結果
| 問題 | No.1810 RGB Biscuits |
| ユーザー |
 nok0
|
| 提出日時 | 2022-01-14 21:38:01 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 22 ms / 2,000 ms |
| コード長 | 33,980 bytes |
| コンパイル時間 | 3,014 ms |
| コンパイル使用メモリ | 223,892 KB |
| 実行使用メモリ | 5,248 KB |
| 最終ジャッジ日時 | 2024-11-20 08:31:48 |
| 合計ジャッジ時間 | 3,592 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge4 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 2 ms
5,248 KB |
| testcase_01 | AC | 2 ms
5,248 KB |
| testcase_02 | AC | 2 ms
5,248 KB |
| testcase_03 | AC | 2 ms
5,248 KB |
| testcase_04 | AC | 2 ms
5,248 KB |
| testcase_05 | AC | 19 ms
5,248 KB |
| testcase_06 | AC | 21 ms
5,248 KB |
| testcase_07 | AC | 22 ms
5,248 KB |
| testcase_08 | AC | 21 ms
5,248 KB |
| testcase_09 | AC | 21 ms
5,248 KB |
| testcase_10 | AC | 14 ms
5,248 KB |
| testcase_11 | AC | 3 ms
5,248 KB |
| testcase_12 | AC | 2 ms
5,248 KB |
| testcase_13 | AC | 3 ms
5,248 KB |
| testcase_14 | AC | 5 ms
5,248 KB |
| testcase_15 | AC | 2 ms
5,248 KB |
| testcase_16 | AC | 3 ms
5,248 KB |
| testcase_17 | AC | 11 ms
5,248 KB |
| testcase_18 | AC | 11 ms
5,248 KB |
| testcase_19 | AC | 2 ms
5,248 KB |
| testcase_20 | AC | 2 ms
5,248 KB |
| testcase_21 | AC | 5 ms
5,248 KB |
ソースコード
#line 1 "e.cpp"
/**
* author: nok0
* created: 2022.01.14 21:32:08
**/
#line 1 "/Users/nok0/Documents/Programming/nok0/cftemp.hpp"
#include <bits/stdc++.h>
using namespace std;
#pragma region Macros
// rep macro
#define foa(v, a) for(auto &v : a)
#define REPname(a, b, c, d, e, ...) e
#define REP(...) REPname(__VA_ARGS__, REP3, REP2, REP1, REP0)(__VA_ARGS__)
#define REP0(x) for(int i = 0; i < (x); ++i)
#define REP1(i, x) for(int i = 0; i < (x); ++i)
#define REP2(i, l, r) for(int i = (l); i < (r); ++i)
#define REP3(i, l, r, c) for(int i = (l); i < (r); i += (c))
#define REPSname(a, b, c, ...) c
#define REPS(...) REPSname(__VA_ARGS__, REPS1, REPS0)(__VA_ARGS__)
#define REPS0(x) for(int i = 1; i <= (x); ++i)
#define REPS1(i, x) for(int i = 1; i <= (x); ++i)
#define RREPname(a, b, c, d, e, ...) e
#define RREP(...) RREPname(__VA_ARGS__, RREP3, RREP2, RREP1, RREP0)(__VA_ARGS__)
#define RREP0(x) for(int i = (x)-1; i >= 0; --i)
#define RREP1(i, x) for(int i = (x)-1; i >= 0; --i)
#define RREP2(i, r, l) for(int i = (r)-1; i >= (l); --i)
#define RREP3(i, r, l, c) for(int i = (r)-1; i >= (l); i -= (c))
#define RREPSname(a, b, c, ...) c
#define RREPS(...) RREPSname(__VA_ARGS__, RREPS1, RREPS0)(__VA_ARGS__)
#define RREPS0(x) for(int i = (x); i >= 1; --i)
#define RREPS1(i, x) for(int i = (x); i >= 1; --i)
// name macro
#define pb push_back
#define eb emplace_back
#define SZ(x) ((int)(x).size())
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define popcnt(x) __builtin_popcountll(x)
template <class T = int>
using V = std::vector<T>;
template <class T = int>
using VV = std::vector<std::vector<T>>;
template <class T>
using pqup = std::priority_queue<T, std::vector<T>, std::greater<T>>;
using ll = long long;
using ld = long double;
using int128 = __int128_t;
using pii = std::pair<int, int>;
using pll = std::pair<long long, long long>;
// input macro
template <class T, class U>
std::istream &operator>>(std::istream &is, std::pair<T, U> &p) {
is >> p.first >> p.second;
return is;
}
template <class T>
std::istream &operator>>(std::istream &is, std::vector<T> &v) {
for(T &i : v) is >> i;
return is;
}
std::istream &operator>>(std::istream &is, __int128_t &a) {
std::string s;
is >> s;
__int128_t ret = 0;
for(int i = 0; i < s.length(); i++)
if('0' <= s[i] and s[i] <= '9')
ret = 10 * ret + s[i] - '0';
a = ret * (s[0] == '-' ? -1 : 1);
return is;
}
namespace scanner {
void scan(int &a) { std::cin >> a; }
void scan(long long &a) { std::cin >> a; }
void scan(std::string &a) { std::cin >> a; }
void scan(char &a) { std::cin >> a; }
void scan(char a[]) { std::scanf("%s", a); }
void scan(double &a) { std::cin >> a; }
void scan(long double &a) { std::cin >> a; }
template <class T, class U>
void scan(std::pair<T, U> &p) { std::cin >> p; }
template <class T>
void scan(std::vector<T> &a) { std::cin >> a; }
void INPUT() {}
template <class Head, class... Tail>
void INPUT(Head &head, Tail &...tail) {
scan(head);
INPUT(tail...);
}
} // namespace scanner
#define VEC(type, name, size) \
std::vector<type> name(size); \
scanner::INPUT(name)
#define VVEC(type, name, h, w) \
std::vector<std::vector<type>> name(h, std::vector<type>(w)); \
scanner::INPUT(name)
#define INT(...) \
int __VA_ARGS__; \
scanner::INPUT(__VA_ARGS__)
#define LL(...) \
long long __VA_ARGS__; \
scanner::INPUT(__VA_ARGS__)
#define STR(...) \
std::string __VA_ARGS__; \
scanner::INPUT(__VA_ARGS__)
#define CHAR(...) \
char __VA_ARGS__; \
scanner::INPUT(__VA_ARGS__)
#define DOUBLE(...) \
double __VA_ARGS__; \
scanner::INPUT(__VA_ARGS__)
#define LD(...) \
long double __VA_ARGS__; \
scanner::INPUT(__VA_ARGS__)
// output-macro
template <class T, class U>
std::ostream &operator<<(std::ostream &os, const std::pair<T, U> &p) {
os << p.first << " " << p.second;
return os;
}
template <class T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &a) {
for(int i = 0; i < int(a.size()); ++i) {
if(i) os << " ";
os << a[i];
}
return os;
}
std::ostream &operator<<(std::ostream &dest, __int128_t &value) {
std::ostream::sentry s(dest);
if(s) {
__uint128_t tmp = value < 0 ? -value : value;
char buffer[128];
char *d = std::end(buffer);
do {
--d;
*d = "0123456789"[tmp % 10];
tmp /= 10;
} while(tmp != 0);
if(value < 0) {
--d;
*d = '-';
}
int len = std::end(buffer) - d;
if(dest.rdbuf()->sputn(d, len) != len) {
dest.setstate(std::ios_base::badbit);
}
}
return dest;
}
template <class T>
void print(const T a) { std::cout << a << '\n'; }
template <class Head, class... Tail>
void print(Head H, Tail... T) {
std::cout << H << ' ';
print(T...);
}
template <class T>
void printel(const T a) { std::cout << a << '\n'; }
template <class T>
void printel(const std::vector<T> &a) {
for(const auto &v : a)
std::cout << v << '\n';
}
template <class Head, class... Tail>
void printel(Head H, Tail... T) {
std::cout << H << '\n';
printel(T...);
}
void Yes(const bool b = true) { std::cout << (b ? "Yes\n" : "No\n"); }
void No() { std::cout << "No\n"; }
void YES(const bool b = true) { std::cout << (b ? "YES\n" : "NO\n"); }
void NO() { std::cout << "NO\n"; }
void err(const bool b = true) {
if(b) {
std::cout << "-1\n", exit(0);
}
}
//debug macro
namespace debugger {
template <class T>
void view(const std::vector<T> &a) {
std::cerr << "{ ";
for(const auto &v : a) {
std::cerr << v << ", ";
}
std::cerr << "\b\b }";
}
template <class T>
void view(const std::vector<std::vector<T>> &a) {
std::cerr << "{\n";
for(const auto &v : a) {
std::cerr << "\t";
view(v);
std::cerr << "\n";
}
std::cerr << "}";
}
template <class T, class U>
void view(const std::vector<std::pair<T, U>> &a) {
std::cerr << "{\n";
for(const auto &p : a) std::cerr << "\t(" << p.first << ", " << p.second << ")\n";
std::cerr << "}";
}
template <class T, class U>
void view(const std::map<T, U> &m) {
std::cerr << "{\n";
for(const auto &p : m) std::cerr << "\t[" << p.first << "] : " << p.second << "\n";
std::cerr << "}";
}
template <class T, class U>
void view(const std::pair<T, U> &p) { std::cerr << "(" << p.first << ", " << p.second << ")"; }
template <class T>
void view(const std::set<T> &s) {
std::cerr << "{ ";
for(auto &v : s) {
view(v);
std::cerr << ", ";
}
std::cerr << "\b\b }";
}
template <class T>
void view(const T &e) { std::cerr << e; }
} // namespace debugger
#ifdef LOCAL
void debug_out() {}
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
debugger::view(H);
std::cerr << ", ";
debug_out(T...);
}
#define debug(...) \
do { \
std::cerr << __LINE__ << " [" << #__VA_ARGS__ << "] : ["; \
debug_out(__VA_ARGS__); \
std::cerr << "\b\b]\n"; \
} while(false)
#else
#define debug(...) (void(0))
#endif
// vector macro
template <class T>
int lb(const std::vector<T> &a, const T x) { return std::distance((a).begin(), std::lower_bound((a).begin(), (a).end(), (x))); }
template <class T>
int ub(const std::vector<T> &a, const T x) { return std::distance((a).begin(), std::upper_bound((a).begin(), (a).end(), (x))); }
template <class T>
void UNIQUE(std::vector<T> &a) {
std::sort(a.begin(), a.end());
a.erase(std::unique(a.begin(), a.end()), a.end());
}
template <class T>
std::vector<T> press(std::vector<T> &a) {
auto res = a;
UNIQUE(res);
for(auto &v : a)
v = lb(res, v);
return res;
}
#define SORTname(a, b, c, ...) c
#define SORT(...) SORTname(__VA_ARGS__, SORT1, SORT0, ...)(__VA_ARGS__)
#define SORT0(a) std::sort((a).begin(), (a).end())
#define SORT1(a, c) std::sort((a).begin(), (a).end(), [](const auto x, const auto y) { return x c y; })
template <class T>
void ADD(std::vector<T> &a, const T x = 1) {
for(auto &v : a) v += x;
}
template <class T>
void SUB(std::vector<T> &a, const T x = 1) {
for(auto &v : a) v -= x;
}
std::vector<std::pair<char, int>> rle(const string &s) {
int n = s.size();
std::vector<std::pair<char, int>> ret;
for(int l = 0; l < n;) {
int r = l + 1;
for(; r < n and s[l] == s[r]; r++) {}
ret.emplace_back(s[l], r - l);
l = r;
}
return ret;
}
template <class T>
std::vector<std::pair<T, int>> rle(const std::vector<T> &v) {
int n = v.size();
std::vector<std::pair<T, int>> ret;
for(int l = 0; l < n;) {
int r = l + 1;
for(; r < n and v[l] == v[r]; r++) {}
ret.emplace_back(v[l], r - l);
l = r;
}
return ret;
}
std::vector<int> iota(int n) {
std::vector<int> p(n);
std::iota(p.begin(), p.end(), 0);
return p;
}
template <class T>
struct cum_vector {
public:
cum_vector() = default;
template <class U>
cum_vector(const std::vector<U> &vec) : cum((int)vec.size() + 1) {
for(int i = 0; i < (int)vec.size(); i++)
cum[i + 1] = cum[i] + vec[i];
}
T prod(int l, int r) {
return cum[r] - cum[l];
}
private:
std::vector<T> cum;
};
// math macro
template <class T, class U>
inline bool chmin(T &a, const U &b) { return a > b ? a = b, true : false; }
template <class T, class U>
inline bool chmax(T &a, const U &b) { return a < b ? a = b, true : false; }
template <class T>
T divup(T x, T y) { return (x + y - 1) / y; }
template <class T>
T POW(T a, long long n) {
T ret = 1;
while(n) {
if(n & 1) ret *= a;
a *= a;
n >>= 1;
}
return ret;
}
// modpow
long long POW(long long a, long long n, const int mod) {
long long ret = 1;
a = (a % mod + mod) % mod;
while(n) {
if(n & 1) (ret *= a) %= mod;
(a *= a) %= mod;
n >>= 1;
}
return ret;
}
template <class T, class F>
T bin_search(T ok, T ng, const F &f) {
while(abs(ok - ng) > 1) {
T mid = (ok + ng) >> 1;
(f(mid) ? ok : ng) = mid;
}
return ok;
}
template <class T, class F>
T bin_search(T ok, T ng, const F &f, int loop) {
for(int i = 0; i < loop; i++) {
T mid = (ok + ng) / 2;
(f(mid) ? ok : ng) = mid;
}
return ok;
}
// others
struct fast_io {
fast_io() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
cout << fixed << setprecision(15);
}
} fast_io_;
const int inf = 1e9;
const ll INF = 1e18;
#pragma endregion
void main_();
int main() {
main_();
return 0;
}
#line 5 "/Users/nok0/Documents/Programming/nok0/math/matrix.hpp"
template <class T>
struct matrix {
private:
std::vector<std::vector<T>> A;
static matrix I(size_t n) {
matrix mat(n);
for(int i = 0; i < n; i++) mat[i][i] = 1;
return mat;
}
public:
matrix() = default;
matrix(std::vector<std::vector<T>> &vvec) { A = vvec; }
matrix(size_t n, size_t m) : A(n, std::vector<T>(m, 0)) {}
matrix(size_t n, size_t m, T init) : A(n, std::vector<T>(m, init)) {}
matrix(size_t n, std::vector<T> &vec) : A(n, vec) {}
matrix(size_t n) : A(n, std::vector<T>(n, 0)) {}
size_t height() const { return A.size(); }
size_t width() const { return A[0].size(); }
inline const std::vector<T> &operator[](int k) const {
return A[k];
}
inline std::vector<T> &operator[](int k) {
return A[k];
}
matrix &operator+=(const matrix &B) {
size_t n = height(), m = width();
assert(n == B.height() and m == B.width());
for(int i = 0; i < n; i++)
for(int j = 0; j < m; j++)
(*this)[i][j] += B[i][j];
return *this;
}
matrix &operator-=(const matrix &B) {
size_t n = height(), m = width();
assert(n == B.height() and m == B.width());
for(int i = 0; i < n; i++)
for(int j = 0; j < m; j++)
(*this)[i][j] -= B[i][j];
return *this;
}
matrix &operator*=(const matrix &B) {
size_t n = height(), m = B.width(), p = width();
assert(p == B.height());
std::vector<std::vector<T>> C(n, std::vector<T>(m, 0));
for(int i = 0; i < n; i++)
for(int j = 0; j < m; j++)
for(int k = 0; k < p; k++)
C[i][j] += (*this)[i][k] * B[k][j];
A.swap(C);
return *this;
}
matrix &operator^=(long long k) {
matrix B = matrix::I(height());
while(k > 0) {
if(k & 1) B *= (*this);
*this *= *this;
k >>= 1ll;
}
A.swap(B.A);
return *this;
}
bool operator==(const matrix &B) {
size_t n = height(), m = width();
if(n != B.height() or m != B.width()) return false;
for(int i = 0; i < n; i++)
for(int j = 0; j < m; j++)
if((*this)[i][j] != B[i][j]) return false;
return true;
}
matrix operator+(const matrix &B) const {
return (matrix(*this) += B);
}
matrix operator-(const matrix &B) const {
return (matrix(*this) -= B);
}
matrix operator*(const matrix &B) const {
return (matrix(*this) *= B);
}
matrix operator^(const long long &k) const {
return (matrix(*this) ^= k);
}
matrix &operator+=(const T &t) {
int n = height(), m = width();
for(int i = 0; i < n; i++)
for(int j = 0; j < m; j++)
(*this)[i][j] += t;
return *this;
}
matrix &operator-=(const T &t) {
int n = height(), m = width();
for(int i = 0; i < n; i++)
for(int j = 0; j < m; j++)
(*this)[i][j] -= t;
return *this;
}
matrix &operator*=(const T &t) {
int n = height(), m = width();
for(int i = 0; i < n; i++)
for(int j = 0; j < m; j++)
(*this)[i][j] *= t;
return *this;
}
matrix &operator/=(const T &t) {
int n = height(), m = width();
for(int i = 0; i < n; i++)
for(int j = 0; j < m; j++)
(*this)[i][j] /= t;
return *this;
}
matrix operator+(const T &t) const {
return (matrix(*this) += t);
}
matrix operator-(const T &t) const {
return (matrix(*this) -= t);
}
matrix operator*(const T &t) const {
return (matrix(*this) *= t);
}
matrix operator/(const T &t) const {
return (matrix(*this) /= t);
}
friend std::ostream &operator<<(std::ostream &os, matrix &p) {
size_t n = p.height(), m = p.width();
for(int i = 0; i < n; i++) {
os << '[';
for(int j = 0; j < m; j++)
os << p[i][j] << (j == m - 1 ? "]\n" : ",");
}
return (os);
}
T determinant() {
matrix B(*this);
size_t n = height(), m = width();
assert(n == m);
T ret = 1;
for(int i = 0; i < n; i++) {
int idx = -1;
for(int j = i; j < n; j++)
if(B[j][i] != 0) idx = j;
if(idx == -1) return 0;
if(i != idx) {
ret *= -1;
swap(B[i], B[idx]);
}
ret *= B[i][i];
T vv = B[i][i];
for(int j = 0; j < n; j++) B[i][j] /= vv;
for(int j = i + 1; j < n; j++) {
T a = B[j][i];
for(int k = 0; k < n; k++) {
B[j][k] -= B[i][k] * a;
}
}
}
return ret;
}
matrix inv() {
int n = height();
if(determinant() == T(0)) return matrix(0);
matrix a(*(this)), l = I(n), u(n);
for(int j = 0; j < n; j++) u[0][j] = a[0][j];
for(int j = 1; j < n; j++) l[j][0] = a[j][0] / u[0][0];
for(int k = 1; k < n; k++) {
for(int j = k; j < n; j++)
for(int i = 0; i < k; i++) a[j][k] -= l[j][i] * u[i][k];
u[k][k] = a[k][k];
for(int j = k + 1; j < n; j++) {
u[k][j] = a[k][j];
for(int i = 0; i < k; i++)
u[k][j] -= l[k][i] * u[i][j];
}
for(int j = k + 1; j < n; j++) l[j][k] = a[j][k] / u[k][k];
}
matrix x(n), y = I(n);
for(int i = 0; i < n; i++)
for(int j = 0; j < n; j++) {
for(int k = 0; k < j; k++) y[j][i] -= l[j][k] * y[k][i];
}
T sigma;
for(int h = 0; h < n; h++)
for(int i = n - 1; i >= 0; i--) {
sigma = y[i][h];
for(int j = i + 1; j < n; j++) {
sigma -= u[i][j] * x[j][h];
}
x[i][h] = sigma / u[i][i];
}
return move(x);
}
};
#line 1 "/Users/nok0/Documents/Programming/nok0/atcoder/modint.hpp"
#line 6 "/Users/nok0/Documents/Programming/nok0/atcoder/modint.hpp"
#include <type_traits>
#ifdef _MSC_VER
#include <intrin.h>
#endif
#line 1 "/Users/nok0/Documents/Programming/nok0/atcoder/internal_math.hpp"
#line 5 "/Users/nok0/Documents/Programming/nok0/atcoder/internal_math.hpp"
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder {
namespace internal {
// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m) {
x %= m;
if (x < 0) x += m;
return x;
}
// Fast modular multiplication by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
unsigned int _m;
unsigned long long im;
// @param m `1 <= m < 2^31`
explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
// @return m
unsigned int umod() const { return _m; }
// @param a `0 <= a < m`
// @param b `0 <= b < m`
// @return `a * b % m`
unsigned int mul(unsigned int a, unsigned int b) const {
// [1] m = 1
// a = b = im = 0, so okay
// [2] m >= 2
// im = ceil(2^64 / m)
// -> im * m = 2^64 + r (0 <= r < m)
// let z = a*b = c*m + d (0 <= c, d < m)
// a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
// c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2
// ((ab * im) >> 64) == c or c + 1
unsigned long long z = a;
z *= b;
#ifdef _MSC_VER
unsigned long long x;
_umul128(z, im, &x);
#else
unsigned long long x =
(unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
unsigned int v = (unsigned int)(z - x * _m);
if (_m <= v) v += _m;
return v;
}
};
// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
if (m == 1) return 0;
unsigned int _m = (unsigned int)(m);
unsigned long long r = 1;
unsigned long long y = safe_mod(x, m);
while (n) {
if (n & 1) r = (r * y) % _m;
y = (y * y) % _m;
n >>= 1;
}
return r;
}
// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
constexpr bool is_prime_constexpr(int n) {
if (n <= 1) return false;
if (n == 2 || n == 7 || n == 61) return true;
if (n % 2 == 0) return false;
long long d = n - 1;
while (d % 2 == 0) d /= 2;
constexpr long long bases[3] = {2, 7, 61};
for (long long a : bases) {
long long t = d;
long long y = pow_mod_constexpr(a, t, n);
while (t != n - 1 && y != 1 && y != n - 1) {
y = y * y % n;
t <<= 1;
}
if (y != n - 1 && t % 2 == 0) {
return false;
}
}
return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);
// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
a = safe_mod(a, b);
if (a == 0) return {b, 0};
// Contracts:
// [1] s - m0 * a = 0 (mod b)
// [2] t - m1 * a = 0 (mod b)
// [3] s * |m1| + t * |m0| <= b
long long s = b, t = a;
long long m0 = 0, m1 = 1;
while (t) {
long long u = s / t;
s -= t * u;
m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b
// [3]:
// (s - t * u) * |m1| + t * |m0 - m1 * u|
// <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
// = s * |m1| + t * |m0| <= b
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
// by [3]: |m0| <= b/g
// by g != b: |m0| < b/g
if (m0 < 0) m0 += b / s;
return {s, m0};
}
// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
constexpr int primitive_root_constexpr(int m) {
if (m == 2) return 1;
if (m == 167772161) return 3;
if (m == 469762049) return 3;
if (m == 754974721) return 11;
if (m == 998244353) return 3;
int divs[20] = {};
divs[0] = 2;
int cnt = 1;
int x = (m - 1) / 2;
while (x % 2 == 0) x /= 2;
for (int i = 3; (long long)(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 (int g = 2;; g++) {
bool ok = true;
for (int i = 0; i < cnt; i++) {
if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
ok = false;
break;
}
}
if (ok) return g;
}
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);
// @param n `n < 2^32`
// @param m `1 <= m < 2^32`
// @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)
unsigned long long floor_sum_unsigned(unsigned long long n,
unsigned long long m,
unsigned long long a,
unsigned long long b) {
unsigned long long ans = 0;
while (true) {
if (a >= m) {
ans += n * (n - 1) / 2 * (a / m);
a %= m;
}
if (b >= m) {
ans += n * (b / m);
b %= m;
}
unsigned long long y_max = a * n + b;
if (y_max < m) break;
// y_max < m * (n + 1)
// floor(y_max / m) <= n
n = (unsigned long long)(y_max / m);
b = (unsigned long long)(y_max % m);
std::swap(m, a);
}
return ans;
}
} // namespace internal
} // namespace atcoder
#line 1 "/Users/nok0/Documents/Programming/nok0/atcoder/internal_type_traits.hpp"
#line 7 "/Users/nok0/Documents/Programming/nok0/atcoder/internal_type_traits.hpp"
namespace atcoder {
namespace internal {
#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value ||
std::is_same<T, __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int128 =
typename std::conditional<std::is_same<T, __uint128_t>::value ||
std::is_same<T, unsigned __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using make_unsigned_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value,
__uint128_t,
unsigned __int128>;
template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
is_signed_int128<T>::value ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
std::is_signed<T>::value) ||
is_signed_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<(is_integral<T>::value &&
std::is_unsigned<T>::value) ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<
is_signed_int128<T>::value,
make_unsigned_int128<T>,
typename std::conditional<std::is_signed<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type>::type;
#else
template <class T> using is_integral = typename std::is_integral<T>;
template <class T>
using is_signed_int =
typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<is_integral<T>::value &&
std::is_unsigned<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type;
#endif
template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
template <class T> using to_unsigned_t = typename to_unsigned<T>::type;
} // namespace internal
} // namespace atcoder
#line 14 "/Users/nok0/Documents/Programming/nok0/atcoder/modint.hpp"
namespace atcoder {
namespace internal {
struct modint_base {};
struct static_modint_base : modint_base {};
template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;
} // namespace internal
template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : internal::static_modint_base {
using mint = static_modint;
public:
static constexpr int mod() { return m; }
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
static_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
static_modint(T v) {
long long x = (long long)(v % (long long)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
static_modint(T v) {
_v = (unsigned int)(v % umod());
}
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
mint& operator*=(const mint& rhs) {
unsigned long long z = _v;
z *= rhs._v;
_v = (unsigned int)(z % umod());
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
if (prime) {
assert(_v);
return pow(umod() - 2);
} else {
auto eg = internal::inv_gcd(_v, m);
assert(eg.first == 1);
return eg.second;
}
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static constexpr unsigned int umod() { return m; }
static constexpr bool prime = internal::is_prime<m>;
};
template <int id> struct dynamic_modint : internal::modint_base {
using mint = dynamic_modint;
public:
static int mod() { return (int)(bt.umod()); }
static void set_mod(int m) {
assert(1 <= m);
bt = internal::barrett(m);
}
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
dynamic_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
dynamic_modint(T v) {
long long x = (long long)(v % (long long)(mod()));
if (x < 0) x += mod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
dynamic_modint(T v) {
_v = (unsigned int)(v % mod());
}
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v += mod() - rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator*=(const mint& rhs) {
_v = bt.mul(_v, rhs._v);
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
auto eg = internal::inv_gcd(_v, mod());
assert(eg.first == 1);
return eg.second;
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static internal::barrett bt;
static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt(998244353);
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
namespace internal {
template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;
template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;
template <class> struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};
template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;
} // namespace internal
} // namespace atcoder
#line 4 "/Users/nok0/Documents/Programming/nok0/math/factorial.hpp"
#line 6 "/Users/nok0/Documents/Programming/nok0/math/factorial.hpp"
template <class T>
struct factorial {
public:
static int MAX;
static std::vector<T> fac, finv, inv;
factorial() {}
T binom(int n, int r) {
if(n < r or n < 0 or r < 0) return T(0);
assert(n < MAX);
return fac[n] * finv[r] * finv[n - r];
}
T large_binom(int n, int r) {
if(n < r or n < 0 or r < 0) return T(0);
assert(r < MAX);
T ret = finv[r];
for(int i = 1; i <= r; ++i)
ret *= (n + 1 - i);
return ret;
}
static void set_size(int n = 3000000) {
MAX = (n > 1 ? n : 1) + 1;
if((int)fac.size() >= MAX) return;
fac.resize(MAX);
finv.resize(MAX);
inv.resize(MAX);
const int MOD = T::mod();
fac[0] = fac[1] = 1;
finv[0] = finv[1] = 1;
inv[1] = 1;
for(int i = 2; i < MAX; i++) {
fac[i] = fac[i - 1] * i;
inv[i] = (T)MOD - inv[MOD % i] * (MOD / i);
finv[i] = finv[i - 1] * inv[i];
}
}
};
template <class T>
int factorial<T>::MAX = 0;
template <class T>
std::vector<T> factorial<T>::fac;
template <class T>
std::vector<T> factorial<T>::finv;
template <class T>
std::vector<T> factorial<T>::inv;
#line 3 "/Users/nok0/Documents/Programming/nok0/math/modint_iostream.hpp"
#line 5 "/Users/nok0/Documents/Programming/nok0/math/modint_iostream.hpp"
template <int m>
std::istream &std::operator>>(std::istream &is, atcoder::static_modint<m> &a) {
long long v;
is >> v;
a = v;
return is;
}
template <int m>
std::istream &std::operator>>(std::istream &is, atcoder::dynamic_modint<m> &a) {
long long v;
is >> v;
a = v;
return is;
}
template <int m>
std::ostream &std::operator<<(std::ostream &os, const atcoder::static_modint<m> &a) { return os << a.val(); }
template <int m>
std::ostream &std::operator<<(std::ostream &os, const atcoder::dynamic_modint<m> &a) { return os << a.val(); }
#line 8 "e.cpp"
using mint = atcoder::modint1000000007;
void main_() {
INT(a, b, n);
VEC(ll, t, n);
matrix<mint> base(3, 1), odd(3), even(3);
base[0][0] = 1, base[1][0] = 1;
odd[0] = {1, 0, 0};
odd[1] = {0, 1, 0};
odd[2] = {a, b, 1};
even[0] = {0, 0, 1};
even[1] = {1, 0, 0};
even[2] = {0, 0, 0};
auto oe = even * odd;
REP(i, n) {
auto res = base;
res = (oe ^ (t[i] / 2)) * res;
if(t[i] & 1) res = odd * res;
print(res[0][0] + res[1][0] + res[2][0]);
}
}