#include #include #include #include using mint = atcoder::modint; namespace atcoder { std::istream& operator>>(std::istream& in, mint& a) { long long e; in >> e; a = e; return in; } std::ostream& operator<<(std::ostream& out, const mint& a) { out << a.val(); return out; } } // namespace atcoder #include #include #include #include namespace suisen { template struct Matrix { std::vector> dat; Matrix() {} Matrix(int n) : Matrix(n, n) {} Matrix(int n, int m, T fill_value = T(0)) : dat(n, std::vector(m, fill_value)) {} Matrix(const std::vector>& dat) : dat(dat) {} const std::vector& operator[](int i) const { return dat[i]; } std::vector& operator[](int i) { return dat[i]; } operator std::vector>() const { return dat; } friend bool operator==(const Matrix& A, const Matrix& B) { return A.dat == B.dat; } friend bool operator!=(const Matrix& A, const Matrix& B) { return A.dat != B.dat; } std::pair shape() const { return dat.empty() ? std::make_pair(0, 0) : std::make_pair(dat.size(), dat[0].size()); } int row_size() const { return dat.size(); } int col_size() const { return dat.empty() ? 0 : dat[0].size(); } friend Matrix& operator+=(Matrix& A, const Matrix& B) { assert(A.shape() == B.shape()); auto [n, m] = A.shape(); for (int i = 0; i < n; ++i) for (int j = 0; j < m; ++j) A.dat[i][j] += B.dat[i][j]; return A; } friend Matrix& operator-=(Matrix& A, const Matrix& B) { assert(A.shape() == B.shape()); auto [n, m] = A.shape(); for (int i = 0; i < n; ++i) for (int j = 0; j < m; ++j) A.dat[i][j] -= B.dat[i][j]; return A; } friend Matrix& operator*=(Matrix& A, const Matrix& B) { return A = A * B; } friend Matrix& operator*=(Matrix& A, const T& val) { for (auto& row : A.dat) for (auto& elm : row) elm *= val; return A; } friend Matrix& operator/=(Matrix& A, const T& val) { return A *= T(1) / val; } friend Matrix& operator/=(Matrix& A, const Matrix& B) { return A *= B.inv(); } friend Matrix operator+(Matrix A, const Matrix& B) { A += B; return A; } friend Matrix operator-(Matrix A, const Matrix& B) { A -= B; return A; } friend Matrix operator*(const Matrix& A, const Matrix& B) { assert(A.col_size() == B.row_size()); const int n = A.row_size(), m = A.col_size(), l = B.col_size(); if (std::min({ n, m, l }) <= 70) { // naive Matrix C(n, l); for (int i = 0; i < n; ++i) for (int j = 0; j < m; ++j) for (int k = 0; k < l; ++k) { C.dat[i][k] += A.dat[i][j] * B.dat[j][k]; } return C; } // strassen const int nl = 0, nm = n >> 1, nr = nm + nm; const int ml = 0, mm = m >> 1, mr = mm + mm; const int ll = 0, lm = l >> 1, lr = lm + lm; auto A00 = A.submatrix(nl, nm, ml, mm), A01 = A.submatrix(nl, nm, mm, mr); auto A10 = A.submatrix(nm, nr, ml, mm), A11 = A.submatrix(nm, nr, mm, mr); auto B00 = B.submatrix(ml, mm, ll, lm), B01 = B.submatrix(ml, mm, lm, lr); auto B10 = B.submatrix(mm, mr, ll, lm), B11 = B.submatrix(mm, mr, lm, lr); auto P0 = (A00 + A11) * (B00 + B11); auto P1 = (A10 + A11) * B00; auto P2 = A00 * (B01 - B11); auto P3 = A11 * (B10 - B00); auto P4 = (A00 + A01) * B11; auto P5 = (A10 - A00) * (B00 + B01); auto P6 = (A01 - A11) * (B10 + B11); Matrix C(n, l); C.assign_submatrix(nl, ll, P0 + P3 - P4 + P6), C.assign_submatrix(nl, lm, P2 + P4); C.assign_submatrix(nm, ll, P1 + P3), C.assign_submatrix(nm, lm, P0 + P2 - P1 + P5); // fractions if (l != lr) { for (int i = 0; i < nr; ++i) for (int j = 0; j < mr; ++j) C.dat[i][lr] += A.dat[i][j] * B.dat[j][lr]; } if (m != mr) { for (int i = 0; i < nr; ++i) for (int k = 0; k < l; ++k) C.dat[i][k] += A.dat[i][mr] * B.dat[mr][k]; } if (n != nr) { for (int j = 0; j < m; ++j) for (int k = 0; k < l; ++k) C.dat[nr][k] += A.dat[nr][j] * B.dat[j][k]; } return C; } friend Matrix operator*(const T& val, Matrix A) { A *= val; return A; } friend Matrix operator*(Matrix A, const T& val) { A *= val; return A; } friend Matrix operator/(const Matrix& A, const Matrix& B) { return A * B.inv(); } friend Matrix operator/(Matrix A, const T& val) { A /= val; return A; } friend Matrix operator/(const T& val, const Matrix& A) { return val * A.inv(); } friend std::vector operator*(const Matrix& A, const std::vector& x) { const auto [n, m] = A.shape(); assert(m == int(x.size())); std::vector b(n, T(0)); for (int i = 0; i < n; ++i) for (int j = 0; j < m; ++j) b[i] += A.dat[i][j] * x[j]; return b; } static Matrix e0(int n) { return Matrix(n, Identity::ADD); } static Matrix e1(int n) { return Matrix(n, Identity::MUL); } Matrix pow(long long b) const { assert_square(); assert(b >= 0); Matrix res = e1(row_size()), p = *this; for (; b; b >>= 1) { if (b & 1) res *= p; p *= p; } return res; } Matrix inv() const { return *safe_inv(); } std::optional> safe_inv() const { assert_square(); Matrix A = *this; const int n = A.row_size(); for (int i = 0; i < n; ++i) { A[i].resize(2 * n, T{ 0 }); A[i][n + i] = T{ 1 }; } for (int i = 0; i < n; ++i) { for (int k = i; k < n; ++k) if (A[k][i] != T{ 0 }) { std::swap(A[i], A[k]); T c = T{ 1 } / A[i][i]; for (int j = i; j < 2 * n; ++j) A[i][j] *= c; break; } if (A[i][i] == T{ 0 }) return std::nullopt; for (int k = 0; k < n; ++k) if (k != i and A[k][i] != T{ 0 }) { T c = A[k][i]; for (int j = i; j < 2 * n; ++j) A[k][j] -= c * A[i][j]; } } for (auto& row : A.dat) row.erase(row.begin(), row.begin() + n); return A; } T det() const { assert_square(); Matrix A = *this; bool sgn = false; const int n = A.row_size(); for (int j = 0; j < n; ++j) for (int i = j + 1; i < n; ++i) if (A[i][j] != T{ 0 }) { std::swap(A[j], A[i]); T q = A[i][j] / A[j][j]; for (int k = j; k < n; ++k) A[i][k] -= A[j][k] * q; sgn = not sgn; } T res = sgn ? T{ -1 } : T{ +1 }; for (int i = 0; i < n; ++i) res *= A[i][i]; return res; } T det_arbitrary_mod() const { assert_square(); Matrix A = *this; bool sgn = false; const int n = A.row_size(); for (int j = 0; j < n; ++j) for (int i = j + 1; i < n; ++i) { for (; A[i][j].val(); sgn = not sgn) { std::swap(A[j], A[i]); T q = A[i][j].val() / A[j][j].val(); for (int k = j; k < n; ++k) A[i][k] -= A[j][k] * q; } } T res = sgn ? -1 : +1; for (int i = 0; i < n; ++i) res *= A[i][i]; return res; } void assert_square() const { assert(row_size() == col_size()); } Matrix submatrix(int row_begin, int row_end, int col_begin, int col_end) const { Matrix A(row_end - row_begin, col_end - col_begin); for (int i = row_begin; i < row_end; ++i) for (int j = col_begin; j < col_end; ++j) { A[i - row_begin][j - col_begin] = dat[i][j]; } return A; } void assign_submatrix(int row_begin, int col_begin, const Matrix& A) { const int n = A.row_size(), m = A.col_size(); assert(row_begin + n <= row_size() and col_begin + m <= col_size()); for (int i = 0; i < n; ++i) for (int j = 0; j < m; ++j) { dat[row_begin + i][col_begin + j] = A[i][j]; } } private: enum class Identity { ADD, MUL }; Matrix(int n, Identity ident) : Matrix::Matrix(n) { if (ident == Identity::MUL) for (int i = 0; i < n; ++i) dat[i][i] = 1; } }; } // namespace suisen int main() { std::ios::sync_with_stdio(false); std::cin.tie(nullptr); int t; std::cin >> t; while (t --> 0) { int n, p; std::cin >> n >> p; mint::set_mod(p); suisen::Matrix a(n, n); std::vector cnt_row(n), cnt_col(n); for (int i = 0; i < n; ++i) for (int j = 0; j < n; ++j) { std::cin >> a[i][j]; if (a[i][j] == -1) { ++cnt_row[i], ++cnt_col[j]; } } if (p != 2 or *std::max_element(cnt_row.begin(), cnt_row.end()) > 1 or *std::max_element(cnt_col.begin(), cnt_col.end()) > 1) { std::cout << 0 << '\n'; } else { std::vector> b; for (int i = 0; i < n; ++i) if (cnt_row[i] == 0) { auto &row = b.emplace_back(); for (int j = 0; j < n; ++j) if (cnt_col[j] == 0) { row.push_back(a[i][j]); } } std::cout << suisen::Matrix(b).det() << '\n'; } } }