結果

問題 No.2365 Present of good number
ユーザー Shirotsume
提出日時 2023-06-30 22:55:20
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 52 ms / 2,000 ms
コード長 10,599 bytes
コンパイル時間 693 ms
コンパイル使用メモリ 82,256 KB
実行使用メモリ 66,944 KB
最終ジャッジ日時 2024-07-07 10:49:11
合計ジャッジ時間 3,265 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge5
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 * 2
other AC * 39
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 #
プレゼンテーションモードにする

import sys, time, random
from collections import deque, Counter, defaultdict
input = lambda: sys.stdin.readline().rstrip()
ii = lambda: int(input())
mi = lambda: map(int, input().split())
li = lambda: list(mi())
from math import gcd
def isprime(n):
    if n <= 2:
        return n == 2
    if n % 2 == 0:
        return False
    s = 0
    t = n - 1
    while t % 2 == 0:
        s += 1
        t //= 2
    
    for a in [2,325,9375,28178,450775,9780504,1795265022]:
        if a >= n:
            break
        x = pow(a, t, n)
        if x == 1 or x == n - 1:
            continue
        for _ in range(s):
            x = (x * x) % n
            if x == n - 1:
                break
        if x == n - 1:
            continue
        return False
    return True
def Pollad(N):
    if N % 2 == 0:
        return 2
    if isprime(N):
        return N
    def f(x):
        return (x * x + 1) % N
    step = 0
    while True:
        step += 1
        x = step
        y = f(x)
        while True:
            p = gcd(y - x + N, N)
            if p == 0 or p == N:
                break
            if p != 1:
                return p
            x = f(x)
            y = f(f(y))
def Primefact(N):
    if N == 1:
        return []
    q = []
    q.append(N)
    ret = []
    while q:
        now = q.pop()
        if now == 1:
            continue
        p = Pollad(now)
        if p == now:
            ret.append(p)
        else:
            q.append(p)
            q.append(now // p)
    return Counter(ret)
from copy import deepcopy
class Modulo_Matrix_Error(Exception):
    pass
Mod = 10 ** 9 + 6
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):
        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 __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):
            if self.col!=other.row:
                raise Modulo_Matrix_Error("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):
        if  self.row!=self.col:
            raise Modulo_Matrix_Error("正方行列ではありません.")
        M=self
        N=M.row
        R=[[int(i==j) 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:
                    raise Modulo_Matrix_Error("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
        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):
        if self.row!=self.col:
            raise Modulo_Matrix_Error("正方行列ではありません.")
        def __mat_mul(A,B,r,Mod):
            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
        def __mat_pow(A,n,r,Mod):
            if n==0:
                return [[1 if i==j else 0 for j in range(r)] for i in range(r)]
            else:
                return __mat_mul(__mat_pow(A,n-1,r,Mod),A,r,Mod) if n&1 else __mat_pow(__mat_mul(A,A,r,Mod),n>>1,r,Mod)
        S=__mat_pow(self.ele,abs(n),self.col,Mod)
        if n>=0:
            return Modulo_Matrix(S)
        else:
            return Modulo_Matrix(S).Inverse()
    #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,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
        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,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)
    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
#=================================================
mod = 10 ** 9 + 7
n, k = mi()
while k > 0:
    now = n
    C = Primefact(now)
    S = set(C.keys())
    S.discard(2)
    S.discard(3)
    if S:
        k -= 1
        n = 1
        for v, c in C.items():
            n *= pow(v + 1, c)
    else:
        break
if k == 0:
    ans = n % mod
else:
    p = 0
    while n % 2 == 0:
        p += 1
        n //= 2
    q = 0
    while n % 3 == 0:
        q += 1
        n //= 3
    
    A = Modulo_Matrix([[0, 2], [1, 0]])
    A = A**k
    A *= Modulo_Matrix([[p,], [q,]])
    ans = pow(2, A[0,0], mod) * pow(3, A[1,0], mod) % mod 
print(ans)
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