結果

問題 No.3006 ベイカーの問題
ユーザー 👑 p-adic
提出日時 2025-01-11 10:13:35
言語 Python3
(3.13.1 + numpy 2.2.1 + scipy 1.14.1)
結果
AC  
実行時間 45 ms / 2,000 ms
コード長 7,091 bytes
コンパイル時間 141 ms
コンパイル使用メモリ 13,056 KB
実行使用メモリ 11,264 KB
最終ジャッジ日時 2025-01-11 14:13:50
合計ジャッジ時間 2,387 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 23
権限があれば一括ダウンロードができます

ソースコード

diff # 

class ModB:
	B = 998244353
	length_bound = 10**6 #User definition
	length_max = min( length_bound , B )
	inverse=None
	factorial=None
	factorial_inverse=None
	def SetModulo(B):
		ModB.B = int(B)
		assert(ModB.B > 0)
		ModB.length_max = min( ModB.length_bound , ModB.B )
		ModB.inverse = [None,1 if ModB.B>1 else 0]
		ModB.factorial = [1 if ModB.B>1 else 0]
		ModB.factorial_inverse = [1 if ModB.B>1 else 0]

	def __init__(self,val,valid = False):
		self.val = int(val)
		if not valid and not(0 <= self.val < ModB.B):self.val %= ModB.B
	def ref(n):
		return n if n.__class__ == __class__ else ModB(n,True)
	def get(n):
		return n.val if n.__class__ == __class__ else n
	def copy(self):
		return ModB(self.val,True)

	def __str__(self):
		return str(self.val)

	def __eq__(self,x):
		return x==self.val
	def __ne__(self,other):
		return not( self == other )

	def __iadd__(self,x):
		self.val += ModB.ref(x).val
		if self.val >= ModB.B:self.val -= ModB.B
		return self
	def __add__(self,x):
		a = self.copy()
		a += x
		return a
	def __radd__(self,x):
		return ModB(x + self.val)

	def __neg__(self):
		return ModB(ModB.B - self.val if self.val else 0,True)
	def __isub__(self,x):
		self.val -= ModB.ref(x).val
		if self.val < 0:self.val += ModB.B
		return self
	def __sub__(self,x):
		a = self.copy()
		a -= x
		return a
	def __rsub__(self,x):
		return ModB(x - self.val)

	def __mul__(self,x):
		return ModB.get(x) * self
	def __rmul__(self,x):
		return ModB(self.val * x)

	def __pow__(self,n): #Supported only if n>=0.
		answer = ModB(1)
		power = self.copy()
		while n > 0:
			if n&1:answer *= power.val
			power *= power.val
			n >>= 1
		return answer
	def __xor__(self,n): #Supported only if B is a prime and val!=0, or n>=0.
		return self ** ( ( n * (2 - ModB.B) )if n < 0 else n )

	def Inverse(n): #Supported only if B is a prime.
		if n < ModB.length_max:
			while len(ModB.inverse) <= n:ModB.inverse+=[ModB.B - ModB.inverse[ModB.B % len(ModB.inverse)] * ( ModB.B // len(ModB.inverse) ) % ModB.B]
			return ModB(ModB.inverse[n],True)
		else:return ModB(n) ** ( ModB.B - 2 )
	def __truediv__(self,x):
		return ModB.Inverse(x) * self
	def __rtruediv__(self,x):
		return x * ModB.Inverse(self.val)

	def Factorial(n):
		while len(ModB.factorial) <= n:ModB.factorial+=[ModB.factorial[-1] * len(ModB.factorial) % ModB.B]
		return ModB(ModB.factorial[n],True)
	def FactorialInverse(n): #Supported only if B is a prime.
		while len(ModB.factorial_inverse) <= n:ModB.factorial_inverse+=[ModB.factorial_inverse[-1] * ModB.Inverse( len(ModB.factorial_inverse) ).val % ModB.B]
		return ModB(ModB.factorial_inverse[n],True)
	def Combination(n,m): #Supported only if B is a prime.
		return ModB.Factorial(n) * (ModB.FactorialInverse(m).val * ModB.FactorialInverse(n-m).val)if 0<=m<=n else ModB(0,True)
ModB.inverse = [None,1 if ModB.B>1 else 0]
ModB.factorial = [1 if ModB.B>1 else 0]
ModB.factorial_inverse = [1 if ModB.B>1 else 0]

def copy(n):return n.copy()if hasattr(n,"copy")else n

class TwoByTwoMatrix:
	zero=None
	one=None

	def __init__(self,M00,M01,M10,M11):
		self.M00 = copy(M00)
		self.M01 = copy(M01)
		self.M10 = copy(M10)
		self.M11 = copy(M11)
	def copy(self):
		return self.__class__(self.M00,self.M01,self.M10,self.M11)

	def __eq__(self,other):
		return self.M00 == other.M00 and self.M01 == other.M01 and self.M10 == other.M10 and self.M11 == other.M11
	def __ne__(self,other):
		return not( self == other )

	def __iadd__(self,other):
		self.M00 += other.M00
		self.M01 += other.M01
		self.M10 += other.M10
		self.M11 += other.M11
		return self
	def __add__(self,other):
		M = self.copy()
		M += other
		return M

	def __isub__(self,other):
		self.M00 -= other.M00
		self.M01 -= other.M01
		self.M10 -= other.M10
		self.M11 -= other.M11
		return self
	def __sub__(self,other):
		M = self.copy()
		M -= other
		return M
	def __neg__(self):
		return self.__class__(-self.M00,-self.M01,-self.M10,-self.M11)

	def __mul__(self,other):
		return self.__class__(self.M00 * other.M00 + self.M01 * other.M10,self.M00 * other.M01 + self.M01 * other.M11,self.M10 * other.M00 + self.M11 * other.M10,self.M10 * other.M01 + self.M11 * other.M11)
	def __imul__(self,other):
		self.M00 , self.M01 , self.M10 , self.M11 = self.M00 * other.M00 + self.M01 * other.M10 , self.M00 * other.M01 + self.M01 * other.M11 , self.M10 * other.M00 + self.M11 * other.M10 , self.M10 * other.M01 + self.M11 * other.M11
		return self
	def ScalarMultiply(self,x):
		self.M00 *= x
		self.M01 *= x
		self.M10 *= x
		self.M11 *= x
		return self

	def det(self):
		return self.M00 * self.M11 - self.M01 * self.M10
	def tr(self):
		return self.M00 + self.M11

	def Adjugate(self):
		return self.__class__( self.M11 , - self.M01 , - self.M10 , self.M00 )
	def Inverse(self):
		return self.Adjugate().ScalarMultiply( 1 / self.det() )
		#d = self.det()
		#assert( d in [1,-1] ) #For the case of integer coefficients
		#return self.Adjugate().ScalarMultiply( d )
	def __truediv__(self,other):
		return self * other.Inverse()
	def __itruediv__(self,other):
		self *= other.Inverse()
		return self

	def __pow__(self,n): #Supported only when n>=0
		answer = self.__class__.one.copy()
		power = self.copy()
		while n > 0:
			if n&1:answer *= power
			power.Square()
			n >>= 1
		return answer
	def __xor__(self,n):
		return self.Inverse()**(-n)if n < 0 else self ** n

	#private:
	def Square(self):
		self.M00 , self.M01 , self.M10 , self.M11 = self.M00 ** 2 + self.M01 * self.M10 , ( self.M00 + self.M11 ) * self.M01 , self.M10 * ( self.M00 + self.M11 ) , self.M10 * self.M01 + self.M11 ** 2
TwoByTwoMatrix.zero = TwoByTwoMatrix(0,0,0,0) #User's definition
TwoByTwoMatrix.one = TwoByTwoMatrix(1,0,0,1) #User's definition

class TwoByOneMatrix:
	zero=None

	def __init__(self,M0,M1):
		self.M0 = copy(M0)
		self.M1 = copy(M1)
	def copy(self):
		return self.__class__(self.M0,self.M1)

	def __eq__(self,other):
		return self.M0 == other.M0 and self.M1 == other.M1
	def __ne__(self,other):
		return not( self == other )

	def __iadd__(self,other):
		self.M0 += other.M0
		self.M1 += other.M1
		return self
	def __add__(self,other):
		M = self.copy()
		M += other
		return M

	def __isub__(self,other):
		self.M0 -= other.M0
		self.M1 -= other.M1
		return self
	def __sub__(self,other):
		M = self.copy()
		M -= other
		return M
	def __neg__(self):
		return self.__class__(-self.M0,-self.M1)

	def __rmul__(self,T):
		return self.copy().Act(T)
	def Act(self,T,n=1):
		if n==1:self.M0 , self.M1 = T.M00 * self.M0 + T.M01 * self.M1 , T.M10 * self.M0 + T.M11 * self.M1
		elif n:
			if n>0:p = T.copy()
			else:n , p = -n , T.Inverse()
			while n:
				if n&1:self.M0 , self.M1 = p.M00 * self.M0 + p.M01 * self.M1 , p.M10 * self.M0 + p.M11 * self.M1
				n >>= 1
				p.Square()
		return self
	def ScalarMultiply(self,x):
		self.M0 *= x
		self.M1 *= x
		return self
TwoByOneMatrix.zero = TwoByOneMatrix(0,0) #User's definition

X,Y,N=map(int,input().split())
X,Y=ModB(X),ModB(Y)
if[X,Y]==[1,0]:exit(print(ModB(N),0))
A=TwoByTwoMatrix(X,-5*Y,Y,X)
E=TwoByTwoMatrix.one
v=TwoByOneMatrix(X,Y)
v.Act(((A^N)-E)/(A-E))
print(v.M0,v.M1)
0