結果
問題 | No.981 一般冪乗根 |
ユーザー | heno239 |
提出日時 | 2020-02-07 22:21:03 |
言語 | C++14 (gcc 12.3.0 + boost 1.83.0) |
結果 |
TLE
(最新)
AC
(最初)
|
実行時間 | - |
コード長 | 4,777 bytes |
コンパイル時間 | 1,574 ms |
コンパイル使用メモリ | 125,972 KB |
実行使用メモリ | 11,428 KB |
最終ジャッジ日時 | 2024-10-09 14:30:54 |
合計ジャッジ時間 | 16,913 ms |
ジャッジサーバーID (参考情報) |
judge5 / judge3 |
(要ログイン)
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 | TLE | - |
testcase_01 | -- | - |
testcase_02 | -- | - |
testcase_03 | -- | - |
testcase_04 | -- | - |
testcase_05 | -- | - |
testcase_06 | -- | - |
testcase_07 | -- | - |
testcase_08 | -- | - |
testcase_09 | -- | - |
testcase_10 | -- | - |
testcase_11 | -- | - |
testcase_12 | -- | - |
testcase_13 | -- | - |
testcase_14 | -- | - |
testcase_15 | -- | - |
testcase_16 | -- | - |
testcase_17 | -- | - |
testcase_18 | -- | - |
testcase_19 | -- | - |
testcase_20 | -- | - |
testcase_21 | -- | - |
testcase_22 | -- | - |
testcase_23 | -- | - |
testcase_24 | -- | - |
testcase_25 | -- | - |
testcase_26 | -- | - |
testcase_27 | -- | - |
testcase_28 | -- | - |
evil_60bit1.txt | -- | - |
evil_60bit2.txt | -- | - |
evil_60bit3.txt | -- | - |
evil_hack | -- | - |
evil_hard_random | -- | - |
evil_hard_safeprime.txt | -- | - |
evil_hard_tonelli0 | -- | - |
evil_hard_tonelli1 | -- | - |
evil_hard_tonelli2 | -- | - |
evil_hard_tonelli3 | -- | - |
evil_sefeprime1.txt | -- | - |
evil_sefeprime2.txt | -- | - |
evil_sefeprime3.txt | -- | - |
evil_tonelli1.txt | -- | - |
evil_tonelli2.txt | -- | - |
ソースコード
#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; const ll mod = 998244353; const ll INF = (1e+18) + 7; 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 long double ld; typedef pair<ld, ld> LDP; const ld eps = 1e-6; const ld pi = acos(-1.0); //typedef vector<vector<ll>> mat; typedef vector<int> vec; ll mod_pow(ll a, ll n,ll m) { ll res = 1; while (n) { if (n & 1)res = res * a%m; a = a * a%m; n >>= 1; } return res; } ll mod_inv(ll a, ll m) { return mod_pow(a, m - 2, m); } 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, int 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 = 500; 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]; } int dx[4] = { 0,1,0,-1 }; int dy[4] = { 1,0,-1,0 }; ll calc_proot(ll p) { vector<ll> ps; int k = sqrt(p + 0.1); int cop = p-1; Rep1(i, 2, k) { if (cop%i == 0) { ps.push_back(i); while (cop%i == 0)cop/= i; } } if (cop > 1)ps.push_back(cop); random_device rnd; mt19937 mt(rnd()); uniform_int_distribution<> ud(0, p - 1); while (true) { ll g = ud(mt); if (g == 0)continue; bool f = true; rep(i, ps.size()) { ll z = ps[i]; ll u = mod_pow(g, (p - 1) / z,p); //cout << g << " " <<z<<" "<<p<<" "<< u << endl; if (u == 1) { f = false; break; } } if (f)return g; } return -1; } //a^x=b(mod p) ll calc_kata(ll p,ll a,ll b) { int k = sqrt(p + 0.1); map<int, int> mp; ll cop = b; ll inva = mod_inv(a, p); rep(i, k+2) { mp[cop] = i; cop = cop * inva%p; } ll sa = mod_pow(a, k,p); cop = 1; rep(i, k + 2) { if (mp.find(cop) != mp.end()) { ll res = i * k + mp[cop]; return res % (p - 1); } cop = cop * sa%p; } return -1; } ll gcd(ll a, ll b) { if (a < b)swap(a, b); while (b) { ll r = a % b; a = b; b = r; } return a; } 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; } bool hantei(ll p, ll r) { ll c = 1; vector<bool> exi(p); for (int i = 0; i < p - 1; i++) { if (exi[c])return false; exi[c] = true; c = c * r%p; } return true; } void solve() { ll p, k, a; cin >> p >> k >> a; ll r = calc_proot(p); ll b = calc_kata(p, r, a); //cout << "!! " << r << endl; //assert(hantei(p,r)); //cout << "?? " << b << endl; assert(b >= 0); ll g = gcd(k, p - 1); if (b%g != 0) { cout << -1 << endl; return; } ll ca = k, cb = p - 1; ll x, y; extgcd(ca, cb,x,y); while (x < 0)x += p-1; x = x * (b / g); x %= (p-1); ll ans = mod_pow(r, x,p); ll z = mod_pow(ans, k,p); //cout << ans << " ! " << z << " " << a << endl; cout << ans << endl; } signed main() { ios::sync_with_stdio(false); cin.tie(0); cout << fixed << setprecision(10); //init_f(); init(); int t; cin >> t; rep(i, t)solve(); //while (cin >> n, n)solve(); //solve(); stop return 0; }