結果
| 問題 |
No.3053 $((0 \And 1)\mathop{|}2)\oplus 3$
|
| ユーザー |
 Aeren
|
| 提出日時 | 2025-03-07 23:55:56 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 23,481 bytes |
| コンパイル時間 | 3,944 ms |
| コンパイル使用メモリ | 293,436 KB |
| 実行使用メモリ | 8,608 KB |
| 最終ジャッジ日時 | 2025-03-07 23:56:12 |
| 合計ジャッジ時間 | 15,053 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge2 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 27 WA * 7 |
ソースコード
// #include <bits/allocator.h> // Temp fix for gcc13 global pragma
// #pragma GCC target("avx2,bmi2,popcnt,lzcnt")
// #pragma GCC optimize("O3,unroll-loops")
#include <bits/stdc++.h>
// #include <x86intrin.h>
using namespace std;
#if __cplusplus >= 202002L
using namespace numbers;
#endif
#ifdef LOCAL
#include "Debug.h"
#else
#define debug_endl() 42
#define debug(...) 42
#define debug2(...) 42
#define debugbin(...) 42
#endif
template<class data_t, data_t _mod>
struct modular_fixed_base{
#define IS_INTEGRAL(T) (is_integral_v<T> || is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>)
#define IS_UNSIGNED(T) (is_unsigned_v<T> || is_same_v<T, __uint128_t>)
static_assert(IS_UNSIGNED(data_t));
static_assert(1 <= _mod && _mod < data_t(1) << 8 * sizeof(data_t) - 1);
static constexpr bool VARIATE_MOD_FLAG = false;
static constexpr data_t mod(){
return _mod;
}
template<class T>
static vector<modular_fixed_base> precalc_power(T base, int SZ){
vector<modular_fixed_base> res(SZ + 1, 1);
for(auto i = 1; i <= SZ; ++ i) res[i] = res[i - 1] * base;
return res;
}
template<class T>
static vector<modular_fixed_base> precalc_geometric_sum(T base, int SZ){
vector<modular_fixed_base> res(SZ + 1);
for(auto i = 1; i <= SZ; ++ i) res[i] = res[i - 1] * base + base;
return res;
}
static vector<modular_fixed_base> _INV;
static void precalc_inverse(int SZ){
if(_INV.empty()) _INV.assign(2, 1);
for(auto x = _INV.size(); x <= SZ; ++ x) _INV.push_back(_mod / x * -_INV[_mod % x]);
}
// _mod must be a prime
static modular_fixed_base _primitive_root;
static modular_fixed_base primitive_root(){
if(_primitive_root) return _primitive_root;
if(_mod == 2) return _primitive_root = 1;
if(_mod == 998244353) return _primitive_root = 3;
data_t divs[20] = {};
divs[0] = 2;
int cnt = 1;
data_t x = (_mod - 1) / 2;
while(x % 2 == 0) x /= 2;
for(auto i = 3; 1LL * i * i <= x; i += 2){
if(x % i == 0){
divs[cnt ++] = i;
while(x % i == 0) x /= i;
}
}
if(x > 1) divs[cnt ++] = x;
for(auto g = 2; ; ++ g){
bool ok = true;
for(auto i = 0; i < cnt; ++ i){
if(modular_fixed_base(g).power((_mod - 1) / divs[i]) == 1){
ok = false;
break;
}
}
if(ok) return _primitive_root = g;
}
}
constexpr modular_fixed_base(){ }
modular_fixed_base(const double &x){ data = _normalize(llround(x)); }
modular_fixed_base(const long double &x){ data = _normalize(llround(x)); }
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr> modular_fixed_base(const T &x){ data = _normalize(x); }
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr> static data_t _normalize(const T &x){
int sign = x >= 0 ? 1 : -1;
data_t v = _mod <= sign * x ? sign * x % _mod : sign * x;
if(sign == -1 && v) v = _mod - v;
return v;
}
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr> operator T() const{ return data; }
modular_fixed_base &operator+=(const modular_fixed_base &otr){ if((data += otr.data) >= _mod) data -= _mod; return *this; }
modular_fixed_base &operator-=(const modular_fixed_base &otr){ if((data += _mod - otr.data) >= _mod) data -= _mod; return *this; }
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr> modular_fixed_base &operator+=(const T &otr){ return *this += modular_fixed_base(otr); }
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr> modular_fixed_base &operator-=(const T &otr){ return *this -= modular_fixed_base(otr); }
modular_fixed_base &operator++(){ return *this += 1; }
modular_fixed_base &operator--(){ return *this += _mod - 1; }
modular_fixed_base operator++(int){ modular_fixed_base result(*this); *this += 1; return result; }
modular_fixed_base operator--(int){ modular_fixed_base result(*this); *this += _mod - 1; return result; }
modular_fixed_base operator-() const{ return modular_fixed_base(_mod - data); }
modular_fixed_base &operator*=(const modular_fixed_base &rhs){
if constexpr(is_same_v<data_t, unsigned int>) data = (unsigned long long)data * rhs.data % _mod;
else if constexpr(is_same_v<data_t, unsigned long long>){
long long res = data * rhs.data - _mod * (unsigned long long)(1.L / _mod * data * rhs.data);
data = res + _mod * (res < 0) - _mod * (res >= (long long)_mod);
}
else data = _normalize(data * rhs.data);
return *this;
}
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>
modular_fixed_base &inplace_power(T e){
if(e == 0) return *this = 1;
if(data == 0) return *this = {};
if(data == 1 || e == 1) return *this;
if(data == mod() - 1) return e % 2 ? *this : *this = -*this;
if(e < 0) *this = 1 / *this, e = -e;
if(e == 1) return *this;
modular_fixed_base res = 1;
for(; e; *this *= *this, e >>= 1) if(e & 1) res *= *this;
return *this = res;
}
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>
modular_fixed_base power(T e) const{
return modular_fixed_base(*this).inplace_power(e);
}
// c + c * x + ... + c * x^{e-1}
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>
modular_fixed_base &inplace_geometric_sum(T e, modular_fixed_base c = 1){
if(e == 0) return *this = {};
if(data == 0) return *this = {};
if(data == 1) return *this = c * e;
if(e == 1) return *this = c;
if(data == mod() - 1) return *this = c * abs(e % 2);
modular_fixed_base res = 0;
if(e < 0) return *this = geometric_sum(-e + 1, -*this) - 1;
if(e == 1) return *this = c * *this;
for(; e; c *= 1 + *this, *this *= *this, e >>= 1) if(e & 1) res += c, c *= *this;
return *this = res;
}
// c + c * x + ... + c * x^{e-1}
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>
modular_fixed_base geometric_sum(T e, modular_fixed_base c = 1) const{
return modular_fixed_base(*this).inplace_geometric_sum(e, c);
}
modular_fixed_base &operator/=(const modular_fixed_base &otr){
make_signed_t<data_t> a = otr.data, m = _mod, u = 0, v = 1;
if(a < _INV.size()) return *this *= _INV[a];
while(a){
make_signed_t<data_t> t = m / a;
m -= t * a; swap(a, m);
u -= t * v; swap(u, v);
}
assert(m == 1);
return *this *= u;
}
#define ARITHMETIC_OP(op, apply_op)\
modular_fixed_base operator op(const modular_fixed_base &x) const{ return modular_fixed_base(*this) apply_op x; }\
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>\
modular_fixed_base operator op(const T &x) const{ return modular_fixed_base(*this) apply_op modular_fixed_base(x); }\
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>\
friend modular_fixed_base operator op(const T &x, const modular_fixed_base &y){ return modular_fixed_base(x) apply_op y; }
ARITHMETIC_OP(+, +=) ARITHMETIC_OP(-, -=) ARITHMETIC_OP(*, *=) ARITHMETIC_OP(/, /=)
#undef ARITHMETIC_OP
#define COMPARE_OP(op)\
bool operator op(const modular_fixed_base &x) const{ return data op x.data; }\
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>\
bool operator op(const T &x) const{ return data op modular_fixed_base(x).data; }\
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>\
friend bool operator op(const T &x, const modular_fixed_base &y){ return modular_fixed_base(x).data op y.data; }
COMPARE_OP(==) COMPARE_OP(!=) COMPARE_OP(<) COMPARE_OP(<=) COMPARE_OP(>) COMPARE_OP(>=)
#undef COMPARE_OP
friend istream &operator>>(istream &in, modular_fixed_base &number){
long long x;
in >> x;
number.data = modular_fixed_base::_normalize(x);
return in;
}
friend ostream &operator<<(ostream &out, const modular_fixed_base &number){
out << number.data;
#ifdef LOCAL
cerr << "(";
for(auto d = 1; ; ++ d){
if((number * d).data <= 1000000){
cerr << (number * d).data;
if(d != 1) cerr << "/" << d;
break;
}
else if((-number * d).data <= 1000000){
cerr << "-" << (-number * d).data;
if(d != 1) cerr << "/" << d;
break;
}
}
cerr << ")";
#endif
return out;
}
data_t data = 0;
#undef IS_INTEGRAL
#undef IS_UNSIGNED
};
template<class data_t, data_t _mod> vector<modular_fixed_base<data_t, _mod>> modular_fixed_base<data_t, _mod>::_INV;
template<class data_t, data_t _mod> modular_fixed_base<data_t, _mod> modular_fixed_base<data_t, _mod>::_primitive_root;
const unsigned int mod = (119 << 23) + 1; // 998244353
// const unsigned int mod = 1e9 + 7; // 1000000007
// const unsigned int mod = 1e9 + 9; // 1000000009
// const unsigned long long mod = (unsigned long long)1e18 + 9;
using modular = modular_fixed_base<decay_t<decltype(mod)>, mod>;
modular operator""_m(const char *x){ return stoll(x); }
template<class T, size_t N, size_t M>
struct matrix_fixed_base{
int n, m;
array<array<T, M>, N> data;
array<T, M> &operator[](int i){
assert(0 <= i && i < n);
return data[i];
}
const array<T, M> &operator[](int i) const{
assert(0 <= i && i < n);
return data[i];
}
matrix_fixed_base &inplace_slice(int il, int ir, int jl, int jr){
assert(0 <= il && il <= ir && ir <= n);
assert(0 <= jl && jl <= jr && jr <= m);
n = ir - il, m = jr - jl;
if(il > 0) for(auto i = 0; i < n; ++ i) swap(data[i], data[il + i]);
data.resize(n);
for(auto &row: data){
row.erase(row.begin(), row.begin() + jl);
row.resize(m);
}
return *this;
}
matrix_fixed_base slice(int il, int ir, int jl, int jr) const{
return matrix_fixed_base(*this).inplace_slice(il, ir, jl, jr);
}
matrix_fixed_base &inplace_row_slice(int il, int ir){
assert(0 <= il && il <= ir && ir <= n);
n = ir - il;
if(il > 0) for(auto i = 0; i < n; ++ i) swap(data[i], data[il + i]);
data.resize(n);
return *this;
}
matrix_fixed_base row_slice(int il, int ir) const{
return matrix_fixed_base(*this).inplace_row_slice(il, ir);
}
matrix_fixed_base &inplace_column_slice(int jl, int jr){
assert(0 <= jl && jl <= jr && jr <= m);
m = jr - jl;
for(auto &row: data){
row.erase(row.begin(), row.begin() + jl);
row.resize(m);
}
return *this;
}
matrix_fixed_base column_slice(int jl, int jr) const{
return matrix_fixed_base(*this).inplace_column_slice(jl, jr);
}
bool operator==(const matrix_fixed_base &a) const{
assert(n == a.n && m == a.m);
return data == a.data;
}
bool operator!=(const matrix_fixed_base &a) const{
assert(n == a.n && m == a.m);
return data != a.data;
}
matrix_fixed_base &operator+=(const matrix_fixed_base &a){
assert(n == a.n && m == a.m);
for(auto i = 0; i < n; ++ i) for(auto j = 0; j < m; ++ j) data[i][j] += a[i][j];
return *this;
}
matrix_fixed_base operator+(const matrix_fixed_base &a) const{
return matrix_fixed_base(*this) += a;
}
matrix_fixed_base &operator-=(const matrix_fixed_base &a){
assert(n == a.n && m == a.m);
for(auto i = 0; i < n; ++ i) for(auto j = 0; j < m; ++ j) data[i][j] -= a[i][j];
return *this;
}
matrix_fixed_base operator-(const matrix_fixed_base &a) const{
return matrix_fixed_base(*this) -= a;
}
matrix_fixed_base operator*=(const matrix_fixed_base &a){
assert(m == a.n);
int l = a.m;
matrix_fixed_base res(n, l);
for(auto i = 0; i < n; ++ i) for(auto j = 0; j < m; ++ j) for(auto k = 0; k < l; ++ k) res[i][k] += data[i][j] * a[j][k];
return *this = res;
}
matrix_fixed_base operator*(const matrix_fixed_base &a) const{
return matrix_fixed_base(*this) *= a;
}
matrix_fixed_base &operator*=(T c){
for(auto i = 0; i < n; ++ i) for(auto j = 0; j < m; ++ j) data[i][j] *= c;
return *this;
}
matrix_fixed_base operator*(T c) const{
return matrix_fixed_base(*this) *= c;
}
friend matrix_fixed_base operator*(T c, matrix_fixed_base a){
for(auto i = 0; i < a.n; ++ i) for(auto j = 0; j < a.m; ++ j) a[i][j] = c * a[i][j];
return a;
}
template<class U, typename enable_if<is_integral<U>::value>::type* = nullptr>
matrix_fixed_base &inplace_power(U e){
assert(n == m && e >= 0);
matrix_fixed_base res(n, n, T{1});
for(; e; *this *= *this, e >>= 1) if(e & 1) res *= *this;
return *this = res;
}
template<class U>
matrix_fixed_base power(U e) const{
return matrix_fixed_base(*this).inplace_power(e);
}
matrix_fixed_base &inplace_transpose(){
assert(n == m);
for(auto i = 0; i < n; ++ i) for(auto j = i + 1; j < n; ++ j) swap(data[i][j], data[j][i]);
return *this;
}
matrix_fixed_base transpose() const{
if(n == m) return matrix_fixed_base(*this).inplace_transpose();
matrix_fixed_base res(m, n);
for(auto i = 0; i < n; ++ i) for(auto j = 0; j < m; ++ j) res[j][i] = data[i][j];
return res;
}
vector<T> operator*(const vector<T> &v) const{
assert(m == (int)v.size());
vector<T> res(n, T{0});
for(auto i = 0; i < n; ++ i) for(auto j = 0; j < m; ++ j) res[i] += data[i][j] * v[j];
return res;
}
friend vector<T> operator*(const vector<T> &v, const matrix_fixed_base &a){
vector<T> res(a.m, T{0});
for(auto i = 0; i < a.n; ++ i) for(auto j = 0; j < a.m; ++ j) res[j] += v[i] * a[i][j];
return res;
}
// Assumes T is either a floating, integral, or a modular type.
// If T is a floating type, O(up_to) divisions with O(n * m * up_to) additions, subtractions, and multiplications.
// Otherwise, O(n * up_to * log(size)) divisions with O(n * m * up_to) additions, subtractions, and multiplications.
// Returns {REF matrix_fixed_base, determinant, rank}
tuple<matrix_fixed_base &, T, int> inplace_REF(int up_to = -1){
if(n == 0) return {*this, T{1}, 0};
if(!~up_to) up_to = m;
T det = 1;
int rank = 0;
for(auto j = 0; j < up_to; ++ j){
if constexpr(is_floating_point_v<T>){
static const T eps = 1e-9;
int pivot = rank;
for(auto i = rank + 1; i < n; ++ i) if(abs(data[pivot][j]) < abs(data[i][j])) pivot = i;
if(rank != pivot){
swap(data[rank], data[pivot]);
det *= -1;
}
if(abs(data[rank][j]) <= eps) continue;
det *= data[rank][j];
T inv = 1 / data[rank][j];
for(auto i = rank + 1; i < n; ++ i) if(abs(data[i][j]) > eps){
T coef = data[i][j] * inv;
for(auto k = j; k < m; ++ k) data[i][k] -= coef * data[rank][k];
}
++ rank;
}
else{
for(auto i = rank + 1; i < n; ++ i) while(data[i][j]){
T q;
if constexpr(is_integral_v<T> || is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>) q = data[rank][j] / data[i][j];
else q = data[rank][j].data / data[i][j].data;
if(q) for(auto k = j; k < m; ++ k) data[rank][k] -= q * data[i][k];
swap(data[rank], data[i]);
det *= -1;
}
if(rank == j) det *= data[rank][j];
else det = T(0);
if(data[rank][j]) ++ rank;
}
if(rank == n) break;
}
return {*this, det, rank};
}
// Assumes T is either a floating, integral, or a modular type.
// If T is a floating type, O(up_to) divisions with O(n * m * up_to) additions, subtractions, and multiplications.
// Otherwise, O(n * up_to * log(size)) divisions with O(n * m * up_to) additions, subtractions, and multiplications.
// Returns {REF matrix_fixed_base, determinant, rank}
tuple<matrix_fixed_base, T, int> REF(int up_to = -1) const{
return matrix_fixed_base(*this).inplace_REF(up_to);
}
// Assumes T is a field.
// O(up_to) divisions with O(n * m * up_to) additions, subtractions, and multiplications.
// Returns {REF matrix_fixed_base, determinant, rank}
tuple<matrix_fixed_base &, T, int> inplace_REF_field(int up_to = -1){
if(n == 0) return {*this, T{1}, 0};
if(!~up_to) up_to = m;
T det = T{1};
int rank = 0;
for(auto j = 0; j < up_to; ++ j){
int pivot = -1;
for(auto i = rank; i < n; ++ i) if(data[i][j] != T(0)){
pivot = i;
break;
}
if(!~pivot){
det = T(0);
continue;
}
if(rank != pivot){
swap(data[rank], data[pivot]);
det *= -1;
}
det *= data[rank][j];
T inv = 1 / data[rank][j];
for(auto i = rank + 1; i < n; ++ i) if(data[i][j] != T(0)){
T coef = data[i][j] * inv;
for(auto k = j; k < m; ++ k) data[i][k] -= coef * data[rank][k];
}
++ rank;
if(rank == n) break;
}
return {*this, det, rank};
}
// Assumes T is a field.
// O(up_to) divisions with O(n * m * up_to) additions, subtractions, and multiplications.
// Returns {REF matrix_fixed_base, determinant, rank}
tuple<matrix_fixed_base, T, int> REF_field(int up_to = -1) const{
return matrix_fixed_base(*this).inplace_REF_field(up_to);
}
// Assumes T is a field.
// O(up_to) divisions with O(n * m * up_to) additions, subtractions, and multiplications.
// Returns {REF matrix_fixed_base, determinant, rank}
tuple<matrix_fixed_base &, T, int> inplace_RREF_field(int up_to = -1){
if(n == 0) return {*this, T{1}, 0};
auto [mat, det, rank] = inplace_REF_field(up_to);
for(auto i = rank - 1; i >= 0; -- i){
int pivot = find_if(mat[i].begin(), mat[i].end(), [&](const T &x){ return x != T{0}; }) - mat[i].begin();
T inv = T{1} / mat[i][pivot];
for(auto t = 0; t < i; ++ t){
T coef = mat[t][pivot] * inv;
for(auto j = 0; j < m; ++ j) mat[t][j] -= coef * mat[i][j];
}
}
return {mat, det, rank};
}
// Assumes T is a field.
// O(up_to) divisions with O(n * m * up_to) additions, subtractions, and multiplications.
// Returns {REF matrix_fixed_base, determinant, rank}
tuple<matrix_fixed_base, T, int> RREF_field(int up_to = -1) const{
return matrix_fixed_base(*this).inplace_RREF_field(up_to);
}
// Assumes T is either a floating, integral, or a modular type.
// If T is a floating type, O(n) divisions with O(n^3) additions, subtractions, and multiplications.
// Otherwise, O(n^2 * log(size)) divisions with O(n^3) additions, subtractions, and multiplications.
T determinant() const{
assert(n == m);
return get<1>(REF());
}
// Assumes T is a field.
// O(n) divisions with O(n^3) additions, subtractions, and multiplications.
T determinant_field() const{
assert(n == m);
return get<1>(REF_field());
}
// Assumes T is either a floating, integral, or a modular type.
// If T is a floating type, O(n) divisions with O(n^3) additions, subtractions, and multiplications.
// Otherwise, O(n^2 * log(size)) divisions with O(n^3) additions, subtractions, and multiplications.
int rank() const{
return get<2>(REF());
}
// Assumes T is a field.
// O(n) divisions with O(n^3) additions, subtractions, and multiplications.
int rank_field() const{
return get<2>(REF_field());
}
// Regarding the matrix as a system of linear equations by separating first m-1 columns,
// find a solution of the system along with the basis for the nullspace
// Assumes T is a field
// O(n * m^2)
optional<pair<vector<T>, vector<vector<T>>>> solve_right() const{
assert(m >= 1);
auto [rref, _, rank] = RREF_field(m - 1);
for(auto i = rank; i < n; ++ i) if(rref[i][m - 1] != T{0}) return {};
vector<T> res(m - 1);
vector<int> pivot(rank), appear_as_pivot(m - 1);
for(auto i = rank - 1; i >= 0; -- i){
pivot[i] = find_if(rref[i].begin(), rref[i].end(), [&](const T &x){ return x != T{0}; }) - rref[i].begin();
assert(pivot[i] < m - 1);
appear_as_pivot[pivot[i]] = true;
res[pivot[i]] = rref[i][m - 1] / rref[i][pivot[i]];
}
vector<vector<T>> basis;
for(auto j = 0; j < m - 1; ++ j){
if(appear_as_pivot[j]) continue;
vector<T> b(m - 1);
b[j] = T{1};
for(auto i = 0; i < rank; ++ i){
if(rref[i][j] == T{0}) continue;
b[pivot[i]] = -rref[i][j] / rref[i][pivot[i]];
}
basis.push_back(b);
}
return pair{res, basis};
}
// Assumes T is a field.
// O(n) divisions with O(n^3) additions, subtractions, and multiplications.
optional<matrix_fixed_base> inverse() const{
assert(n == m);
if(n == 0) return *this;
auto a = data;
auto res = multiplicative_identity();
for(auto j = 0; j < n; ++ j){
int rank = j, pivot = -1;
if constexpr(is_floating_point_v<T>){
static const T eps = 1e-9;
pivot = rank;
for(auto i = rank + 1; i < n; ++ i) if(abs(a[pivot][j]) < abs(a[i][j])) pivot = i;
if(abs(a[pivot][j]) <= eps) return {};
}
else{
for(auto i = rank; i < n; ++ i) if(a[i][j] != T(0)){
pivot = i;
break;
}
if(!~pivot) return {};
}
swap(a[rank], a[pivot]), swap(res[rank], res[pivot]);
T inv = 1 / a[rank][j];
for(auto k = 0; k < n; ++ k) a[rank][k] *= inv, res[rank][k] *= inv;
for(auto i = 0; i < n; ++ i){
if constexpr(is_floating_point_v<T>){
static const T eps = 1e-9;
if(i != rank && abs(a[i][j]) > eps){
T d = a[i][j];
for(auto k = 0; k < n; ++ k) a[i][k] -= d * a[rank][k], res[i][k] -= d * res[rank][k];
}
}
else if(i != rank && a[i][j] != T(0)){
T d = a[i][j];
for(auto k = 0; k < n; ++ k) a[i][k] -= d * a[rank][k], res[i][k] -= d * res[rank][k];
}
}
}
return res;
}
// O(n * 2^n)
T permanent() const{
assert(n <= 30 && n == m);
T perm = n ? 0 : 1;
array<T, N> sum;
sum.fill(T{0});
for(auto order = 1; order < 1 << n; ++ order){
int j = __lg(order ^ order >> 1 ^ order - 1 ^ order - 1 >> 1), sign = (order ^ order >> 1) & 1 << j ? 1 : -1;
T prod = order & 1 ? -1 : 1;
if((order ^ order >> 1) & 1 << j) for(auto i = 0; i < n; ++ i) prod *= sum[i] += data[i][j];
else for(auto i = 0; i < n; ++ i) prod *= sum[i] -= data[i][j];
perm += prod;
}
return perm * (n & 1 ? -1 : 1);
}
template<class output_stream>
friend output_stream &operator<<(output_stream &out, const matrix_fixed_base &a){
out << "\n";
for(auto i = 0; i < a.n; ++ i){
for(auto j = 0; j < a.m; ++ j) out << a[i][j] << " ";
if(i < a.n - 1) out << "\n";
}
return out;
}
matrix_fixed_base(int n, int m, T init_diagonal = T{0}, T init_off_diagonal = T{0}): n(n), m(m){
assert(0 <= n && n <= N && 0 <= m && m <= M);
for(auto i = 0; i < n; ++ i) for(auto j = 0; j < m; ++ j) data[i][j] = i == j ? init_diagonal : init_off_diagonal;
}
matrix_fixed_base(int n, int m, const array<array<T, M>, N> &a): n(n), m(m), data(a){ assert(0 <= n && n <= N && 0 <= m && m <= M); }
matrix_fixed_base(int n, int m, const array<T, N * M> &a): n(n), m(m){
assert(0 <= n && n <= N && 0 <= m && m <= M);
for(auto i = 0; i < n; ++ i) for(auto j = 0; j < m; ++ j) data[i][j] = a[m * i + j];
}
static matrix_fixed_base additive_identity(int n, int m){
return matrix_fixed_base(n, m, T{0}, T{0});
}
static matrix_fixed_base multiplicative_identity(int n, int m){
return matrix_fixed_base(n, m, T{1}, T{0});
}
};
template<class T>
using matrix = matrix_fixed_base<T, 2, 2>;
int main(){
cin.tie(0)->sync_with_stdio(0);
cin.exceptions(ios::badbit | ios::failbit);
using M = matrix<modular>;
string n;
cin >> n;
{
ranges::reverse(n);
int i = 0;
++ n[i];
while(i < (int)n.size() - 1 && n[i] == '2'){
n[i] = '0';
++ n[i + 1];
}
if(n.back() == '2'){
n.back() = '0';
n += '1';
}
}
modular res = 0, base = 1;
const M m0(2, 2, array{3_m, 1_m, 0_m, 2_m});
const M m1(2, 2, array{1_m, 1_m, 2_m, 2_m});
M p0 = m0;
M p1 = m1;
vector<int> p_exp((int)n.size());
for(auto i = (int)n.size() - 2; i >= 0; -- i){
p_exp[i] = (p_exp[i + 1] * 2 + (n[i + 1] - '0')) % (modular::mod() - 1);
}
M extra0 = M::multiplicative_identity(2, 2), extra1 = extra0;
for(auto bit = 0; bit < (int)n.size(); ++ bit, base *= 2){
M p = p1 * p0;
assert(p[0][0] == p[0][1] && p[1][0] == p[1][1]);
if(p_exp[bit] == 0){
p = M::multiplicative_identity(2, 2);
}
else{
p *= (p[0][0] + p[1][0]).power(p_exp[bit] - 1);
}
if(n[bit] == '0'){
p = extra0 * p;
}
else{
p = extra1 * p0 * p;
}
res += base * p[1][0] / 3;
if(n[bit] == '1'){
extra0 *= p0;
extra1 *= p1;
}
p0 *= p0;
p1 *= p1;
}
cout << res << "\n";
return 0;
}
/*
*/