#506605 (PyPy3) No.1105 Many Triplets

• 問題: No.1105 Many Triplets
• ユーザー: 👑 Kazun
• 提出日時: 2020-07-03 23:27:58
• 言語: PyPy3 (7.3.15)
• 結果: AC
• 実行時間: 62 ms / 2,000 ms
• コード長: 8,888 bytes
• コンパイル時間: 1,093 ms
• コンパイル使用メモリ: 81,848 KB
• 実行使用メモリ: 68,532 KB
• 最終ジャッジ日時: 2023-10-17 06:24:41
• 合計ジャッジ時間: 4,645 ms
• ジャッジサーバーID （参考情報）: judge12 / judge11

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	49 ms; 57,784 KB
testcase_01	AC	48 ms; 57,784 KB
testcase_02	AC	48 ms; 57,784 KB
testcase_03	AC	48 ms; 57,784 KB
testcase_04	AC	49 ms; 57,784 KB
testcase_05	AC	50 ms; 57,784 KB
testcase_06	AC	48 ms; 57,784 KB
testcase_07	AC	48 ms; 57,784 KB
testcase_08	AC	48 ms; 57,784 KB
testcase_09	AC	49 ms; 57,784 KB
testcase_10	AC	61 ms; 68,532 KB
testcase_11	AC	62 ms; 68,532 KB
testcase_12	AC	61 ms; 68,532 KB
testcase_13	AC	61 ms; 68,532 KB
testcase_14	AC	61 ms; 68,532 KB
testcase_15	AC	62 ms; 68,532 KB
testcase_16	AC	61 ms; 68,532 KB
testcase_17	AC	62 ms; 68,532 KB
testcase_18	AC	62 ms; 68,532 KB
testcase_19	AC	61 ms; 68,532 KB
testcase_20	AC	45 ms; 55,736 KB
testcase_21	AC	45 ms; 55,736 KB
testcase_22	AC	45 ms; 55,736 KB
testcase_23	AC	46 ms; 55,736 KB
testcase_24	AC	47 ms; 55,736 KB
testcase_25	AC	47 ms; 55,736 KB
testcase_26	AC	46 ms; 55,736 KB
testcase_27	AC	47 ms; 57,784 KB

ソースコード

from copy import copy,deepcopy

class Matrix_Error(Exception):
    pass

class Matrix():
    #入力
    def __init__(self,M=[]):
        self.ele=M
        R=len(M)
        if R!=0:
            C=len(M[1])
        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__(A,B):
        if A.size!=B.size:
            raise 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=[]
        for i in range(A.row):
            E=[]
            for j in range(A.col):
                E.append(M[i][j]+N[i][j])

            L.append(E)
        return Matrix(L)

    #減法
    def __sub__(A,B):
        return A+(-B)

    #乗法
    def __mul__(A,B):
        if isinstance(B,Matrix):
            R=A.row
            C=B.col

            if A.col!=B.row:
                 raise 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=[]
            for i in range(R):
                F=[]
                for j in range(C):
                    S=0
                    for k in range(G):
                        S+=M[i][k]*N[k][j]
                    F.append(S)
                E.append(F)

            return Matrix(E)
        
        elif isinstance(B,int):
            return A.__scale__(B)

    def __rmul__(A,B):
        if isinstance(B,int):
            return A*B

    def Inverse(M):
        if M.row!=M.col:
            raise 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(Matrix(I))
        G=G.Row_Reduce()
        
        A,B=[],[]
        for i in range(R):
            A.append(copy(G.ele[i][:R]))
            B.append(copy(G.ele[i][R:]))

        if A==I:
            return Matrix(B)
        else:
            raise Matrix_Error("正則ではありません.")
        
    #スカラー倍
    def __scale__(A,r):
        M=A.ele
        L=[[r*M[i][j] for j in range(A.col)] for i in range(A.row)]
        return Matrix(L)

    #累乗
    def __pow__(A,n):
        if A.row!=A.col:
            raise Matrix_Error("正方行列ではありません.")

        if n<0:
            return (A**(-n)).Inverse()
        
        R=Matrix([[1*(i==j) for j in range(A.row)] for i in range(A.row)])
        D=A

        while n>0:
            if n%2==1:
                R*=D
            D*=D
            n=n>>1
                
        return R        

    #等号
    def __eq__(A,B):
        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__(A,B):
        return not(A==B)

    #転置
    def Transpose(self):
        (R,C)=self.size
        E=[[0]*R for _ in range(C)]

        for i in range(C):
            for j in range(R):
                E[i][j]=(self.ele)[j][i]

        return Matrix(E)
    
    #行基本変形
    def Row_Reduce(M):
        (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]
                for j in range(C):
                    T[I][j]/=u

                for i in range(R):
                    if i!=I:
                        v=T[i][J]
                        for j in range(C):
                            T[i][j]-=v*T[I][j]
                I+=1
                if I==R:
                    break
                
        return Matrix(T)
    
    #列基本変形
    def Column_Reduce(M):
        (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]
                for i in range(R):
                    T[i][J]/=u

                for j in range(C):
                    if j!=J:
                        v=T[I][j]
                        for i in range(R):
                            T[i][j]-=v*T[i][J]
                J+=1
                if J==C:
                    break
                
        return Matrix(T)
    
    #行列の階数
    def Rank(M,ep=None):
        M=M.Row_Reduce()
        (R,C)=M.size
        T=M.ele
        
        S=0
        for i in range(R):
            f=False
            if ep==None:
                for j in range(C):
                    if T[i][j]!=0:
                        f=True
            else:
                for j in range(C):
                    if abs(T[i][j])>=ep:
                        f=True

            if f:
                S+=1
            else:
                break

        return S

    #行の結合
    def Row_Union(self,other):
        return 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 Matrix(E)
#-------------------------------------------------------
class Modulo_Error(Exception):
    pass

class Modulo():
    def __init__(self,a,n):
        self.a=a%n
        self.n=n

    def __str__(self):
        return "{} (mod {})".format(self.a,self.n)

    #+,-
    def __pos__(self):
        return self

    def __neg__(self):
        return  Modulo(-self.a,self.n)

    #等号,不等号
    def __eq__(self,other):
        if isinstance(other,Modulo):
            return (self.a==other.a) and (self.n==other.n)
        elif isinstance(other,int):
            return (self-other).a==0

    def __neq__(self,other):
        return not(self==other)
    
    #加法
    def __add__(self,other):
        if isinstance(other,Modulo):
            if self.n!=other.n:
                raise Modulo_Error("異なる法同士の演算です.")
            return Modulo(self.a+other.a,self.n)
        elif isinstance(other,int):
            return Modulo(self.a+other,self.n)

    def __radd__(self,other):
        if isinstance(other,int):
            return Modulo(self.a+other,self.n)
        
    #減法
    def __sub__(self,other):
        return self+(-other)

    def __rsub__(self,other):
        if isinstance(other,int):
            return -self+other
        
    #乗法
    def __mul__(self,other):
        if isinstance(other,Modulo):
            if self.n!=other.n:
                raise Modulo_Error("異なる法同士の演算です.")
            return Modulo(self.a*other.a,self.n)
        elif isinstance(other,int):
            return Modulo(self.a*other,self.n)
        
    def __rmul__(self,other):
        if isinstance(other,int):
            return Modulo(self.a*other,self.n)
        
    #Modulo逆数
    def Modulo_Inverse(self):
        x0, y0, x1, y1 = 1, 0, 0, 1
        a,b=self.a,self.n
        while b != 0:
            q, a, b = a // b, b, a % b
            x0, x1 = x1, x0 - q * x1
            y0, y1 = y1, y0 - q * y1

        if a!=1:
            raise Modulo_Error("{}の逆数が存在しません".format(self))
        else:
            return Modulo(x0,self.n)
        
    #除法
    def __truediv__(self,other):
        return self*other.Modulo_Inverse()

    #累乗
    def __pow__(self,m):
        u=abs(m)

        r=Modulo(1,self.n)

        while u>0:
            if u%2==1:
                r*=self
            self*=self
            u=u>>1

        if m>=0:
            return r
        else:
            return r.Modulo_Inverse()
#-----------------------------------------------------------
N=int(input())
A,B,C=map(int,input().split())
M=10**9+7

P=Modulo(1,M)
Q=Modulo(0,M)

X=Matrix([[P,-P,Q],[Q,P,-P],[-P,Q,P]])
Y=X**(N-1)

U=Y*Matrix([[A],[B],[C]])
print(U.ele[0][0].a,U.ele[1][0].a,U.ele[2][0].a)