結果
| 問題 |
No.1050 Zero (Maximum)
|
| コンテスト | |
| ユーザー |
👑  Kazun
|
| 提出日時 | 2021-02-19 05:02:35 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
AC
|
| 実行時間 | 196 ms / 2,000 ms |
| コード長 | 6,914 bytes |
| コンパイル時間 | 139 ms |
| コンパイル使用メモリ | 82,132 KB |
| 実行使用メモリ | 76,380 KB |
| 最終ジャッジ日時 | 2024-09-15 08:55:47 |
| 合計ジャッジ時間 | 2,654 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge6 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 15 |
ソースコード
class Modulo_Matrix():
#入力
def __init__(self,M,Mod):
self.ele=[[x%Mod for x in X] for X in M]
self.Mod=Mod
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):
T=""
(r,c)=self.size
for i in range(r):
U="["
for j in range(c):
U+=str(self.ele[i][j])+" "
T+=U[:-1]+"]\n"
return "["+T[:-1]+"]"
#+,-
def __pos__(self):
return self
def __neg__(self):
return self.__scale__(-1)
#加法
def __add__(self,other):
A=self
B=other
if A.size!=B.size:
raise Modulo_Matrix_Error("2つの行列のサイズが異なります.({},{})".format(A.size,B.size))
M=A.ele
N=B.ele
L=[0]*self.row
for i in range(A.row):
E,F=M[i],N[i]
L[i]=[(E[j]+F[j])%self.Mod for j in range(self.col)]
return Modulo_Matrix(L,self.Mod)
#減法
def __sub__(self,other):
return self+(-other)
#乗法
def __mul__(self,other):
A=self
B=other
if isinstance(B,Modulo_Matrix):
R=A.row
C=B.col
if A.col!=B.row:
raise Modulo_Matrix_Error("左側の列と右側の行が一致しません.({},{})".format(A.size,B.size))
G=A.col
M=A.ele
N=B.ele
E=[[0]*other.col for _ in range(self.row)]
for i in range(R):
F=M[i]
for j in range(C):
for k in range(G):
E[i][j]=(E[i][j]+F[k]*N[k][j])%self.Mod
return Modulo_Matrix(E,self.Mod)
elif isinstance(B,int):
return A.__scale__(B)
def __rmul__(self,other):
if isinstance(other,int):
return self*other
def Inverse(self):
M=self
if M.row!=M.col:
raise Modulo_Matrix_Error("正方行列ではありません.")
R=M.row
I=[[1*(i==j) for j in range(R)] for i in range(R)]
G=M.Column_Union(Modulo_Matrix(I,self.Mod))
G=G.Row_Reduce()
A,B=[None]*R,[None]*R
for i in range(R):
A[i]=G.ele[i][:R]
B[i]=G.ele[i][R:]
if A==I:
return Modulo_Matrix(B,self.Mod)
else:
raise Modulo_Matrix_Error("正則ではありません.")
#スカラー倍
def __scale__(self,r):
M=self.ele
L=[[(r*M[i][j])%self.Mod for j in range(self.col)] for i in range(self.row)]
return Modulo_Matrix(L,self.Mod)
#累乗
def __pow__(self,n):
A=self
if A.row!=A.col:
raise Modulo_Matrix_Error("正方行列ではありません.")
if n<0:
return (A**(-n)).Inverse()
R=Modulo_Matrix([[1*(i==j) for j in range(A.row)] for i in range(A.row)],self.Mod)
D=A
while n>0:
if n%2==1:
R*=D
D*=D
n=n>>1
return R
#等号
def __eq__(self,other):
A=self
B=other
if A.size!=B.size:
return False
for i in range(A.row):
for j in range(A.col):
if A.ele[i][j]!=B.ele[i][j]:
return False
return True
#不等号
def __neq__(self,other):
return not(self==other)
#転置
def Transpose(self):
self.col,self.row=self.row,self.col
self.ele=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,self.Mod-2,self.Mod)
for j in range(C):
T[I][j]*=u_inv
T[I][j]%=self.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]%=self.Mod
I+=1
if I==R:
break
return Modulo_Matrix(T,self.Mod)
#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,self.Mod-2,self.Mod)
for i in range(R):
T[i][J]*=u_inv
T[i][J]%=self.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]%=self.Mod
J+=1
if J==C:
break
return Modulo_Matrix(T,self.Mod)
#行列の階数
def Rank(self):
M=self.Row_Reduce()
(R,C)=M.size
T=M.ele
S=0
for i in range(R):
f=False
for j in range(C):
if T[i][j]!=0:
f=True
break
if f:
S+=1
else:
break
return S
#行の結合
def Row_Union(self,other):
return Modulo_Matrix(self.ele+other.ele,self.Mod)
#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,self.Mod)
def __getitem__(self,index):
assert isinstance(index,tuple) and len(index)==2
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
#================================================
M,K=map(int,input().split())
Mod=10**9+7
X=Modulo_Matrix([[1]*M for _ in range(M)],Mod)
for i in range(M):
for j in range(M):
X[(i*j)%M,i]+=1
print(pow(X,K)[0,0])