結果
問題 | No.1025 Modular Equation |
ユーザー |
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提出日時 | 2023-06-27 04:36:29 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 424 ms / 5,000 ms |
コード長 | 7,994 bytes |
コンパイル時間 | 2,106 ms |
コンパイル使用メモリ | 167,472 KB |
最終ジャッジ日時 | 2025-02-15 02:33:20 |
ジャッジサーバーID (参考情報) |
judge4 / judge1 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 32 |
ソースコード
#pragma GCC optimize("O3")#pragma GCC optimize("unroll-loops")#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<unordered_set>#include<utility>#include<cassert>#include<complex>#include<numeric>#include<array>#include<chrono>using namespace std;//#define int long longtypedef long long ll;typedef unsigned long long ul;typedef unsigned int ui;//ll mod = 1;//constexpr ll mod = 998244353;constexpr ll mod = 1000000007;const int mod17 = 1000000007;const ll INF = mod * mod;typedef pair<int, int>P;#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;using ld = long double;typedef pair<ld, ld> LDP;const ld eps = 1e-10;const ld pi = acosl(-1.0);template<typename T>void chmin(T& a, T b) {a = min(a, b);}template<typename T>void chmax(T& a, T b) {a = max(a, b);}template<typename T>vector<T> vmerge(vector<T>& a, vector<T>& b) {vector<T> res;int ida = 0, idb = 0;while (ida < a.size() || idb < b.size()) {if (idb == b.size()) {res.push_back(a[ida]); ida++;}else if (ida == a.size()) {res.push_back(b[idb]); idb++;}else {if (a[ida] < b[idb]) {res.push_back(a[ida]); ida++;}else {res.push_back(b[idb]); idb++;}}}return res;}template<typename T>void cinarray(vector<T>& v) {rep(i, v.size())cin >> v[i];}template<typename T>void coutarray(vector<T>& v) {rep(i, v.size()) {if (i > 0)cout << " "; cout << v[i];}cout << "\n";}ll mod_pow(ll x, ll n, ll m = mod) {if (n < 0) {ll res = mod_pow(x, -n, m);return mod_pow(res, m - 2, m);}if (abs(x) >= m)x %= m;if (x < 0)x += m;//if (x == 0)return 0;ll res = 1;while (n) {if (n & 1)res = res * x % m;x = x * x % m; n >>= 1;}return res;}//mod should be <2^31struct modint {int n;modint() :n(0) { ; }modint(ll m) {if (m < 0 || mod <= m) {m %= mod; if (m < 0)m += mod;}n = m;}operator int() { return n; }};bool operator==(modint a, modint b) { return a.n == b.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 -= (int)mod; return a; }modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += (int)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)); }modint operator/=(modint& a, modint b) { a = a / b; return a; }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];}modint combP(int a, int b) {if (a < 0 || b < 0 || a < b)return 0;return fact[a] * factinv[a - b];}ll gcd(ll a, ll b) {a = abs(a); b = abs(b);if (a < b)swap(a, b);while (b) {ll r = a % b; a = b; b = r;}return a;}template<typename T>void addv(vector<T>& v, int loc, T val) {if (loc >= v.size())v.resize(loc + 1, 0);v[loc] += val;}/*const int mn = 2000005;bool isp[mn];vector<int> ps;void init() {fill(isp + 2, isp + mn, true);for (int i = 2; i < mn; i++) {if (!isp[i])continue;ps.push_back(i);for (int j = 2 * i; j < mn; j += i) {isp[j] = false;}}}*///[,val)template<typename T>auto prev_itr(set<T>& st, T val) {auto res = st.lower_bound(val);if (res == st.begin())return st.end();res--; return res;}//[val,)template<typename T>auto next_itr(set<T>& st, T val) {auto res = st.lower_bound(val);return res;}using mP = pair<modint, modint>;mP operator+(mP a, mP b) {return { a.first + b.first,a.second + b.second };}mP operator+=(mP& a, mP b) {a = a + b; return a;}mP operator-(mP a, mP b) {return { a.first - b.first,a.second - b.second };}mP operator-=(mP& a, mP b) {a = a - b; return a;}LP operator+(LP a, LP b) {return { a.first + b.first,a.second + b.second };}LP operator+=(LP& a, LP b) {a = a + b; return a;}LP operator-(LP a, LP b) {return { a.first - b.first,a.second - b.second };}LP operator-=(LP& a, LP b) {a = a - b; return a;}mt19937 mt(time(0));const string drul = "DRUL";string senw = "SENW";//DRUL,or SENW//int dx[4] = { 1,0,-1,0 };//int dy[4] = { 0,1,0,-1 };//-----------------------------------------int get_premitive_root(const ll& p) {int primitive_root = 0;if (!primitive_root) {primitive_root = [&]() {set<int> fac;int v = p - 1;for (ll i = 2; i * i <= v; i++) while (v % i == 0) fac.insert(i), v /= i;if (v > 1) fac.insert(v);for (int g = 1; g < p; g++) {bool ok = true;for (auto i : fac) if (mod_pow(g, (p - 1) / i, p) == 1) { ok = false; break; }if (ok) return g;}return -1;}();}return primitive_root;}void solve() {int p, n, k, b; cin >> p >> n >> k >> b;int r = get_premitive_root(p);//cout << r << "\n";r = mod_pow(r, k, p);vector<int> a(n);rep(i, n)cin >> a[i];vector<vector<int>> vs;vector<bool> used(p);for (int i = 1; i < p; i++) {if (used[i])continue;vector<int> ids;int cur = i;while (!used[cur]) {ids.push_back(cur);used[cur] = true;cur = (ll)cur * r % p;}vs.push_back(ids);}//rep(i, vs.size())coutarray(vs[i]);//rep(i, vs.size())cout << vs[i].size() << "\n";vector<modint> dp(p);dp[0] = 1;rep(i, n) {vector<modint> ndp = dp;vector<modint> dp2(p);rep(j, p) {int nj = j + a[i]; if (nj >= p)nj -= p;dp2[nj] += dp[j];}for (auto& ids : vs) {modint sum = 0;for (int id : ids)sum += dp2[id];sum *= vs.size();for (int id : ids) {ndp[id] += sum;}}ndp[0] += dp2[0] * (modint)(p - 1);swap(dp, ndp);/* modint al = 0;rep(i, dp.size())al += dp[i];cout << al << "\n";*/}cout << dp[b] << "\n";/*modint al = 0;rep(i, dp.size())al += dp[i];cout << al << "\n";*/}signed main() {ios::sync_with_stdio(false);cin.tie(0);//cout << fixed<<setprecision(12);//init_f();//init();//while(true)//expr();//int t; cin >> t; rep(i, t)solve();return 0;}