#line 1 "test.cpp" //#pragma GCC target("avx") //#pragma GCC optimize("O3") //#pragma GCC optimize("unroll-loops") #include #ifdef LOCAL #include #define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__) #else #define debug(...) (static_cast(0)) #endif using namespace std; using ll = long long; using ld = long double; using pll = pair; using pii = pair; using vi = vector; using vvi = vector; using vvvi = vector; using vl = vector; using vvl = vector; using vvvl = vector; using vpii = vector; using vpll = vector; using vs = vector; template using pq = priority_queue, greater>; #define overload4(_1, _2, _3, _4, name, ...) name #define overload3(a,b,c,name,...) name #define rep1(n) for (ll UNUSED_NUMBER = 0; UNUSED_NUMBER < (n); ++UNUSED_NUMBER) #define rep2(i, n) for (ll i = 0; i < (n); ++i) #define rep3(i, a, b) for (ll i = (a); i < (b); ++i) #define rep4(i, a, b, c) for (ll i = (a); i < (b); i += (c)) #define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__) #define rrep1(n) for(ll i = (n) - 1;i >= 0;i--) #define rrep2(i,n) for(ll i = (n) - 1;i >= 0;i--) #define rrep3(i,a,b) for(ll i = (b) - 1;i >= (a);i--) #define rrep4(i,a,b,c) for(ll i = (a) + ((b)-(a)-1) / (c) * (c);i >= (a);i -= c) #define rrep(...) overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)(__VA_ARGS__) #define all1(i) begin(i) , end(i) #define all2(i,a) begin(i) , begin(i) + a #define all3(i,a,b) begin(i) + a , begin(i) + b #define all(...) overload3(__VA_ARGS__, all3, all2, all1)(__VA_ARGS__) #define sum(...) accumulate(all(__VA_ARGS__),0LL) template bool chmin(T &a, const T &b){ if(a > b){ a = b; return 1; } else return 0; } template bool chmax(T &a, const T &b){ if(a < b){ a = b; return 1; } else return 0; } template auto min(const T& a){ return *min_element(all(a)); } template auto max(const T& a){ return *max_element(all(a)); } template void in(Ts&... t); #define INT(...) int __VA_ARGS__; in(__VA_ARGS__) #define LL(...) ll __VA_ARGS__; in(__VA_ARGS__) #define STR(...) string __VA_ARGS__; in(__VA_ARGS__) #define CHR(...) char __VA_ARGS__; in(__VA_ARGS__) #define DBL(...) double __VA_ARGS__; in(__VA_ARGS__) #define LD(...) ld __VA_ARGS__; in(__VA_ARGS__) #define VEC(type, name, size) vector name(size); in(name) #define VV(type, name, h, w) vector> name(h, vector(w)); in(name) ll intpow(ll a, ll b){ ll ans = 1; while(b){if(b & 1) ans *= a; a *= a; b /= 2;} return ans;} ll modpow(ll a, ll b, ll p){ ll ans = 1; a %= p;if(a < 0) a += p;while(b){ if(b & 1) (ans *= a) %= p; (a *= a) %= p; b /= 2; } return ans; } ll GCD(ll a,ll b) { if(a == 0 || b == 0) return 0; if(a % b == 0) return b; else return GCD(b,a%b);} ll LCM(ll a,ll b) { if(a == 0) return b; if(b == 0) return a;return a / GCD(a,b) * b;} namespace IO{ #define VOID(a) decltype(void(a)) struct setting{ setting(){cin.tie(nullptr); ios::sync_with_stdio(false);fixed(cout); cout.precision(15);}} setting; template struct P : P{}; template<> struct P<0>{}; template void i(T& t){ i(t, P<3>{}); } void i(vector::reference t, P<3>){ int a; i(a); t = a; } template auto i(T& t, P<2>) -> VOID(cin >> t){ cin >> t; } template auto i(T& t, P<1>) -> VOID(begin(t)){ for(auto&& x : t) i(x); } template void ituple(T& t, index_sequence){ in(get(t)...);} template auto i(T& t, P<0>) -> VOID(tuple_size{}){ ituple(t, make_index_sequence::value>{});} #undef VOID } #define unpack(a) (void)initializer_list{(a, 0)...} template void in(Ts&... t){ unpack(IO :: i(t)); } #undef unpack static const double PI = 3.1415926535897932; template struct REC { F f; REC(F &&f_) : f(forward(f_)) {} template auto operator()(Args &&...args) const { return f(*this, forward(args)...); }}; constexpr int mod = 1000000007; //constexpr int mod = 998244353; #line 2 "library/modint/barrett-reduction.hpp" struct Barrett { using u32 = unsigned int; using i64 = long long; using u64 = unsigned long long; u32 m; u64 im; Barrett() : m(), im() {} Barrett(int n) : m(n), im(u64(-1) / m + 1) {} constexpr inline i64 quo(u64 n) { u64 x = u64((__uint128_t(n) * im) >> 64); u32 r = n - x * m; return m <= r ? x - 1 : x; } constexpr inline i64 rem(u64 n) { u64 x = u64((__uint128_t(n) * im) >> 64); u32 r = n - x * m; return m <= r ? r + m : r; } constexpr inline pair quorem(u64 n) { u64 x = u64((__uint128_t(n) * im) >> 64); u32 r = n - x * m; if (m <= r) return {x - 1, r + m}; return {x, r}; } constexpr inline i64 pow(u64 n, i64 p) { u32 a = rem(n), r = m == 1 ? 0 : 1; while (p) { if (p & 1) r = rem(u64(r) * a); a = rem(u64(a) * a); p >>= 1; } return r; } }; #line 3 "library/modint/ArbitaryModint.hpp" struct ArbitraryModint { int x; ArbitraryModint():x(0) {} ArbitraryModint(int64_t y) { int z = y % get_mod(); if(z < 0) z += get_mod(); x = z; } ArbitraryModint &operator+=(const ArbitraryModint &p) { if((x += p.x) >= get_mod()) x -= get_mod(); return *this; } ArbitraryModint &operator-=(const ArbitraryModint &p) { if((x += get_mod() - p.x) >= get_mod()) x -= get_mod(); return *this; } ArbitraryModint &operator*=(const ArbitraryModint &p) { x = rem((unsigned long long)x * p.x); return *this; } ArbitraryModint &operator/=(const ArbitraryModint &p) { *this *= p.inverse(); return *this; } ArbitraryModint operator-() const {return ArbitraryModint(-x);}; ArbitraryModint operator+(const ArbitraryModint &p) const{ return ArbitraryModint(*this) += p; } ArbitraryModint operator-(const ArbitraryModint &p) const{ return ArbitraryModint(*this) -= p; } ArbitraryModint operator*(const ArbitraryModint &p) const{ return ArbitraryModint(*this) *= p; } ArbitraryModint operator/(const ArbitraryModint &p) const { return ArbitraryModint(*this) /= p; } bool operator==(const ArbitraryModint &p) {return x == p.x;} bool operator!=(const ArbitraryModint &p) {return x != p.x;} ArbitraryModint inverse() const { int a = x,b = get_mod(),u = 1,v = 0,t; while(b > 0) { t = a / b; swap(a -= t * b,b); swap(u -= t * v,v); } return ArbitraryModint(u); } ArbitraryModint pow(int64_t n) const { ArbitraryModint ret(1),mul(x); while(n > 0) { if(n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } friend ostream &operator<<(ostream &os,const ArbitraryModint &p) { return os << p.x; } friend istream &operator>>(istream &is,ArbitraryModint &a) { int64_t t; is >> t; a = ArbitraryModint(t); return (is); } int get() const {return x;} inline unsigned int rem(unsigned long long p) {return barrett().rem(p);}; static inline Barrett &barrett() { static Barrett b; return b; } static inline int &get_mod() { static int mod = 0; return mod; } static void set_mod(int md) { assert(0 < md && md <= (1LL << 30) - 1); get_mod() = md; barrett() = Barrett(md); } }; #line 87 "test.cpp" using mint = ArbitraryModint; using vm = vector; using vvm = vector; using vvvm = vector; #line 2 "library/matrix/matrix.hpp" template struct Matrix { vector> A; Matrix() = default; Matrix(int n, int m) : A(n, vector(m, T())) {} Matrix(int n) : A(n, vector(n, T())){}; int H() const { return A.size(); } int W() const { return A[0].size(); } int size() const { return A.size(); } inline const vector &operator[](int k) const { return A[k]; } inline vector &operator[](int k) { return A[k]; } static Matrix I(int n) { Matrix mat(n); for (int i = 0; i < n; i++) mat[i][i] = 1; return (mat); } Matrix &operator+=(const Matrix &B) { int n = H(), m = W(); assert(n == B.H() && m == B.W()); 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) { int n = H(), m = W(); assert(n == B.H() && m == B.W()); 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) { int n = H(), m = B.W(), p = W(); assert(p == B.H()); vector> C(n, vector(m, T{})); for (int i = 0; i < n; i++) for (int k = 0; k < p; k++) for (int j = 0; j < m; j++) C[i][j] += (*this)[i][k] * B[k][j]; A.swap(C); return (*this); } Matrix &operator^=(long long k) { Matrix B = Matrix::I(H()); while (k > 0) { if (k & 1) B *= *this; *this *= *this; k >>= 1LL; } A.swap(B.A); return (*this); } 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); } bool operator==(const Matrix &B) const { assert(H() == B.H() && W() == B.W()); for (int i = 0; i < H(); i++) for (int j = 0; j < W(); j++) { if (A[i][j] != B[i][j]) return false; } return true; } bool operator!=(const Matrix &B) const { assert(H() == B.H() && W() == B.W()); for (int i = 0; i < H(); i++) for (int j = 0; j < W(); j++) { if (A[i][j] != B[i][j]) return true; } return false; } friend ostream &operator<<(ostream &os, const Matrix &p) { int n = p.H(), m = p.W(); for (int i = 0; i < n; i++) { os << (i ? " " : "") << "["; for (int j = 0; j < m; j++) { os << p[i][j] << (j + 1 == m ? "]\n" : ","); } } return (os); } T determinant() const { Matrix B(*this); assert(H() == W()); T ret = 1; for (int i = 0; i < H(); i++) { int idx = -1; for (int j = i; j < W(); j++) { if (B[j][i] != 0) { idx = j; break; } } if (idx == -1) return 0; if (i != idx) { ret *= T(-1); swap(B[i], B[idx]); } ret *= B[i][i]; T inv = T(1) / B[i][i]; for (int j = 0; j < W(); j++) { B[i][j] *= inv; } for (int j = i + 1; j < H(); j++) { T a = B[j][i]; if (a == 0) continue; for (int k = i; k < W(); k++) { B[j][k] -= B[i][k] * a; } } } return ret; } }; #line 92 "test.cpp" void solve() { INT(n,p); mint::set_mod(p); VV(int,a,n,n); Matrix mat(n),mat2(n); int c = 0; rep(i,n) rep(j,n) { if(a[i][j] == -1) { mat[i][j] = 1LL * p * (p - 1) / 2; mat2[i][j] = 0; c++; } else { mat[i][j] = a[i][j]; mat2[i][j] = a[i][j]; } } cout << mat.determinant() - mat2.determinant() << '\n'; } int main() { INT(TT); while(TT--) solve(); }