結果
| 問題 |
No.1561 connect x connect
|
| コンテスト | |
| ユーザー |
 emthrm
|
| 提出日時 | 2021-08-11 11:48:53 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 10,940 bytes |
| コンパイル時間 | 3,806 ms |
| コンパイル使用メモリ | 246,168 KB |
| 最終ジャッジ日時 | 2025-01-23 17:31:50 |
|
ジャッジサーバーID （参考情報） |
judge4 / judge4 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 9 WA * 18 TLE * 8 |
ソースコード
#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;
#define FOR(i,m,n) for(int i=(m);i<(n);++i)
#define REP(i,n) FOR(i,0,n)
#define ALL(v) (v).begin(),(v).end()
using ll = long long;
constexpr int INF = 0x3f3f3f3f;
constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL;
constexpr double EPS = 1e-8;
constexpr int MOD = 1000000007;
// constexpr int MOD = 998244353;
constexpr int dy[] = {1, 0, -1, 0}, dx[] = {0, -1, 0, 1};
constexpr int dy8[] = {1, 1, 0, -1, -1, -1, 0, 1}, dx8[] = {0, -1, -1, -1, 0, 1, 1, 1};
template <typename T, typename U> inline bool chmax(T &a, U b) { return a < b ? (a = b, true) : false; }
template <typename T, typename U> inline bool chmin(T &a, U b) { return a > b ? (a = b, true) : false; }
struct IOSetup {
IOSetup() {
std::cin.tie(nullptr);
std::ios_base::sync_with_stdio(false);
std::cout << fixed << setprecision(20);
}
} iosetup;
template <int M>
struct MInt {
unsigned int val;
MInt(): val(0) {}
MInt(long long x) : val(x >= 0 ? x % M : x % M + M) {}
static constexpr int get_mod() { return M; }
static void set_mod(int divisor) { assert(divisor == M); }
static void init(int x = 10000000) { inv(x, true); fact(x); fact_inv(x); }
static MInt inv(int x, bool init = false) {
// assert(0 <= x && x < M && std::__gcd(x, M) == 1);
static std::vector<MInt> inverse{0, 1};
int prev = inverse.size();
if (init && x >= prev) {
// "x!" and "M" must be disjoint.
inverse.resize(x + 1);
for (int i = prev; i <= x; ++i) inverse[i] = -inverse[M % i] * (M / i);
}
if (x < inverse.size()) return inverse[x];
unsigned int a = x, b = M; int u = 1, v = 0;
while (b) {
unsigned int q = a / b;
std::swap(a -= q * b, b);
std::swap(u -= q * v, v);
}
return u;
}
static MInt fact(int x) {
static std::vector<MInt> f{1};
int prev = f.size();
if (x >= prev) {
f.resize(x + 1);
for (int i = prev; i <= x; ++i) f[i] = f[i - 1] * i;
}
return f[x];
}
static MInt fact_inv(int x) {
static std::vector<MInt> finv{1};
int prev = finv.size();
if (x >= prev) {
finv.resize(x + 1);
finv[x] = inv(fact(x).val);
for (int i = x; i > prev; --i) finv[i - 1] = finv[i] * i;
}
return finv[x];
}
static MInt nCk(int n, int k) {
if (n < 0 || n < k || k < 0) return 0;
if (n - k > k) k = n - k;
return fact(n) * fact_inv(k) * fact_inv(n - k);
}
static MInt nPk(int n, int k) { return n < 0 || n < k || k < 0 ? 0 : fact(n) * fact_inv(n - k); }
static MInt nHk(int n, int k) { return n < 0 || k < 0 ? 0 : (k == 0 ? 1 : nCk(n + k - 1, k)); }
static MInt large_nCk(long long n, int k) {
if (n < 0 || n < k || k < 0) return 0;
inv(k, true);
MInt res = 1;
for (int i = 1; i <= k; ++i) res *= inv(i) * n--;
return res;
}
MInt pow(long long exponent) const {
MInt tmp = *this, res = 1;
while (exponent > 0) {
if (exponent & 1) res *= tmp;
tmp *= tmp;
exponent >>= 1;
}
return res;
}
MInt &operator+=(const MInt &x) { if((val += x.val) >= M) val -= M; return *this; }
MInt &operator-=(const MInt &x) { if((val += M - x.val) >= M) val -= M; return *this; }
MInt &operator*=(const MInt &x) { val = static_cast<unsigned long long>(val) * x.val % M; return *this; }
MInt &operator/=(const MInt &x) { return *this *= inv(x.val); }
bool operator==(const MInt &x) const { return val == x.val; }
bool operator!=(const MInt &x) const { return val != x.val; }
bool operator<(const MInt &x) const { return val < x.val; }
bool operator<=(const MInt &x) const { return val <= x.val; }
bool operator>(const MInt &x) const { return val > x.val; }
bool operator>=(const MInt &x) const { return val >= x.val; }
MInt &operator++() { if (++val == M) val = 0; return *this; }
MInt operator++(int) { MInt res = *this; ++*this; return res; }
MInt &operator--() { val = (val == 0 ? M : val) - 1; return *this; }
MInt operator--(int) { MInt res = *this; --*this; return res; }
MInt operator+() const { return *this; }
MInt operator-() const { return MInt(val ? M - val : 0); }
MInt operator+(const MInt &x) const { return MInt(*this) += x; }
MInt operator-(const MInt &x) const { return MInt(*this) -= x; }
MInt operator*(const MInt &x) const { return MInt(*this) *= x; }
MInt operator/(const MInt &x) const { return MInt(*this) /= x; }
friend std::ostream &operator<<(std::ostream &os, const MInt &x) { return os << x.val; }
friend std::istream &operator>>(std::istream &is, MInt &x) { long long val; is >> val; x = MInt(val); return is; }
};
namespace std { template <int M> MInt<M> abs(const MInt<M> &x) { return x; } }
using ModInt = MInt<MOD>;
struct UnionFind {
UnionFind(int n) : data(n, -1) {}
int root(int ver) { return data[ver] < 0 ? ver : data[ver] = root(data[ver]); }
bool unite(int u, int v) {
u = root(u);
v = root(v);
if (u == v) return false;
if (data[u] > data[v]) std::swap(u, v);
data[u] += data[v];
data[v] = u;
return true;
}
bool same(int u, int v) { return root(u) == root(v); }
int size(int ver) { return -data[root(ver)]; }
private:
std::vector<int> data;
};
template <typename T>
struct Matrix {
Matrix(int m, int n, T val = 0) : dat(m, std::vector<T>(n, val)) {}
int height() const { return dat.size(); }
int width() const { return dat.front().size(); }
Matrix pow(long long exponent) const {
int n = height();
Matrix<T> tmp = *this, res(n, n, 0);
for (int i = 0; i < n; ++i) res[i][i] = 1;
while (exponent > 0) {
if (exponent & 1) res *= tmp;
tmp *= tmp;
exponent >>= 1;
}
return res;
}
inline const std::vector<T> &operator[](const int idx) const { return dat[idx]; }
inline std::vector<T> &operator[](const int idx) { return dat[idx]; }
Matrix &operator=(const Matrix &x) {
int m = x.height(), n = x.width();
dat.resize(m, std::vector<T>(n));
for (int i = 0; i < m; ++i) for (int j = 0; j < n; ++j) dat[i][j] = x[i][j];
return *this;
}
Matrix &operator+=(const Matrix &x) {
int m = height(), n = width();
for (int i = 0; i < m; ++i) for (int j = 0; j < n; ++j) dat[i][j] += x[i][j];
return *this;
}
Matrix &operator-=(const Matrix &x) {
int m = height(), n = width();
for (int i = 0; i < m; ++i) for (int j = 0; j < n; ++j) dat[i][j] -= x[i][j];
return *this;
}
Matrix &operator*=(const Matrix &x) {
int m = height(), n = x.width(), l = width();
std::vector<std::vector<T>> res(m, std::vector<T>(n, 0));
for (int i = 0; i < m; ++i) for (int j = 0; j < n; ++j) {
for (int k = 0; k < l; ++k) res[i][j] += dat[i][k] * x[k][j];
}
std::swap(dat, res);
return *this;
}
Matrix operator+(const Matrix &x) const { return Matrix(*this) += x; }
Matrix operator-(const Matrix &x) const { return Matrix(*this) -= x; }
Matrix operator*(const Matrix &x) const { return Matrix(*this) *= x; }
private:
std::vector<std::vector<T>> dat;
};
template <typename T>
T kita_masa(const std::vector<T> &c, const std::vector<T> &a, long long n) {
if (n == 0) return a[0];
int k = c.size();
std::vector<T> coefficient[3];
for (int i = 0; i < 3; ++i) coefficient[i].assign(k, 0);
if (k == 1) {
coefficient[0][0] = c[0] * a[0];
} else {
coefficient[0][1] = 1;
}
auto succ = [&c, k, &coefficient]() -> void {
for (int i = 0; i < k - 1; ++i) coefficient[0][i] += coefficient[0].back() * c[i + 1];
coefficient[0].back() *= c[0];
std::rotate(coefficient[0].begin(), coefficient[0].begin() + k - 1, coefficient[0].end());
};
for (int bit = 62 - __builtin_clzll(n); bit >= 0; --bit) {
for (int i = 1; i < 3; ++i) std::copy(coefficient[0].begin(), coefficient[0].end(), coefficient[i].begin());
for (T &e : coefficient[1]) e *= coefficient[2][0];
for (int i = 1; i < k; ++i) {
succ();
for (int j = 0; j < k; ++j) coefficient[1][j] += coefficient[2][i] * coefficient[0][j];
}
coefficient[0].swap(coefficient[1]);
if (n >> bit & 1) succ();
}
T res = 0;
for (int i = 0; i < k; ++i) res += coefficient[0][i] * a[i];
return res;
}
// https://github.com/beet-aizu/library/blob/bca52958e61426377b8f56817d63f912070b3487/polynomial/berlekampmassey.cpp
template<typename T>
vector<T> berlekamp_massey(vector<T> &as){
using Poly = vector<T>;
int n=as.size();
Poly bs({-T(1)}),cs({-T(1)});
T y(1);
for(int ed=1;ed<=n;ed++){
int l=cs.size(),m=bs.size();
T x(0);
for(int i=0;i<l;i++) x+=cs[i]*as[ed-l+i];
bs.emplace_back(0);
m++;
if(x==T(0)) continue;
T freq=x/y;
if(m<=l){
for(int i=0;i<m;i++)
cs[l-1-i]-=freq*bs[m-1-i];
continue;
}
auto ts=cs;
cs.insert(cs.begin(),m-l,T(0));
for(int i=0;i<m;i++) cs[m-1-i]-=freq*bs[m-1-i];
bs=ts;
y=x;
}
for(auto &c:cs) c/=cs.back();
return cs;
}
int main() {
int n; ll m; cin >> n >> m;
int size = 2;
map<vector<int>, int> mp;
mp[vector<int>(n, -1)] = 0;
vector<vector<int>> reach(size);
vector<bool> finish{false, true};
queue<vector<int>> que({vector<int>(n, -1)});
while (!que.empty()) {
vector<int> prev = que.front(); que.pop();
int id = mp[prev];
if (id > 0) {
bool is_con = true;
int only = *max_element(ALL(prev));
REP(i, n) is_con &= prev[i] == -1 || prev[i] == only;
if (is_con) reach[id].emplace_back(1);
}
FOR(b, 1, 1 << n) {
UnionFind uf(n * 2);
REP(i, n) {
if (prev[i] == -1) continue;
FOR(j, i + 1, n) {
if (prev[j] == prev[i]) uf.unite(i, j);
}
}
FOR(i, 1, n) {
if ((b >> (i - 1) & 1) && (b >> i & 1)) uf.unite(n + i - 1, n + i);
}
REP(i, n) {
if (prev[i] != -1 && (b >> i & 1)) uf.unite(i, n + i);
}
vector<int> nx(n, -1);
map<int, int> root;
REP(i, n) {
if (b >> i & 1) {
int rt = uf.root(n + i);
if (root.count(rt) == 0) {
int tmp = root.size();
root[rt] = tmp;
}
nx[i] = root[rt];
}
}
bool is_con = true;
REP(i, n) is_con &= prev[i] == -1 || root.count(uf.root(i)) == 1;
if (is_con) {
if (mp.count(nx) == 0) {
mp[nx] = size++;
que.emplace(nx);
reach.emplace_back();
finish.emplace_back(root.size() == 1);
}
reach[id].emplace_back(mp[nx]);
}
}
}
vector<ModInt> dp(size, 0), a;
dp[0] = 1;
while (a.size() < size * 2) {
vector<ModInt> nx(size, 0);
nx[0] += dp[0];
nx[1] += dp[1];
REP(i, size) for (int j : reach[i]) nx[j] += dp[i];
dp.swap(nx);
a.emplace_back(0);
REP(i, size) {
if (finish[i]) a.back() += dp[i];
}
}
vector<ModInt> c = berlekamp_massey(a);
reverse(ALL(c));
cout << kita_masa(c, a, m - 1) << '\n';
return 0;
}