QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#519706 | #7688. Alea Iacta Est | pandapythoner | RE | 237ms | 52320kb | C++23 | 16.3kb | 2024-08-15 00:14:18 | 2024-08-15 00:14:18 |
Judging History
answer
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define rep(i, n) for(int i = 0; i < (n); i += 1)
#define rng(i, start, end, step) for(int i = start; i < end; i += step)
#define len(a) ((int)(a).size())
mt19937 rnd(234);
const ll mod = 998244353;
ll bin_pow(ll x, ll n) {
ll rs = 1;
for (ll i = 1, a = x; i <= n; i *= 2, a = a * a % mod)
if (n & i) rs = rs * a % mod;
return rs;
}
ll inv(ll x) {
return bin_pow(x, mod - 2);
}
namespace fft {
int mxpw;
int mxn;
ll w;
void build_w() {
ll phi = mod - 1;
ll f = phi;
vector<ll> p;
for (ll i = 2; i * i <= f; i += 1) {
if (f % i == 0) {
p.push_back(i);
while (f % i == 0) {
f /= i;
}
}
}
if (f > 1) {
p.push_back(f);
}
for (int i = 1; i < mod; i += 1) {
bool ok = true;
for (auto q : p) {
if (bin_pow(i, phi / q) == 1) {
ok = false;
break;
}
}
if (ok) {
w = bin_pow(i, phi / (1 << mxpw));
break;
}
}
}
vector<ll> rvx;
void build_rvx(int n) {
rvx.resize(n + 1);
for (int i = 1; i <= n; i += 1) {
rvx[i] = inv(i);
}
}
vector<ll> rvi, wpws;
void build(int _mxpw) {
mxpw = _mxpw;
mxn = (1 << mxpw);
build_w();
int n = (1 << mxpw);
rvi.resize(n);
rvi[0] = 0;
for (int i = 1; i < n; i += 1) {
rvi[i] = (rvi[i >> 1] >> 1);
if (i & 1) {
rvi[i] += (1 << (mxpw - 1));
}
}
wpws.resize(n + 1);
wpws[0] = 1;
for (int i = 1; i <= n; i += 1) {
wpws[i] = (wpws[i - 1] * w) % mod;
}
build_rvx(mxn);
}
void fft(vector<ll>& a, int nk) {
int n = (1 << nk);
for (int i = 0; i < n; i += 1) {
int mrv = (rvi[i] >> (mxpw - nk));
if (mrv < i) {
swap(a[mrv], a[i]);
}
}
for (int ln = 1; ln < n; ln *= 2) {
int ln2 = ln + ln;
for (int i = 0; i < n; i += ln2) {
for (int j = 0; j < ln; j += 1) {
ll mw = wpws[mxn / ln2 * j];
int u = i + j;
int v = u + ln;
ll y = a[v] * mw % mod;
a[v] = a[u] - y;
if (a[v] < 0) {
a[v] += mod;
}
a[u] += y;
if (a[u] >= mod) {
a[u] -= mod;
}
}
}
}
}
void rev_fft(vector<ll>& a, int nk) {
int n = (1 << nk);
fft(a, nk);
ll rvn = inv(n);
reverse(a.begin() + 1, a.end());
for (int i = 0; i < n; i += 1) {
a[i] = (a[i] * rvn) % mod;
}
}
vector<ll> square(vector<ll> a) {
int nk = 0;
while ((1 << nk) < (int)a.size() + (int)a.size() - 1) {
nk += 1;
}
int n = (1 << nk);
a.resize(n, 0);
fft(a, nk);
for (int i = 0; i < n; i += 1) {
a[i] = (a[i] * a[i]) % mod;
}
rev_fft(a, nk);
while (!a.empty() && a.back() == 0) {
a.pop_back();
}
return a;
}
vector<ll> mul(vector<ll> a, vector<ll> b) {
int nk = 0;
while ((1 << nk) < (int)a.size() + (int)b.size() - 1) {
nk += 1;
}
int n = (1 << nk);
a.resize(n, 0);
b.resize(n, 0);
fft(a, nk);
fft(b, nk);
for (int i = 0; i < n; i += 1) {
a[i] = (a[i] * b[i]) % mod;
}
rev_fft(a, nk);
while (!a.empty() && a.back() == 0) {
a.pop_back();
}
return a;
}
void add_inplace(vector<ll>& a, const vector<ll>& b, ll k = 1) {
a.resize(max(a.size(), b.size()), 0);
for (int i = 0; i < (int)b.size(); i += 1) {
a[i] = (a[i] + b[i] * k) % mod;
}
}
vector<ll> add(vector<ll> a, const vector<ll>& b, ll k = 1) {
a.resize(max(a.size(), b.size()), 0);
for (int i = 0; i < (int)b.size(); i += 1) {
a[i] = (a[i] + b[i] * k) % mod;
}
return a;
}
vector<ll> sub(vector<ll> a, const vector<ll>& b, ll k = 1) {
a.resize(max(a.size(), b.size()), 0);
for (int i = 0; i < (int)b.size(); i += 1) {
a[i] = (a[i] + mod - b[i] * k % mod) % mod;
}
return a;
}
vector<ll> replace_x_slow(vector<ll>& a, const vector<ll>& b) {
vector<ll> rs = {};
vector<ll> bpw = { 1 };
for (int i = 0; i < (int)a.size(); i += 1) {
if (i > 0) {
bpw = mul(bpw, b);
}
add_inplace(rs, bpw, a[i]);
}
return rs;
}
vector<ll> replace_x(vector<ll>& a, const vector<ll>& b) {
vector<ll> rs = {};
vector<ll> bpw = b;
int n = a.size();
vector<vector<ll>> d(n);
for (int i = 0; i < n; i += 1) {
d[i] = { a[i] };
}
while (n > 1) {
int m = (n + 1) / 2;
vector<vector<ll>> nd(m);
for (int i = 0; i < n; i += 1) {
if (i % 2 == 0) {
nd[i / 2] = d[i];
} else {
add_inplace(nd[i / 2], mul(d[i], bpw));
}
}
n = m;
d.swap(nd);
if (n != 1) {
bpw = square(bpw);
}
}
return d[0];
}
vector<ll> shift_x(vector<ll> a, ll t) {
if (a.empty()) {
return {};
}
int n = (int)a.size() - 1;
vector<ll> f(n + 1), rf(n + 1);
f[0] = rf[0] = 1;
for (int i = 1; i <= n; i += 1) {
f[i] = (f[i - 1] * i) % mod;
rf[i] = inv(f[i]);
}
vector<ll> b(n + 1), c(n + 1);
ll tpw = 1;
for (int i = 0; i <= n; i += 1) {
b[i] = (a[i] * tpw % mod * f[i] % mod);
tpw = (tpw * t) % mod;
}
for (int i = 0; i <= n; i += 1) {
c[n - i] = rf[i];
}
a = mul(b, c);
vector<ll> d(n + 1);
ll rvt = inv(t);
ll rvt_pw = 1;
for (int i = 0; i <= n; i += 1) {
d[i] = rvt_pw * rf[i] % mod * a[i + n] % mod;
rvt_pw = (rvt_pw * rvt) % mod;
}
return d;
}
vector<ll> rev_polynom(const vector<ll>& a, int n) {
int sz = a.size();
vector<ll> b = { inv(a[0]) };
int m = 1;
int mk = 0;
while (m < n) {
int m2 = m + m;
int m4 = m2 + m2;
b.resize(m4);
fft(b, mk + 2);
vector<ll> nb(m4);
for (int i = 0; i < sz && i < m2; i += 1) {
nb[i] = a[i];
}
fft(nb, mk + 2);
for (int i = 0; i < m4; i += 1) {
nb[i] = (2 * b[i] - nb[i] * b[i] % mod * b[i]) % mod;
if (nb[i] < 0) {
nb[i] += mod;
}
}
rev_fft(nb, mk + 2);
nb.resize(m2);
b.swap(nb);
m = m2;
mk += 1;
}
b.resize(n);
return b;
}
vector<ll> square_root(const vector<ll>& a, int n) {
ll sz = a.size();
ll rv2 = inv(2);
vector<ll> b = { 1 };
int m = 1;
while (m < n) {
ll m2 = m + m;
vector<ll> rvb = rev_polynom(b, m2);
vector<ll> ab(m2);
for (int i = 0; i < m2 && i < sz; i += 1) {
ab[i] = a[i];
}
ab = mul(ab, rvb);
ab.resize(m2);
b.resize(m2);
for (int i = 0; i < m2; i += 1) {
b[i] = (rv2 * ((b[i] + ab[i]) % mod)) % mod;
}
m = m2;
}
b.resize(n);
return b;
}
vector<ll> derivative(vector<ll> a) {
int n = a.size();
if (n == 0) {
return {};
}
for (int i = 0; i + 1 < n; i += 1) {
a[i] = (a[i + 1] * (i + 1)) % mod;
}
a.resize(n - 1);
return a;
}
vector<ll> integrate(vector<ll> a) {
int n = a.size();
a.resize(n + 1);
for (int i = n; i > 0; i -= 1) {
a[i] = (a[i - 1] * rvx[i]) % mod;
}
a[0] = 0;
return a;
}
vector<ll> sin_polynomial(int n) {
vector<ll> a(n, 0);
ll fct = 1;
for (int i = 0; i < n; i += 1) {
if (i != 0) {
fct = (fct * i) % mod;
}
if (i % 2 == 1) {
int sign = 1;
if ((i / 2) % 2 == 1) {
sign = -1;
}
a[i] = (mod + sign * inv(fct)) % mod;
}
}
return a;
}
vector<ll> cos_polynomial(int n) {
vector<ll> a(n, 0);
ll fct = 1;
for (int i = 0; i < n; i += 1) {
if (i != 0) {
fct = (fct * i) % mod;
}
if (i % 2 == 0) {
int sign = 1;
if ((i / 2) % 2 == 1) {
sign = -1;
}
a[i] = (mod + sign * inv(fct)) % mod;
}
}
return a;
}
vector<ll> super_cos_polynomial(int n, int k) {
vector<ll> a(n, 0);
ll fct = 1;
for (int i = 0; i < n; i += 1) {
if (i != 0) {
fct = (fct * i) % mod;
}
if (i % k == 0) {
int sign = 1;
if ((i / k) % 2 == 1) {
sign = -1;
}
a[i] = (mod + sign * inv(fct)) % mod;
}
}
return a;
}
vector<ll> logarithm(const vector<ll>& a, int n) {
if (n == 0) {
return {};
}
vector<ll> b = integrate(mul(derivative(a), rev_polynom(a, n)));
b.resize(n);
return b;
}
vector<ll> exponent(const vector<ll>& a, int n) {
vector<ll> b = { 1 };
int m = 1;
while (m < n) {
int m2 = m + m;
vector<ll> t = logarithm(b, m2);
for (int i = 0; i < m2 && i < (int)a.size(); i += 1) {
t[i] = (t[i] - a[i]);
if (t[i] < 0) {
t[i] += mod;
}
}
vector<ll> q = fft::mul(t, b);
q.resize(m2);
b.resize(m2);
for (int i = 0; i < m2; i += 1) {
b[i] -= q[i];
if (b[i] < 0) {
b[i] += mod;
}
}
m = m2;
}
b.resize(n);
return b;
}
vector<ll> solve_differential(const vector<ll>& a, const vector<ll>& b, int n) {
vector<ll> e = exponent(integrate(a), n);
vector<ll> result = mul(e, integrate(mul(b, rev_polynom(e, n))));
result.resize(n);
return result;
}
vector<ll> pure_exponent(int n, ll k = 1) {
if (n == 0) {
return {};
}
k %= mod;
if (k < 0) {
k += mod;
}
vector<ll> rs(n);
rs[0] = 1;
ll rv_fct = 1;
for (int i = 1; i < n; i += 1) {
rv_fct = (rv_fct * rvx[i]) % mod * k % mod;
rs[i] = rv_fct;
}
return rs;
}
} // namespace fft
vector<ll> get_flex(int step, int num_steps) {
vector<ll> result(step * num_steps);
rep(i, num_steps) result[i * step] = 1;
return result;
}
vector<ll> get_dice(vector<ll> flex) {
vector<ll> result;
rep(i, len(flex)) {
assert(flex[i] >= 0);
rep(j, flex[i]) result.push_back(i);
}
return result;
}
void print_flex(ll n, ll m, ll a, ll b) {
ll nm = n * m;
assert(n % a == 0 and m % b == 0);
auto first_dice = get_dice(fft::mul(get_flex(1, n / a), get_flex(1, b)));
auto second_dice = get_dice(fft::mul(get_flex(b, m / b), get_flex(n / a, a)));
cout << len(first_dice); for (auto x : first_dice) cout << " " << x + 1;
cout << "\n";
cout << len(second_dice); for (auto x : second_dice) cout << " " << x + 1;
cout << "\n\n";
}
int32_t main() {
fft::build(21);
if (1) {
ios::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
}
int t;
cin >> t;
rep(itr, t) {
int n, m;
cin >> n >> m;
if (n > m) swap(n, m);
ll nm = ll(n) * m;
ll opt = 1;
for (ll x = 1; x * x <= nm; x += 1) {
if (nm % x != 0) continue;
if (opt + nm / opt > x + nm / x) opt = x;
}
if (opt != n) {
ll g = gcd(opt, n);
ll a = n / g;
ll b = opt / g;
print_flex(n, m, a, b);
continue;
}
ll g = gcd(n, m);
ll frst = -1;
for (ll i = 2; i <= g and i < n; i += 1) if (g % i == 0) { frst = i; break; }
assert(g == 1 or frst != -1);
if (frst != -1 and frst < m) {
print_flex(n, m, frst, frst);
continue;
}
bool ok = false;
rep(itr, 2) {
ll a = -1, b = -1;
for (ll i = 2; i < n; i += 1) if (n % i == 0 and gcd(n / i, i) == 1) {
a = i; b = n / i; break;
};
if (a != -1) {
vector<ll> biba(a + b);
vector<ll> boba(n + m);
biba[0] = boba[0] = 1;
for (int i = len(biba) - 1; i - a >= 0; i -= 1) {
biba[i] -= biba[i - a];
}
for (int i = len(biba) - 1; i - b >= 0; i -= 1) {
biba[i] -= biba[i - b];
}
for (int i = 1; i < len(biba); i += 1) {
biba[i] += biba[i - 1];
}
for (int i = 1; i < len(biba); i += 1) {
biba[i] += biba[i - 1];
}
for (int i = len(boba) - 1; i - n >= 0; i -= 1) {
boba[i] -= boba[i - n];
}
for (int i = len(boba) - 1; i - m >= 0; i -= 1) {
boba[i] -= boba[i - m];
}
for (int i = a; i < len(boba); i += 1) {
boba[i] += boba[i - a];
}
for (int i = b; i < len(boba); i += 1) {
boba[i] += boba[i - b];
}
for (auto x : boba) assert(0 <= x and x <= 1);
auto first_dice = get_dice(biba);
auto second_dice = get_dice(boba);
cout << len(first_dice); for (auto x : first_dice) cout << " " << x + 1;
cout << "\n";
cout << len(second_dice); for (auto x : second_dice) cout << " " << x + 1;
cout << "\n\n";
ok = true;
break;
}
swap(n, m);
}
if (ok) {
continue;
}
opt = -1;
for (ll x = 1; x * x <= nm; x += 1) {
if (nm % x != 0) continue;
if (x == n) continue;
if (opt == -1 or opt + nm / opt > x + nm / x) opt = x;
}
if (opt != -1 and opt + nm / opt < 2 * n + m) {
ll g = gcd(opt, n);
ll a = n / g;
ll b = opt / g;
print_flex(n, m, a, b);
continue;
}
cout << 2 * n; rep(i, n) cout << " " << i + 1 << " " << i + 1; cout << "\n";
cout << m; rep(i, m) cout << " " << i + 1; cout << "\n";
cout << "\n";
}
return 0;
}
Details
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Test #1:
score: 100
Accepted
time: 237ms
memory: 52320kb
input:
3 2 8 1 9 2 9
output:
4 1 2 2 3 4 1 3 5 7 3 1 2 3 3 1 4 7 3 1 2 3 6 1 2 4 5 7 8
result:
ok Correct. (3 test cases)
Test #2:
score: -100
Runtime Error
input:
1 40013 40013