from copy import deepcopy class Modulo_Matrix(): __slots__=("ele","row","col","size") #入力 def __init__(self,M): """ 行列 M の定義 M: 行列 ※ Mod: 法はグローバル変数から指定 """ self.ele=[[x%Mod for x in X] for X in M] R=len(M) if R!=0: C=len(M[0]) else: C=0 self.row=R self.col=C self.size=(R,C) #出力 def __str__(self): return "["+"\n".join(map(str,self.ele))+"]" def __repr__(self): return str(self) #+,- def __pos__(self): return self def __neg__(self): return self.__scale__(-1) #加法 def __add__(self,other): M=self.ele; N=other.ele L=[[0]*self.col for _ in range(self.row)] for i in range(self.row): Li,Mi,Ni=L[i],M[i],N[i] for j in range(self.col): Li[j]=Mi[j]+Ni[j] return Modulo_Matrix(L) def __iadd__(self,other): M=self.ele; N=other.ele for i in range(self.row): Mi,Ni=M[i],N[i] for j in range(self.col): Mi[j]+=Ni[j] Mi[j]%=Mod return self #減法 def __sub__(self,other): M=self.ele; N=other.ele L=[[0]*self.col for _ in range(self.row)] for i in range(self.row): Li,Mi,Ni=L[i],M[i],N[i] for j in range(self.col): Li[j]=Mi[j]-Ni[j] return Modulo_Matrix(L) def __isub__(self,other): M=self.ele; N=other.ele for i in range(self.row): Mi,Ni=M[i],N[i] for j in range(self.col): Mi[j]-=Ni[j] Mi[j]%=Mod return self #乗法 def __mul__(self,other): if isinstance(other,Modulo_Matrix): assert self.col==other.row, "左側の列と右側の行が一致しません.({},{})".format(self.size,other.size) M=self.ele; N=other.ele E=[[0]*other.col for _ in range(self.row)] for i in range(self.row): Ei,Mi=E[i],M[i] for k in range(self.col): m_ik,Nk=Mi[k],N[k] for j in range(other.col): Ei[j]+=m_ik*Nk[j] Ei[j]%=Mod return Modulo_Matrix(E) elif isinstance(other,int): return self.__scale__(other) def __rmul__(self,other): if isinstance(other,int): return self.__scale__(other) def inverse(self): assert self.row==self.col,"正方行列ではありません." M=self N=M.row R=[[1 if i==j else 0 for j in range(N)] for i in range(N)] T=deepcopy(M.ele) for j in range(N): if T[j][j]==0: for i in range(j+1,N): if T[i][j]: break else: assert 0, "正則行列ではありません" T[j],T[i]=T[i],T[j] R[j],R[i]=R[i],R[j] Tj,Rj=T[j],R[j] inv=pow(Tj[j],Mod-2,Mod) for k in range(N): Tj[k]*=inv; Tj[k]%=Mod Rj[k]*=inv; Rj[k]%=Mod for i in range(N): if i==j: continue c=T[i][j] Ti,Ri=T[i],R[i] for k in range(N): Ti[k]-=Tj[k]*c; Ti[k]%=Mod Ri[k]-=Rj[k]*c; Ri[k]%=Mod return Modulo_Matrix(R) #スカラー倍 def __scale__(self,r): M=self.ele r%=Mod L=[[(r*M[i][j])%Mod for j in range(self.col)] for i in range(self.row)] return Modulo_Matrix(L) #累乗 def __pow__(self,n): assert self.row==self.col, "正方行列ではありません." r=self.col def __mat_mul(A,B): E=[[0]*r for _ in range(r)] for i in range(r): a=A[i]; e=E[i] for k in range(r): b=B[k] for j in range(r): e[j]+=a[k]*b[j] e[j]%=Mod return E X=deepcopy(self.ele) E=[[1 if i==j else 0 for j in range(r)] for i in range(r)] sgn=1 if n>=0 else -1 n=abs(n) while True: if n&1: E=__mat_mul(E,X) n>>=1 if n: X=__mat_mul(X,X) else: break if sgn==1: return Modulo_Matrix(E) else: return Modulo_Matrix(E).inverse() #等号 def __eq__(self,other): return self.ele==other.ele #不等号 def __neq__(self,other): return not(self==other) #転置 def transpose(self): return Modulo_Matrix(list(map(list,zip(*self.ele)))) #行基本変形 def row_reduce(self): M=self (R,C)=M.size T=[] for i in range(R): U=[] for j in range(C): U.append(M.ele[i][j]) T.append(U) I=0 for J in range(C): if T[I][J]==0: for i in range(I+1,R): if T[i][J]!=0: T[i],T[I]=T[I],T[i] break if T[I][J]!=0: u=T[I][J] u_inv=pow(u,Mod-2,Mod) for j in range(C): T[I][j]*=u_inv T[I][j]%=Mod for i in range(R): if i!=I: v=T[i][J] for j in range(C): T[i][j]-=v*T[I][j] T[i][j]%=Mod I+=1 if I==R: break return Modulo_Matrix(T) #列基本変形 def column_reduce(self): M=self (R,C)=M.size T=[] for i in range(R): U=[] for j in range(C): U.append(M.ele[i][j]) T.append(U) J=0 for I in range(R): if T[I][J]==0: for j in range(J+1,C): if T[I][j]!=0: for k in range(R): T[k][j],T[k][J]=T[k][J],T[k][j] break if T[I][J]!=0: u=T[I][J] u_inv=pow(u,Mod-2,Mod) for i in range(R): T[i][J]*=u_inv T[i][J]%=Mod for j in range(C): if j!=J: v=T[I][j] for i in range(R): T[i][j]-=v*T[i][J] T[i][j]%=Mod J+=1 if J==C: break return Modulo_Matrix(T) #行列の階数 def rank(self): M=self.row_reduce() (R,C)=M.size T=M.ele rnk=0 for i in range(R): f=False for j in range(C): if T[i][j]!=0: f=True break if f: rnk+=1 else: break return rnk #行の結合 def row_union(self,other): return Modulo_Matrix(self.ele+other.ele) #列の結合 def column_union(self,other): E=[] for i in range(self.row): E.append(self.ele[i]+other.ele[i]) return Modulo_Matrix(E) def __getitem__(self,index): if isinstance(index, int): return self.ele[index] else: return self.ele[index[0]][index[1]] def __setitem__(self,index,val): assert isinstance(index,tuple) and len(index)==2 self.ele[index[0]][index[1]]=val #正方行列? def Is_Square(M): return M.row==M.col def Determinant(M): """ 正方行列 M の行列式 (素数 mod) を求める.""" assert Is_Square(M) N=M.row T=deepcopy(M.ele) det=1 for j in range(N): if T[j][j]==0: for i in range(j+1,N): if T[i][j]: break else: return 0 T[j],T[i]=T[i],T[j] det=-det Tj=T[j] inv=pow(Tj[j],Mod-2,Mod) for i in range(j+1,N): Ti=T[i] c=-inv*Ti[j]%Mod for k in range(N): Ti[k]+=c*Tj[k] Ti[k]%=Mod for i in range(N): det*=T[i][i] det%=Mod return det #================================================== def solve(): N,P=map(int,input().split()) global Mod; Mod=P A=[None]*N for i in range(N): A[i]=list(map(int,input().split())) if P!=2: return 0 else: I=set(); J=set() for i in range(N): if A[i].count(-1)==0: continue elif A[i].count(-1)>=2: return 0 j=A[i].index(-1) if j in J: return 0 I.add(i) J.add(j) B=[[A[i][j] for j in range(N) if j not in J] for i in range(N) if i not in I] return Determinant(Modulo_Matrix(B)) #================================================== import sys input=sys.stdin.readline write=sys.stdout.write T=int(input()) write("\n".join(map(str,[solve() for t in range(T)])))