結果

問題 No.1025 Modular Equation
コンテスト
ユーザー sbite
提出日時 2020-04-10 22:51:10
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
WA  
実行時間 -
コード長 4,687 bytes
コンパイル時間 2,913 ms
コンパイル使用メモリ 227,792 KB
最終ジャッジ日時 2025-01-09 16:36:18
ジャッジサーバーID
（参考情報） 		judge3 / judge3
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 * 3
other AC * 1 WA * 6 TLE * 25
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("Ofast")
#include <bits/stdc++.h>
#define _overload3(_1, _2, _3, name, ...) name
#define _rep(i, n) repi(i, 0, n)
#define repi(i, a, b) for (int i = (a); i < (b); ++i)
#define rep(...) _overload3(__VA_ARGS__, repi, _rep, )(__VA_ARGS__)
#define ALL(x) x.begin(), x.end()
#define chmax(x, y) x = max(x, y)
#define chmin(x, y) x = min(x, y)
using namespace std;
random_device rnd;
mt19937 mt(rnd());
using ll = long long;
using lld = long double;
using VI = vector<int>;
using VVI = vector<VI>;
using VL = vector<ll>;
using VVL = vector<VL>;
using PII = pair<int, int>;
const double EPS = 1e-3;
const double PI = 3.1415926535897932384626433832795028841971;
const int IINF = 1 << 30;
const ll INF = 1ll << 60;
const ll MOD = 1000000007;

VVL nums;
ll p, n, k, b;
VL v(101010);

//FFT from https://ei1333.github.io/luzhiled/snippets/math/fast-fourier-transform.html
namespace FastFourierTransform
{
using real = long double;

struct C
{
    real x, y;

    C() : x(0), y(0) {}

    C(real x, real y) : x(x), y(y) {}

    inline C operator+(const C &c) const { return C(x + c.x, y + c.y); }

    inline C operator-(const C &c) const { return C(x - c.x, y - c.y); }

    inline C operator*(const C &c) const { return C(x * c.x - y * c.y, x * c.y + y * c.x); }

    inline C conj() const { return C(x, -y); }
};

const real PI = acosl(-1);
int base = 1;
vector<C> rts = {{0, 0},
                 {1, 0}};
vector<int> rev = {0, 1};

void ensure_base(int nbase)
{
    if (nbase <= base)
        return;
    rev.resize(1 << nbase);
    rts.resize(1 << nbase);
    for (int i = 0; i < (1 << nbase); i++)
    {
        rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
    }
    while (base < nbase)
    {
        real angle = PI * 2.0 / (1 << (base + 1));
        for (int i = 1 << (base - 1); i < (1 << base); i++)
        {
            rts[i << 1] = rts[i];
            real angle_i = angle * (2 * i + 1 - (1 << base));
            rts[(i << 1) + 1] = C(cos(angle_i), sin(angle_i));
        }
        ++base;
    }
}

void fft(vector<C> &a, int n)
{
    assert((n & (n - 1)) == 0);
    int zeros = __builtin_ctz(n);
    ensure_base(zeros);
    int shift = base - zeros;
    for (int i = 0; i < n; i++)
    {
        if (i < (rev[i] >> shift))
        {
            swap(a[i], a[rev[i] >> shift]);
        }
    }
    for (int k = 1; k < n; k <<= 1)
    {
        for (int i = 0; i < n; i += 2 * k)
        {
            for (int j = 0; j < k; j++)
            {
                C z = a[i + j + k] * rts[j + k];
                a[i + j + k] = a[i + j] - z;
                a[i + j] = a[i + j] + z;
            }
        }
    }
}

vector<int64_t> multiply(const vector<ll> &a, const vector<ll> &b)
{
    int need = (int)a.size() + (int)b.size() - 1;
    int nbase = 1;
    while ((1 << nbase) < need)
        nbase++;
    ensure_base(nbase);
    int sz = 1 << nbase;
    vector<C> fa(sz);
    for (int i = 0; i < sz; i++)
    {
        int x = (i < (int)a.size() ? a[i] : 0);
        int y = (i < (int)b.size() ? b[i] : 0);
        fa[i] = C(x, y);
    }
    fft(fa, sz);
    C r(0, -0.25 / (sz >> 1)), s(0, 1), t(0.5, 0);
    for (int i = 0; i <= (sz >> 1); i++)
    {
        int j = (sz - i) & (sz - 1);
        C z = (fa[j] * fa[j] - (fa[i] * fa[i]).conj()) * r;
        fa[j] = (fa[i] * fa[i] - (fa[j] * fa[j]).conj()) * r;
        fa[i] = z;
    }
    for (int i = 0; i < (sz >> 1); i++)
    {
        C A0 = (fa[i] + fa[i + (sz >> 1)]) * t;
        C A1 = (fa[i] - fa[i + (sz >> 1)]) * t * rts[(sz >> 1) + i];
        fa[i] = A0 + A1 * s;
    }
    fft(fa, sz >> 1);
    vector<int64_t> ret(need);
    for (int i = 0; i < need; i++)
    {
        ret[i] = llround(i & 1 ? fa[i >> 1].y : fa[i >> 1].x);
    }
    return ret;
}
}; // namespace FastFourierTransform

ll pmod(ll base, ll n)
{
    if (n == 0)
        return 1;
    ll prev = pmod(base, n / 2);
    if (n % 2 == 0)
    {
        return (prev * prev) % p;
    }
    else
    {
        return (prev * prev * base) % p;
    }
}

int main()
{
    cin >> p >> n >> k >> b;
    nums.resize(n);
    rep(i, n) nums[i] = VL(p, 0);
    rep(i, n) cin >> v[i];
    ll tmp;
    rep(i, n)
    {
        rep(j, p)
        {
            tmp = pmod(j, k);
            tmp = (tmp * v[i]) % p;
            nums[i][tmp]++;
        }
    }
    VL ans = nums[0];
    //cerr << "calc" << endl;
    rep(i, 1, n)
    {
        vector<int64_t> nans = FastFourierTransform::multiply(ans, nums[i]);
        rep(j, p)
        {
            ans[j] = 0;
        }
        rep(j, nans.size())
        {
            ans[j % p] += nans[j] % MOD;
            ans[j % p] %= MOD;
        }
    }
    cout << ans[b] << endl;
    return 0;
}
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