結果

問題 No.1409 Simple Math in yukicoder
ユーザー mjtaimjtai
提出日時 2024-10-17 03:56:49
言語 C++17(gcc12)
(gcc 12.3.0 + boost 1.87.0)
結果
AC  
実行時間 18 ms / 2,000 ms
コード長 7,888 bytes
コンパイル時間 9,462 ms
コンパイル使用メモリ 260,480 KB
実行使用メモリ 6,820 KB
最終ジャッジ日時 2024-10-17 03:57:27
合計ジャッジ時間 37,897 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge5
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 * 2
other AC * 58
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 # 

///////////////////////////////////////////////////////////////////////////////

#include <bits/stdc++.h>
#include <unistd.h>
#include <time.h>
#include <sys/time.h>
#include <ext/pb_ds/assoc_container.hpp>

using namespace std;
using namespace __gnu_pbds;

///////////////////////////////////////////////////////////////////////////////

typedef long long ll;
typedef unsigned long long ull;
typedef __int128_t ll128;
typedef tuple<ll, ll> t2;
typedef tuple<ll, ll, ll> t3;
typedef tuple<ll, ll, ll, ll> t4;
typedef tuple<ll, ll, ll, ll, ll> t5;
template <typename T>
using priority_queue_incr = priority_queue<T, vector<T>, greater<T>>;
template <typename T>
using binary_search_tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;

#define pb push_back
#define V vector
#define S static
#define SP << " " <<

#define rep(i,n) for(ll i=0LL; i<n; ++i)
#define srep(i,s,n) for(ll i=s; i<n; ++i)
#define rrep(i,n) for(ll i=n-1LL; i>=0LL; --i)
#define rfrep(i,f,n) for(ll i=n-1LL; i>=f; --i)
#define cfor(i,x) for(const auto & (i) : (x))
#define ALL(a) (a).begin(),(a).end()
#define RALL(a) (a).rbegin(),(a).rend()
#define CIN(x) do { \
        assert(!cin.eof()); \
        cin >> x; \
        assert(!cin.fail()); \
} while(0);
#define E18(x) ((x) * 1'000'000'000'000'000'000LL)
#ifdef DEBUG
#include "../../../template/debug.h"
#else // DEBUG
#define debug_print(...)
#define debug_printf(...)
#define debug_print_mod(...)
#endif // DEBUG

///////////////////////////////////////////////////////////////////////////////

ll llin()
{
    ll a; CIN(a); return a;
}

V<ll> llina(ll count)
{
    V<ll> v;
    for (ll i = 0LL; i < count; ++i) {
        ll a; CIN(a); v.push_back(a);
    }
    return v;
}

V<V<ll>> llinaa(ll h, ll w)
{
    V<V<ll>> v(h, V<ll>(w));
    rep (hh, h) rep (ww, w) {
        ll a; CIN(a); v[hh][ww] = a;
    }
    return v;
}

V<t2> llinl2(ll count)
{
    V<t2> v;
    for (ll i = 0LL; i < count; ++i) {
        ll a, b; CIN(a >> b); v.push_back(t2(a, b));
    }
    return v;
}

V<t3> llinl3(ll count)
{
    V<t3> v;
    for (ll i = 0LL; i < count; ++i) {
        ll a, b, c; CIN(a >> b >> c); v.push_back(t3(a, b, c));
    }
    return v;
}

V<t4> llinl4(ll count)
{
    V<t4> v;
    for (ll i = 0LL; i < count; ++i) {
        ll a, b, c, d; CIN(a >> b >> c >> d); v.push_back(t4(a, b, c, d));
    }
    return v;
}

string strin()
{
    string s; CIN(s); return s;
}

V<string> strina(ll count)
{
    V<string> slist(count);
    for (ll i = 0; i < count; ++i) CIN(slist[i]);
    return slist;
}

template <typename T>
void sort(V<T> &v)
{
    sort(v.begin(), v.end());
}

template <typename T>
void sort_reverse(V<T> &v)
{
    sort(v.begin(), v.end(), greater<T>());
}

t2 _ext_gcd(ll a, ll b, ll g)
{
    if (!b) return t2(1, 0);
    ll q = a / b;
    ll r = a % b;
    auto [sx, sy] = _ext_gcd(b, r, g);
    ll x = sy;
    ll y = sx - q * sy;
    return t2(x, y);
}

t2 ext_gcd(ll a, ll b)
{
    return _ext_gcd(a, b, gcd(a, b));
}

// x and mod must be coprime
ll mod_inv(ll x, ll mod)
{
    auto [ret, xxxx] = ext_gcd(x, mod);
    while (ret < 0) ret += mod;
    ret %= mod;
    return ret;
}



// O(log(exp))
ll mod_pow(ll base, ll exp, ll mod)
{
    ll ret = 1LL;

    for ( ; exp; ) {
        if (exp & 1LL) {
            ret *= base;
            ret %= mod;
        }
        base = (base * base) % mod;
        exp >>= 1;
    }

    return ret;
}

ll mod_mlt(ll x, ll y, ll mod)
{
    ll ret = 0LL;
    x %= mod;

    while (y) {
        if (y & 1LL) {
            ret += x;
            ret %= mod;
        }
        y >>= 1;
        x <<= 1;
        x %= mod;
    }

    return ret;
}

// returns t2(solution, mod)
t2 chinese_remainder(ll a1, ll m1, ll a2, ll m2)
{
    assert(a1 >= 0);
    assert(m1 > 0);
    assert(a2 >= 0);
    assert(m2 > 0);

    ll mgcd = gcd(m1, m2);
    if (a1 % mgcd != a2 % mgcd) return t2(0, 0);
    ll mlcm = m1 * m2 / mgcd;
    t2 z = ext_gcd(m1, m2);
    ll z1 = get<0>(z);
    ll z2 = get<1>(z);

    // ll x = a1 + ((a2 - a1) / mgcd) * m1 * z1;

    ll x = z1;
    while (x < 0) x += mlcm;

    x = mod_mlt(x, m1, mlcm);

    ll coef = (a2 - a1) / mgcd;
    while (coef < 0) coef += mlcm;
    x = mod_mlt(x, coef, mlcm);

    x += a1;
    x %= mlcm;

    return t2(x, mlcm);
}

void get_divisors(V<ll> &retlist, ll x)
{
    for (ll i = 1LL; i < sqrt(x) + 3LL; ++i) {
        if (x % i == 0LL) {
            retlist.push_back(i);
            retlist.push_back(x / i);
        }
    }
}

// returns factors and 1
void get_factors(V<ll> &retlist, ll x)
{
    retlist.pb(1LL);
    for (ll i = 2LL; i < (ll)(sqrt(x)) + 3LL; ++i) {
        while (x % i == 0LL) {
            retlist.pb(i);
            x /= i;
        }
    }
    retlist.pb(x);
}

bool is_prime(ll x)
{
    V<ll> factors, factors2;

    get_factors(factors, x);

    for (auto factor : factors) {
        if (factor > 1) factors2.pb(factor);
    }

    return factors2.size() == 1 && x == factors2[0];
}

V<ll> eratosthenes(ll n)
{
    V<ll> primes;

    bool *is_not_prime = new bool[n+3LL];
    memset(is_not_prime, 0, sizeof(bool) * (n+3LL));

    srep (v, 2LL, (ll)sqrt(n)+10LL) {
        if (is_not_prime[v]) continue;
        for (ll vv = v * 2LL; vv <= n; vv += v) {
            is_not_prime[vv] = true;
        }
    }

    srep (v, 2LL, n+1LL) if (!is_not_prime[v]) primes.pb(v);

    delete [] is_not_prime;
    return primes;
}

// p must be prime
ll mod_root(ll p)
{
    if (p == 2) return 1;
    if (p == 3) return 2;

    V<ll> flist;
    get_factors(flist, p-1LL);
    set<ll> fs;
    for (auto f : flist) if (f > 1) fs.insert(f);

    srep (a, 2, p) {
        bool ok = true;
        for (auto f : fs) {
            if (mod_pow(a, (p-1LL) / f, p) == 1) {
                ok = false;
                break;
            }
        }
        if (ok) return a;
    }

    assert(false);
}

ull combination(ll x, ll y)
{
    if (y > x / 2LL) y = x - y;

    ull ret = 1LL;
    for (ll i = 0LL; i < y; ++i) {
        ret *= x--;
        ret /= (i + 1LL);
    }

    return ret;
}

// count of integers coprime with x (1<=k<=x)
ll euler_phi(ll x)
{
    V<ll> flist;
    get_factors(flist, x);

    map<ll, ll> fcnts;
    cfor (f, flist) {
        if (f == 1) continue;
        fcnts[f]++;
    }

    ll ret = 1;
    cfor (item, fcnts) {
        ll f = item.first;
        ll fc = item.second;
        ll a = 1;
        rep (xx, fc) a *= f;
        ll b = 1;
        rep (xx, fc-1) b *= f;
        ret *= a - b;
    }

    return ret;
}

#if 0

// (base[0] * x^0 + base[1] * x^1 + base[2] * x^2 + ... ) / (div[0] * x^0 + div[1] * x^1 + div[2] * x^2 + ... )
void polynomial_div(V<mint> &q, V<mint> &r, V<mint> base, V<mint> div)
{
    ll blen = base.size();
    ll dlen = div.size();
    reverse(ALL(base));
    reverse(ALL(div));

    mint basemlt = div[0].inv();

    rep (i, blen - dlen + 1) {
        mint mlt = basemlt * base[i];
        rep (j, dlen) base[i+j] -= div[j] * mlt;
        q.pb(mlt);
    }
    reverse(ALL(q));

    ll idx = blen;
    rep (xxx, dlen - 1) r.pb(base[--idx]);
}

#endif





///////////////////////////////////////////////////////////////////////////////

void _main();
int main()
{
    cout << fixed << setprecision(18);
#ifndef DEBUG
    ios::sync_with_stdio(false);
    cin.tie(0);
#endif // DEBUG

    _main();
    return 0;
}

///////////////////////////////////////////////////////////////////////////////

void slv()
{
    ll v = llin();
    ll x = llin();

    ll mod = v * x + 1LL;
    ll root = mod_root(mod);
    ll a = mod_pow(root, v, mod);

    V<ll> anslist;
    ll b = a;
    rep (i, x) {
        anslist.pb(b);
        b = (b * a) % mod;
    }
    sort(anslist);

    cfor (ans, anslist) cout << ans << " ";
    cout << "\n";
}

void _main()
{
    ll t = llin();
    rep (i, t) slv();
}

///////////////////////////////////////////////////////////////////////////////
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