結果
| 問題 | No.1112 冥界の音楽 |
| ユーザー |
 ebi_fly
|
| 提出日時 | 2024-06-26 21:50:37 |
| 言語 | C++23 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 3 ms / 2,000 ms |
| コード長 | 31,802 bytes |
| コンパイル時間 | 4,044 ms |
| コンパイル使用メモリ | 278,028 KB |
| 実行使用メモリ | 6,944 KB |
| 最終ジャッジ日時 | 2024-06-26 21:50:43 |
| 合計ジャッジ時間 | 5,340 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge5 |
（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
6,816 KB |
| testcase_01 | AC | 2 ms
6,940 KB |
| testcase_02 | AC | 2 ms
6,940 KB |
| testcase_03 | AC | 2 ms
6,944 KB |
| testcase_04 | AC | 2 ms
6,940 KB |
| testcase_05 | AC | 2 ms
6,940 KB |
| testcase_06 | AC | 2 ms
6,940 KB |
| testcase_07 | AC | 2 ms
6,940 KB |
| testcase_08 | AC | 2 ms
6,940 KB |
| testcase_09 | AC | 2 ms
6,940 KB |
| testcase_10 | AC | 2 ms
6,944 KB |
| testcase_11 | AC | 2 ms
6,944 KB |
| testcase_12 | AC | 2 ms
6,944 KB |
| testcase_13 | AC | 2 ms
6,940 KB |
| testcase_14 | AC | 2 ms
6,944 KB |
| testcase_15 | AC | 2 ms
6,944 KB |
| testcase_16 | AC | 2 ms
6,944 KB |
| testcase_17 | AC | 2 ms
6,940 KB |
| testcase_18 | AC | 2 ms
6,940 KB |
| testcase_19 | AC | 2 ms
6,944 KB |
| testcase_20 | AC | 2 ms
6,940 KB |
| testcase_21 | AC | 2 ms
6,940 KB |
| testcase_22 | AC | 3 ms
6,944 KB |
| testcase_23 | AC | 2 ms
6,940 KB |
| testcase_24 | AC | 2 ms
6,944 KB |
| testcase_25 | AC | 2 ms
6,940 KB |
| testcase_26 | AC | 2 ms
6,940 KB |
| testcase_27 | AC | 2 ms
6,940 KB |
| testcase_28 | AC | 2 ms
6,944 KB |
| testcase_29 | AC | 2 ms
6,944 KB |
| testcase_30 | AC | 3 ms
6,940 KB |
| testcase_31 | AC | 2 ms
6,944 KB |
| testcase_32 | AC | 3 ms
6,940 KB |
| testcase_33 | AC | 2 ms
6,940 KB |
| testcase_34 | AC | 2 ms
6,944 KB |
| testcase_35 | AC | 2 ms
6,940 KB |
| testcase_36 | AC | 2 ms
6,944 KB |
ソースコード
#line 2 "convolution/convolution.hpp"
#include <algorithm>
#include <bit>
#include <vector>
#line 2 "convolution/ntt.hpp"
#line 4 "convolution/ntt.hpp"
#include <array>
#line 6 "convolution/ntt.hpp"
#include <cassert>
#line 8 "convolution/ntt.hpp"
#line 2 "math/internal_math.hpp"
#line 4 "math/internal_math.hpp"
namespace ebi {
namespace internal {
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;
if (m == 880803841) return 26;
if (m == 924844033) return 5;
return -1;
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);
} // namespace internal
} // namespace ebi
#line 2 "modint/base.hpp"
#include <concepts>
#include <iostream>
#include <utility>
namespace ebi {
template <class T>
concept Modint = requires(T a, T b) {
a + b;
a - b;
a * b;
a / b;
a.inv();
a.val();
a.pow(std::declval<long long>());
T::mod();
};
template <Modint mint> std::istream &operator>>(std::istream &os, mint &a) {
long long x;
os >> x;
a = x;
return os;
}
template <Modint mint>
std::ostream &operator<<(std::ostream &os, const mint &a) {
return os << a.val();
}
} // namespace ebi
#line 2 "template/int_alias.hpp"
#include <cstdint>
namespace ebi {
using ld = long double;
using std::size_t;
using i8 = std::int8_t;
using u8 = std::uint8_t;
using i16 = std::int16_t;
using u16 = std::uint16_t;
using i32 = std::int32_t;
using u32 = std::uint32_t;
using i64 = std::int64_t;
using u64 = std::uint64_t;
using i128 = __int128_t;
using u128 = __uint128_t;
} // namespace ebi
#line 12 "convolution/ntt.hpp"
namespace ebi {
namespace internal {
template <Modint mint, int g = internal::primitive_root<mint::mod()>>
struct ntt_info {
static constexpr int rank2 =
std::countr_zero((unsigned int)(mint::mod() - 1));
std::array<mint, rank2 + 1> root, inv_root;
ntt_info() {
root[rank2] = mint(g).pow((mint::mod() - 1) >> rank2);
inv_root[rank2] = root[rank2].inv();
for (int i = rank2 - 1; i >= 0; i--) {
root[i] = root[i + 1] * root[i + 1];
inv_root[i] = inv_root[i + 1] * inv_root[i + 1];
}
}
};
template <Modint mint> void fft2(std::vector<mint>& a) {
static const ntt_info<mint> info;
int n = int(a.size());
int bit_size = std::countr_zero(a.size());
assert(n == 1 << bit_size);
for (int bit = bit_size - 1; bit >= 0; bit--) {
int m = 1 << bit;
for (int i = 0; i < n; i += 2 * m) {
mint w = 1;
for (int j = 0; j < m; j++) {
mint p1 = a[i + j];
mint p2 = a[i + j + m];
a[i + j] = p1 + p2;
a[i + j + m] = (p1 - p2) * w;
w *= info.root[bit + 1];
}
}
}
}
template <Modint mint> void ifft2(std::vector<mint>& a) {
static const ntt_info<mint> info;
int n = int(a.size());
int bit_size = std::countr_zero(a.size());
assert(n == 1 << bit_size);
for (int bit = 0; bit < bit_size; bit++) {
for (int i = 0; i < n / (1 << (bit + 1)); i++) {
mint w = 1;
for (int j = 0; j < (1 << bit); j++) {
int idx = i * (1 << (bit + 1)) + j;
int jdx = idx + (1 << bit);
mint p1 = a[idx];
mint p2 = w * a[jdx];
a[idx] = p1 + p2;
a[jdx] = p1 - p2;
w *= info.inv_root[bit + 1];
}
}
}
}
template <Modint mint> void fft4(std::vector<mint>& a) {
static const ntt_info<mint> info;
const u32 mod = mint::mod();
const u64 iw = info.root[2].val();
int n = int(a.size());
int bit_size = std::countr_zero(a.size());
assert(n == 1 << bit_size);
int len = bit_size;
while (len > 0) {
if (len == 1) {
for (int i = 0; i < n; i += 2) {
mint p0 = a[i];
mint p1 = a[i + 1];
a[i] = p0 + p1;
a[i + 1] = p0 - p1;
}
len--;
} else {
int m = 1 << (len - 2);
u64 w1 = 1, w2 = 1, w3 = 1, iw1 = iw, iw3 = iw;
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j += 4 * m) {
int i0 = i + j, i1 = i0 + m, i2 = i1 + m, i3 = i2 + m;
u32 a0 = a[i0].val();
u32 a1 = a[i1].val();
u32 a2 = a[i2].val();
u32 a3 = a[i3].val();
u32 a0_plus_a2 = a0 + a2;
u32 a1_plus_a3 = a1 + a3;
u32 a0_minus_a2 = a0 + mod - a2;
u32 a1_minus_a3 = a1 + mod - a3;
a[i0] = a0_plus_a2 + a1_plus_a3;
a[i1] = a0_minus_a2 * w1 + a1_minus_a3 * iw1;
a[i2] = (a0_plus_a2 + 2 * mod - a1_plus_a3) * w2;
a[i3] = a0_minus_a2 * w3 + (2 * mod - a1_minus_a3) * iw3;
}
w1 = w1 * info.root[len].val() % mod;
w2 = w1 * w1 % mod;
w3 = w2 * w1 % mod;
iw1 = iw * w1 % mod;
iw3 = iw * w3 % mod;
}
len -= 2;
}
}
}
template <Modint mint> void ifft4(std::vector<mint>& a) {
static const ntt_info<mint> info;
const u32 mod = mint::mod();
const u64 mod2 = u64(mod) * mod;
const u64 iw = info.inv_root[2].val();
int n = int(a.size());
int bit_size = std::countr_zero(a.size());
assert(n == 1 << bit_size);
int len = (bit_size & 1 ? 1 : 2);
while (len <= bit_size) {
if (len == 1) {
for (int i = 0; i < n; i += 2) {
mint a0 = a[i];
mint a1 = a[i + 1];
a[i] = a0 + a1;
a[i + 1] = a0 - a1;
}
} else {
int m = 1 << (len - 2);
u64 w1 = 1, w2 = 1, w3 = 1, iw1 = iw, iw3 = iw;
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j += 4 * m) {
int i0 = i + j, i1 = i0 + m, i2 = i1 + m, i3 = i2 + m;
u64 a0 = a[i0].val();
u64 a1 = w1 * a[i1].val();
u64 a2 = w2 * a[i2].val();
u64 a3 = w3 * a[i3].val();
u64 b1 = iw1 * a[i1].val();
u64 b3 = iw3 * a[i3].val();
u64 a0_plus_a2 = a0 + a2;
u64 a1_plus_a3 = a1 + a3;
u64 a0_minus_a2 = a0 + mod2 - a2;
u64 b1_minus_b3 = b1 + mod2 - b3;
a[i0] = a0_plus_a2 + a1_plus_a3;
a[i1] = a0_minus_a2 + b1_minus_b3;
a[i2] = a0_plus_a2 + mod2 * 2 - a1_plus_a3;
a[i3] = a0_minus_a2 + mod2 * 2 - b1_minus_b3;
}
w1 = w1 * info.inv_root[len].val() % mod;
w2 = w1 * w1 % mod;
w3 = w2 * w1 % mod;
iw1 = iw * w1 % mod;
iw3 = iw * w3 % mod;
}
}
len += 2;
}
}
} // namespace internal
} // namespace ebi
#line 9 "convolution/convolution.hpp"
namespace ebi {
template <Modint mint>
std::vector<mint> convolution_naive(const std::vector<mint>& f,
const std::vector<mint>& g) {
if (f.empty() || g.empty()) return {};
int n = int(f.size()), m = int(g.size());
std::vector<mint> c(n + m - 1);
if (n < m) {
for (int j = 0; j < m; j++) {
for (int i = 0; i < n; i++) {
c[i + j] += f[i] * g[j];
}
}
} else {
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
c[i + j] += f[i] * g[j];
}
}
}
return c;
}
template <Modint mint>
std::vector<mint> convolution(const std::vector<mint>& f,
const std::vector<mint>& g) {
if (f.empty() || g.empty()) return {};
if (std::min(f.size(), g.size()) < 60) return convolution_naive(f, g);
int n = (int)std::bit_ceil(f.size() + g.size() - 1);
std::vector<mint> a(n), b(n);
std::copy(f.begin(), f.end(), a.begin());
std::copy(g.begin(), g.end(), b.begin());
internal::fft4(a);
internal::fft4(b);
for (int i = 0; i < n; i++) {
a[i] *= b[i];
}
internal::ifft4(a);
a.resize(f.size() + g.size() - 1);
mint inv_n = mint(n).inv();
for (auto& x : a) x *= inv_n;
return a;
}
} // namespace ebi
#line 2 "fps/fps.hpp"
#line 5 "fps/fps.hpp"
#include <optional>
#line 7 "fps/fps.hpp"
#line 9 "fps/fps.hpp"
namespace ebi {
template <Modint mint> struct FormalPowerSeries : std::vector<mint> {
private:
using std::vector<mint>::vector;
using std::vector<mint>::vector::operator=;
using FPS = FormalPowerSeries;
public:
FormalPowerSeries(const std::vector<mint> &a) {
*this = a;
}
FPS operator+(const FPS &rhs) const noexcept {
return FPS(*this) += rhs;
}
FPS operator-(const FPS &rhs) const noexcept {
return FPS(*this) -= rhs;
}
FPS operator*(const FPS &rhs) const noexcept {
return FPS(*this) *= rhs;
}
FPS operator/(const FPS &rhs) const noexcept {
return FPS(*this) /= rhs;
}
FPS operator%(const FPS &rhs) const noexcept {
return FPS(*this) %= rhs;
}
FPS operator+(const mint &rhs) const noexcept {
return FPS(*this) += rhs;
}
FPS operator-(const mint &rhs) const noexcept {
return FPS(*this) -= rhs;
}
FPS operator*(const mint &rhs) const noexcept {
return FPS(*this) *= rhs;
}
FPS operator/(const mint &rhs) const noexcept {
return FPS(*this) /= rhs;
}
FPS &operator+=(const FPS &rhs) noexcept {
if (this->size() < rhs.size()) this->resize(rhs.size());
for (int i = 0; i < (int)rhs.size(); ++i) {
(*this)[i] += rhs[i];
}
return *this;
}
FPS &operator-=(const FPS &rhs) noexcept {
if (this->size() < rhs.size()) this->resize(rhs.size());
for (int i = 0; i < (int)rhs.size(); ++i) {
(*this)[i] -= rhs[i];
}
return *this;
}
FPS &operator*=(const FPS &);
FPS &operator/=(const FPS &rhs) noexcept {
int n = deg() - 1;
int m = rhs.deg() - 1;
if (n < m) {
*this = {};
return *this;
}
*this = (*this).rev() * rhs.rev().inv(n - m + 1);
(*this).resize(n - m + 1);
std::reverse((*this).begin(), (*this).end());
return *this;
}
FPS &operator%=(const FPS &rhs) noexcept {
*this -= *this / rhs * rhs;
shrink();
return *this;
}
FPS &operator+=(const mint &rhs) noexcept {
if (this->empty()) this->resize(1);
(*this)[0] += rhs;
return *this;
}
FPS &operator-=(const mint &rhs) noexcept {
if (this->empty()) this->resize(1);
(*this)[0] -= rhs;
return *this;
}
FPS &operator*=(const mint &rhs) noexcept {
for (int i = 0; i < deg(); ++i) {
(*this)[i] *= rhs;
}
return *this;
}
FPS &operator/=(const mint &rhs) noexcept {
mint inv_rhs = rhs.inv();
for (int i = 0; i < deg(); ++i) {
(*this)[i] *= inv_rhs;
}
return *this;
}
FPS operator>>(int d) const {
if (deg() <= d) return {};
FPS f = *this;
f.erase(f.begin(), f.begin() + d);
return f;
}
FPS operator<<(int d) const {
FPS f = *this;
f.insert(f.begin(), d, 0);
return f;
}
FPS operator-() const {
FPS g(this->size());
for (int i = 0; i < (int)this->size(); i++) g[i] = -(*this)[i];
return g;
}
FPS pre(int sz) const {
return FPS(this->begin(), this->begin() + std::min(deg(), sz));
}
FPS rev() const {
auto f = *this;
std::reverse(f.begin(), f.end());
return f;
}
FPS differential() const {
int n = deg();
FPS g(std::max(0, n - 1));
for (int i = 0; i < n - 1; i++) {
g[i] = (*this)[i + 1] * (i + 1);
}
return g;
}
FPS integral() const {
int n = deg();
FPS g(n + 1);
g[0] = 0;
if (n > 0) g[1] = 1;
auto mod = mint::mod();
for (int i = 2; i <= n; i++) g[i] = (-g[mod % i]) * (mod / i);
for (int i = 0; i < n; i++) g[i + 1] *= (*this)[i];
return g;
}
FPS inv(int d = -1) const {
int n = 1;
if (d < 0) d = deg();
FPS g(n);
g[0] = (*this)[0].inv();
while (n < d) {
n <<= 1;
g = (g * 2 - g * g * this->pre(n)).pre(n);
}
g.resize(d);
return g;
}
FPS log(int d = -1) const {
assert((*this)[0].val() == 1);
if (d < 0) d = deg();
return ((*this).differential() * (*this).inv(d)).pre(d - 1).integral();
}
FPS exp(int d = -1) const {
assert((*this)[0].val() == 0);
int n = 1;
if (d < 0) d = deg();
FPS g(n);
g[0] = 1;
while (n < d) {
n <<= 1;
g = (g * (this->pre(n) - g.log(n) + 1)).pre(n);
}
g.resize(d);
return g;
}
FPS pow(long long k, int d = -1) const {
assert(k >= 0);
int n = deg();
if (d < 0) d = n;
if (k == 0) {
FPS f(d);
if (d > 0) f[0] = 1;
return f;
}
int low = d;
for (int i = n - 1; i >= 0; i--)
if ((*this)[i] != 0) low = i;
if (low >= (d + k - 1) / k) return FPS(d, 0);
int offset = k * low;
mint c = (*this)[low];
FPS g(d - offset);
for (int i = 0; i < std::min(n - low, d - offset); i++) {
g[i] = (*this)[i + low];
}
g /= c;
g = g.pow_1(k);
return (g << offset) * c.pow(k);
}
FPS pow_1(mint k, int d = -1) const {
assert((*this)[0] == 1);
return ((*this).log(d) * k).exp(d);
}
FPS pow_newton(long long k, int d = -1) const {
assert(k >= 0);
const int n = deg();
if (d < 0) d = n;
if (k == 0) {
FPS f(d);
if (d > 0) f[0] = 1;
return f;
}
for (int i = 0; i < n; i++) {
if ((*this)[i] != 0) {
mint rev = (*this)[i].inv();
FPS f = (((*this * rev) >> i).log(d) * k).exp(d);
f *= (*this)[i].pow(k);
f = (f << (i * k)).pre(d);
if (f.deg() < d) f.resize(d);
return f;
}
if (i + 1 >= (d + k - 1) / k) break;
}
return FPS(d);
}
int deg() const {
return (*this).size();
}
void shrink() {
while ((!this->empty()) && this->back() == 0) this->pop_back();
}
int count_terms() const {
int c = 0;
for (int i = 0; i < deg(); i++) {
if ((*this)[i] != 0) c++;
}
return c;
}
std::optional<FPS> sqrt(int d = -1) const;
static FPS exp_x(int n) {
FPS f(n);
mint fact = 1;
for (int i = 1; i < n; i++) fact *= i;
f[n - 1] = fact.inv();
for (int i = n - 1; i >= 0; i--) f[i - 1] = f[i] * i;
return f;
}
void fft();
void ifft();
};
} // namespace ebi
#line 2 "matrix/black_box_linear_algebra.hpp"
#line 5 "matrix/black_box_linear_algebra.hpp"
#line 2 "fps/berlekamp_massey.hpp"
#line 5 "fps/berlekamp_massey.hpp"
#line 7 "fps/berlekamp_massey.hpp"
namespace ebi {
template <Modint mint>
std::vector<mint> berlekamp_massey(const std::vector<mint> &s) {
std::vector<mint> C = {1}, B = {1};
int L = 0, m = 1;
mint b = 1;
for (int n = 0; n < (int)s.size(); n++) {
mint d = s[n];
for (int i = 1; i <= L; i++) {
d += s[n - i] * C[i];
}
if (d == 0) {
m++;
} else if (2 * L <= n) {
auto T = C;
mint f = d / b;
C.resize((int)B.size() + m);
for (int i = 0; i < (int)B.size(); i++) {
C[i + m] -= f * B[i];
}
L = n + 1 - L;
B = T;
b = d;
m = 1;
} else {
mint f = d / b;
for (int i = 0; i < (int)B.size(); i++) {
C[i + m] -= f * B[i];
}
m++;
}
}
return C;
}
} // namespace ebi
#line 2 "fps/poly_mod_pow.hpp"
#line 5 "fps/poly_mod_pow.hpp"
namespace ebi {
template <Modint mint>
FormalPowerSeries<mint> poly_mod_pow(FormalPowerSeries<mint> f, long long k,
const FormalPowerSeries<mint> &g) {
FormalPowerSeries<mint> res = {1};
while (k > 0) {
if (k & 1) {
res *= f;
res %= g;
res.shrink();
}
f *= f;
f %= g;
f.shrink();
k >>= 1;
}
return res;
}
} // namespace ebi
#line 2 "utility/random_number_generator.hpp"
#line 4 "utility/random_number_generator.hpp"
#include <random>
namespace ebi {
struct random_number_generator {
random_number_generator(int seed = -1) {
if (seed < 0) seed = rnd();
mt.seed(seed);
}
void set_seed(int seed) {
mt.seed(seed);
}
template <class T> T get(T a, T b) {
std::uniform_int_distribution<T> dist(a, b - 1);
return dist(mt);
}
private:
std::mt19937_64 mt;
std::random_device rnd;
};
} // namespace ebi
#line 10 "matrix/black_box_linear_algebra.hpp"
namespace ebi {
template <Modint mint, class F>
std::vector<mint> matrix_minimum_poly(int n, F Ax) {
static random_number_generator rng;
std::vector<mint> s(2 * n + 10, 0), u(n), b(n);
for (int i = 0; i < n; i++) {
u[i] = rng.get(0, mint::mod());
b[i] = rng.get(0, mint::mod());
}
for (int i = 0; i < 2 * n + 10; i++) {
for (int j = 0; j < n; j++) {
s[i] += u[j] * b[j];
}
b = Ax(b);
}
auto c = berlekamp_massey(s);
std::reverse(c.begin(), c.end());
return c;
}
template <Modint mint, class F>
std::vector<mint> pow(int n, F Ax, const std::vector<mint> &b, long long k) {
assert(n == (int)b.size());
using FPS = FormalPowerSeries<mint>;
auto g = matrix_minimum_poly<mint>(n, Ax);
auto c = poly_mod_pow<mint>({0, 1}, k, g);
FPS res(n, 0), Ab = b;
for (int i = 0; i < (int)c.size(); i++) {
res += Ab * c[i];
Ab = FPS(Ax(Ab));
}
return res;
}
template <Modint mint, class F> mint det(int n, F Ax) {
static random_number_generator rng;
std::vector<mint> d(n);
mint r = 1;
for (int i = 0; i < n; i++) {
d[i] = rng.get(1, mint::mod());
r *= d[i];
}
auto ADx = [&](std::vector<mint> v) -> std::vector<mint> {
assert(n == (int)v.size());
for (int i = 0; i < n; i++) {
v[i] *= d[i];
}
return Ax(v);
};
auto f = matrix_minimum_poly<mint>(n, ADx);
mint res = ((int)f.size() == n + 1 ? f[0] : 0);
if (n % 2 == 1) res = -res;
return res / r;
}
} // namespace ebi
#line 2 "modint/modint.hpp"
#line 5 "modint/modint.hpp"
#line 7 "modint/modint.hpp"
namespace ebi {
template <int m> struct static_modint {
private:
using modint = static_modint;
public:
static constexpr int mod() {
return m;
}
static constexpr modint raw(int v) {
modint x;
x._v = v;
return x;
}
constexpr static_modint() : _v(0) {}
template <std::signed_integral T> constexpr static_modint(T v) {
long long x = (long long)(v % (long long)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
template <std::unsigned_integral T> constexpr static_modint(T v) {
_v = (unsigned int)(v % umod());
}
constexpr unsigned int val() const {
return _v;
}
constexpr unsigned int value() const {
return val();
}
constexpr modint &operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
constexpr modint &operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
constexpr modint operator++(int) {
modint res = *this;
++*this;
return res;
}
constexpr modint operator--(int) {
modint res = *this;
--*this;
return res;
}
constexpr modint &operator+=(const modint &rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
constexpr modint &operator-=(const modint &rhs) {
_v -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
constexpr modint &operator*=(const modint &rhs) {
unsigned long long x = _v;
x *= rhs._v;
_v = (unsigned int)(x % (unsigned long long)umod());
return *this;
}
constexpr modint &operator/=(const modint &rhs) {
return *this = *this * rhs.inv();
}
constexpr modint operator+() const {
return *this;
}
constexpr modint operator-() const {
return modint() - *this;
}
constexpr modint pow(long long n) const {
assert(0 <= n);
modint x = *this, res = 1;
while (n) {
if (n & 1) res *= x;
x *= x;
n >>= 1;
}
return res;
}
constexpr modint inv() const {
assert(_v);
return pow(umod() - 2);
}
friend modint operator+(const modint &lhs, const modint &rhs) {
return modint(lhs) += rhs;
}
friend modint operator-(const modint &lhs, const modint &rhs) {
return modint(lhs) -= rhs;
}
friend modint operator*(const modint &lhs, const modint &rhs) {
return modint(lhs) *= rhs;
}
friend modint operator/(const modint &lhs, const modint &rhs) {
return modint(lhs) /= rhs;
}
friend bool operator==(const modint &lhs, const modint &rhs) {
return lhs.val() == rhs.val();
}
friend bool operator!=(const modint &lhs, const modint &rhs) {
return !(lhs == rhs);
}
private:
unsigned int _v = 0;
static constexpr unsigned int umod() {
return m;
}
};
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
} // namespace ebi
#line 1 "template/template.hpp"
#include <bits/stdc++.h>
#define rep(i, a, n) for (int i = (int)(a); i < (int)(n); i++)
#define rrep(i, a, n) for (int i = ((int)(n)-1); i >= (int)(a); i--)
#define Rep(i, a, n) for (i64 i = (i64)(a); i < (i64)(n); i++)
#define RRep(i, a, n) for (i64 i = ((i64)(n)-i64(1)); i >= (i64)(a); i--)
#define all(v) (v).begin(), (v).end()
#define rall(v) (v).rbegin(), (v).rend()
#line 2 "template/debug_template.hpp"
#line 4 "template/debug_template.hpp"
namespace ebi {
#ifdef LOCAL
#define debug(...) \
std::cerr << "LINE: " << __LINE__ << " [" << #__VA_ARGS__ << "]:", \
debug_out(__VA_ARGS__)
#else
#define debug(...)
#endif
void debug_out() {
std::cerr << std::endl;
}
template <typename Head, typename... Tail> void debug_out(Head h, Tail... t) {
std::cerr << " " << h;
if (sizeof...(t) > 0) std::cerr << " :";
debug_out(t...);
}
} // namespace ebi
#line 2 "template/io.hpp"
#line 7 "template/io.hpp"
namespace ebi {
template <typename T1, typename T2>
std::ostream &operator<<(std::ostream &os, const std::pair<T1, T2> &pa) {
return os << pa.first << " " << pa.second;
}
template <typename T1, typename T2>
std::istream &operator>>(std::istream &os, std::pair<T1, T2> &pa) {
return os >> pa.first >> pa.second;
}
template <typename T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &vec) {
for (std::size_t i = 0; i < vec.size(); i++)
os << vec[i] << (i + 1 == vec.size() ? "" : " ");
return os;
}
template <typename T>
std::istream &operator>>(std::istream &os, std::vector<T> &vec) {
for (T &e : vec) std::cin >> e;
return os;
}
template <typename T>
std::ostream &operator<<(std::ostream &os, const std::optional<T> &opt) {
if (opt) {
os << opt.value();
} else {
os << "invalid value";
}
return os;
}
void fast_io() {
std::cout << std::fixed << std::setprecision(15);
std::cin.tie(nullptr);
std::ios::sync_with_stdio(false);
}
} // namespace ebi
#line 2 "template/utility.hpp"
#line 5 "template/utility.hpp"
#line 2 "graph/base.hpp"
#line 5 "graph/base.hpp"
#include <ranges>
#line 7 "graph/base.hpp"
#line 2 "data_structure/simple_csr.hpp"
#line 6 "data_structure/simple_csr.hpp"
namespace ebi {
template <class E> struct simple_csr {
simple_csr() = default;
simple_csr(int n, const std::vector<std::pair<int, E>>& elements)
: start(n + 1, 0), elist(elements.size()) {
for (auto e : elements) {
start[e.first + 1]++;
}
for (auto i : std::views::iota(0, n)) {
start[i + 1] += start[i];
}
auto counter = start;
for (auto [i, e] : elements) {
elist[counter[i]++] = e;
}
}
simple_csr(const std::vector<std::vector<E>>& es)
: start(es.size() + 1, 0) {
int n = es.size();
for (auto i : std::views::iota(0, n)) {
start[i + 1] = (int)es[i].size() + start[i];
}
elist.resize(start.back());
for (auto i : std::views::iota(0, n)) {
std::copy(es[i].begin(), es[i].end(), elist.begin() + start[i]);
}
}
int size() const {
return (int)start.size() - 1;
}
const auto operator[](int i) const {
return std::ranges::subrange(elist.begin() + start[i],
elist.begin() + start[i + 1]);
}
auto operator[](int i) {
return std::ranges::subrange(elist.begin() + start[i],
elist.begin() + start[i + 1]);
}
const auto operator()(int i, int l, int r) const {
return std::ranges::subrange(elist.begin() + start[i] + l,
elist.begin() + start[i + 1] + r);
}
auto operator()(int i, int l, int r) {
return std::ranges::subrange(elist.begin() + start[i] + l,
elist.begin() + start[i + 1] + r);
}
private:
std::vector<int> start;
std::vector<E> elist;
};
} // namespace ebi
#line 9 "graph/base.hpp"
namespace ebi {
template <class T> struct Edge {
int from, to;
T cost;
int id;
};
template <class E> struct Graph {
using cost_type = E;
using edge_type = Edge<cost_type>;
Graph(int n_) : n(n_) {}
Graph() = default;
void add_edge(int u, int v, cost_type c) {
buff.emplace_back(u, edge_type{u, v, c, m});
edges.emplace_back(edge_type{u, v, c, m++});
}
void add_undirected_edge(int u, int v, cost_type c) {
buff.emplace_back(u, edge_type{u, v, c, m});
buff.emplace_back(v, edge_type{v, u, c, m});
edges.emplace_back(edge_type{u, v, c, m});
m++;
}
void read_tree(int offset = 1, bool is_weighted = false) {
read_graph(n - 1, offset, false, is_weighted);
}
void read_parents(int offset = 1) {
for (auto i : std::views::iota(1, n)) {
int p;
std::cin >> p;
p -= offset;
add_undirected_edge(p, i, 1);
}
build();
}
void read_graph(int e, int offset = 1, bool is_directed = false,
bool is_weighted = false) {
for (int i = 0; i < e; i++) {
int u, v;
std::cin >> u >> v;
u -= offset;
v -= offset;
if (is_weighted) {
cost_type c;
std::cin >> c;
if (is_directed) {
add_edge(u, v, c);
} else {
add_undirected_edge(u, v, c);
}
} else {
if (is_directed) {
add_edge(u, v, 1);
} else {
add_undirected_edge(u, v, 1);
}
}
}
build();
}
void build() {
assert(!prepared);
csr = simple_csr<edge_type>(n, buff);
buff.clear();
prepared = true;
}
int size() const {
return n;
}
int node_number() const {
return n;
}
int edge_number() const {
return m;
}
edge_type get_edge(int i) const {
return edges[i];
}
std::vector<edge_type> get_edges() const {
return edges;
}
const auto operator[](int i) const {
return csr[i];
}
auto operator[](int i) {
return csr[i];
}
private:
int n, m = 0;
std::vector<std::pair<int,edge_type>> buff;
std::vector<edge_type> edges;
simple_csr<edge_type> csr;
bool prepared = false;
};
} // namespace ebi
#line 8 "template/utility.hpp"
namespace ebi {
template <class T> inline bool chmin(T &a, T b) {
if (a > b) {
a = b;
return true;
}
return false;
}
template <class T> inline bool chmax(T &a, T b) {
if (a < b) {
a = b;
return true;
}
return false;
}
template <class T> T safe_ceil(T a, T b) {
if (a % b == 0)
return a / b;
else if (a >= 0)
return (a / b) + 1;
else
return -((-a) / b);
}
template <class T> T safe_floor(T a, T b) {
if (a % b == 0)
return a / b;
else if (a >= 0)
return a / b;
else
return -((-a) / b) - 1;
}
constexpr i64 LNF = std::numeric_limits<i64>::max() / 4;
constexpr int INF = std::numeric_limits<int>::max() / 2;
const std::vector<int> dy = {1, 0, -1, 0, 1, 1, -1, -1};
const std::vector<int> dx = {0, 1, 0, -1, 1, -1, 1, -1};
} // namespace ebi
#line 6 "a.cpp"
namespace ebi {
template <Modint mint>
FormalPowerSeries<mint> &FormalPowerSeries<mint>::operator*=(
const FormalPowerSeries<mint> &rhs) {
*this = convolution_naive(*this, rhs);
return *this;
}
template <Modint mint> void FormalPowerSeries<mint>::fft() {
assert(false);
}
template <Modint mint> void FormalPowerSeries<mint>::ifft() {
assert(false);
}
} // namespace ebi
namespace ebi {
using mint = modint1000000007;
void main_() {
int k, m;
i64 n;
std::cin >> k >> m >> n;
const int sz = k * k;
std::vector<std::pair<int, int>> a;
rep(i, 0, m) {
int p, q, r;
std::cin >> p >> q >> r;
p--;
q--;
r--;
a.emplace_back(q + r * k, p + q * k);
}
std::sort(all(a));
a.erase(std::unique(all(a)), a.end());
auto Ax = [&](const std::vector<mint> &b) -> std::vector<mint> {
std::vector<mint> res(sz, 0);
for (auto [i, j] : a) {
res[i] += b[j];
}
return res;
};
std::vector<mint> b(sz, 0);
rep(i, 0, k) {
b[i * k] = 1;
}
auto res = pow<mint>(sz, Ax, b, n - 2);
mint ans = 0;
rep(i, 0, k) {
ans += res[i];
}
std::cout << ans << '\n';
}
} // namespace ebi
int main() {
ebi::fast_io();
int t = 1;
// std::cin >> t;
while (t--) {
ebi::main_();
}
return 0;
}