	ll x = r0;
	ll y = (r1 - r0) * mod_inverse(m0, m1);
	y = (y % m1 + m1) % m1;
	return x + y * m0;
}
ll calc(ll a, ll n, ll m) {
	if (n == 0)return 1;
	if (m == 1)return 0;

	ll r = 0, p = 1;
	rep(j, ps[m].size()) {
		int sp = ps[m][j].first;
		int np = 1;
		rep(i, ps[m][j].second) {
			np *= sp;
		}
		int nm = np*(sp-1)/sp;
		//a^^n mod np
		int cnt = 0;
		int cop = a;
		while (cop % sp == 0) {
			cnt++; cop /= sp;
		}
		ll r1, r2;
		{
			//cop
			ll v = calc(a, n - 1, nm);
			r1 = 1;
			rep(i, v)r1 = r1 * cop % np;
		}
		{
			//sp
			ll cc = num(a, n - 1);
			if (cc * cnt >= ps[m][j].second)r2 = 0;
			else {
				r2 = 1;
				rep(aa, cc* cnt)r2 *= sp;
			}
		}
		ll nr = r1 * r2 % np;

		r = rem(r, p, nr, np);
		p *= np;
	}
	return r;
}
void solve() {
	ll a, n, m; cin >> a >> n >> m;
	if (m == 1) {
		cout << 0 << "\n"; return;
	}
	if (a == 1) {
		cout << 1%m << "\n"; return;
	}
	cout << calc(a, n, m) << "\n";
}




signed main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	//cout << fixed << setprecision(10);
	//init_f();
	init();
	//expr();
	//int t; cin >> t; rep(i, t)
	solve();
	return 0;
}

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結果

テストケース

ソースコード