#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using Int = long long; template ostream &operator<<(ostream &os, const pair &a) { return os << "(" << a.first << ", " << a.second << ")"; }; template ostream &operator<<(ostream &os, const vector &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; } template void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; } template bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; } template bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; } //////////////////////////////////////////////////////////////////////////////// struct ModInt { static unsigned M; unsigned x; ModInt() : x(0U) {} ModInt(unsigned x_) : x(x_ % M) {} ModInt(unsigned long long x_) : x(x_ % M) {} ModInt(int x_) : x(((x_ %= static_cast(M)) < 0) ? (x_ + static_cast(M)) : x_) {} ModInt(long long x_) : x(((x_ %= static_cast(M)) < 0) ? (x_ + static_cast(M)) : x_) {} ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; } ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; } ModInt &operator*=(const ModInt &a) { x = (static_cast(x) * a.x) % M; return *this; } ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); } ModInt pow(long long e) const { if (e < 0) return inv().pow(-e); ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b; } ModInt inv() const { unsigned a = M, b = x; int y = 0, z = 1; for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast(q) * z; y = z; z = w; } assert(a == 1U); return ModInt(y); } ModInt operator+() const { return *this; } ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; } ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); } ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); } ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); } ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); } template friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); } template friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); } template friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); } template friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); } explicit operator bool() const { return x; } bool operator==(const ModInt &a) const { return (x == a.x); } bool operator!=(const ModInt &a) const { return (x != a.x); } friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; } }; unsigned ModInt::M; //////////////////////////////////////////////////////////////////////////////// // det(a + x I) // O(n^3) // Call by value: Modifies a (Watch out when using C-style array!) template vector charPoly(vector> a) { const int n = a.size(); // upper Hessenberg for (int j = 0; j < n - 2; ++j) { for (int i = j + 1; i < n; ++i) { if (a[i][j]) { swap(a[j + 1], a[i]); for (int ii = 0; ii < n; ++ii) swap(a[ii][j + 1], a[ii][i]); break; } } if (a[j + 1][j]) { const T s = 1 / a[j + 1][j]; for (int i = j + 2; i < n; ++i) { const T t = s * a[i][j]; for (int jj = j; jj < n; ++jj) a[i][jj] -= t * a[j + 1][jj]; for (int ii = 0; ii < n; ++ii) a[ii][j + 1] += t * a[ii][i]; } } } // fss[i] := det(a[0..i][0..i] + x I_i) vector> fss(n + 1); fss[0] = {1}; for (int i = 0; i < n; ++i) { fss[i + 1].assign(i + 2, 0); for (int k = 0; k <= i; ++k) fss[i + 1][k + 1] = fss[i][k]; for (int k = 0; k <= i; ++k) fss[i + 1][k] += a[i][i] * fss[i][k]; T prod = 1; for (int j = i - 1; j >= 0; --j) { prod *= -a[j + 1][j]; const T t = prod * a[j][i]; for (int k = 0; k <= j; ++k) fss[i + 1][k] += t * fss[j][k]; } } return fss[n]; } // det(a + x b) // O(n^3) // Call by value: Modifies a, b (Watch out when using C-style array!) template vector detPoly(vector> a, vector> b) { const int n = a.size(); T prod = 1; int off = 0; for (int h = 0; h < n; ++h) { for (; ; ) { if (b[h][h]) break; for (int j = h + 1; j < n; ++j) { if (b[h][j]) { prod *= -1; for (int i = 0; i < n; ++i) { swap(a[i][h], a[i][j]); swap(b[i][h], b[i][j]); } break; } } if (b[h][h]) break; if (++off > n) return vector(n + 1, 0); for (int j = 0; j < n; ++j) { b[h][j] = a[h][j]; a[h][j] = 0; } for (int i = 0; i < h; ++i) { const T t = b[h][i]; for (int j = 0; j < n; ++j) { a[h][j] -= t * a[i][j]; b[h][j] -= t * b[i][j]; } } } prod *= b[h][h]; const T s = 1 / b[h][h]; for (int j = 0; j < n; ++j) { a[h][j] *= s; b[h][j] *= s; } for (int i = 0; i < n; ++i) if (h != i) { const T t = b[i][h]; for (int j = 0; j < n; ++j) { a[i][j] -= t * a[h][j]; b[i][j] -= t * b[h][j]; } } } const vector fs = charPoly(a); vector gs(n + 1, 0); for (int i = 0; off + i <= n; ++i) gs[i] = prod * fs[off + i]; return gs; } using Mint = ModInt; int N, P; int A[60][60]; int main() { for (int numCases; ~scanf("%d", &numCases); ) { for (int caseId = 1; caseId <= numCases; ++caseId) { scanf("%d%d", &N, &P); for (int i = 0; i < N; ++i) for (int j = 0; j < N; ++j) { scanf("%d", &A[i][j]); } Mint::M = P; int K = 0; vector> a(N, vector(N, 0)); vector> b(N, vector(N, 0)); for (int i = 0; i < N; ++i) for (int j = 0; j < N; ++j) { if (~A[i][j]) { a[i][j] = A[i][j]; } else { ++K; b[i][j] = 1; } } const auto res = detPoly(a, b); // cerr<<"res = "< 0) { if (P != 2) prod = 0; } if (K - i > 0) { prod = 0; } ans += prod; } printf("%u\n", ans.x); } #ifndef LOCAL break; #endif } return 0; }