結果

問題 No.1025 Modular Equation
ユーザー heno239heno239
提出日時 2023-06-27 04:36:29
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 554 ms / 5,000 ms
コード長 7,994 bytes
コンパイル時間 2,208 ms
コンパイル使用メモリ 167,436 KB
実行使用メモリ 18,164 KB
最終ジャッジ日時 2024-07-03 23:05:33
合計ジャッジ時間 12,099 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge1
このコードへのチャレンジ
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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 7 ms
11,848 KB
testcase_01 AC 8 ms
11,720 KB
testcase_02 AC 9 ms
11,976 KB
testcase_03 AC 8 ms
11,648 KB
testcase_04 AC 8 ms
11,776 KB
testcase_05 AC 8 ms
11,724 KB
testcase_06 AC 8 ms
11,776 KB
testcase_07 AC 9 ms
11,716 KB
testcase_08 AC 8 ms
11,720 KB
testcase_09 AC 217 ms
13,016 KB
testcase_10 AC 228 ms
13,028 KB
testcase_11 AC 313 ms
12,928 KB
testcase_12 AC 337 ms
13,180 KB
testcase_13 AC 296 ms
13,056 KB
testcase_14 AC 321 ms
13,056 KB
testcase_15 AC 334 ms
13,068 KB
testcase_16 AC 319 ms
12,928 KB
testcase_17 AC 330 ms
13,168 KB
testcase_18 AC 310 ms
12,928 KB
testcase_19 AC 340 ms
15,096 KB
testcase_20 AC 411 ms
14,348 KB
testcase_21 AC 361 ms
14,152 KB
testcase_22 AC 397 ms
13,772 KB
testcase_23 AC 524 ms
17,784 KB
testcase_24 AC 245 ms
13,180 KB
testcase_25 AC 337 ms
13,200 KB
testcase_26 AC 345 ms
13,308 KB
testcase_27 AC 356 ms
13,212 KB
testcase_28 AC 355 ms
13,072 KB
testcase_29 AC 359 ms
13,208 KB
testcase_30 AC 347 ms
14,456 KB
testcase_31 AC 376 ms
15,480 KB
testcase_32 AC 554 ms
18,164 KB
testcase_33 AC 9 ms
11,648 KB
testcase_34 AC 326 ms
13,004 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#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 long
typedef 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 <2^31
struct 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;
}
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