結果
| 問題 |
No.1973 Divisor Sequence
|
| コンテスト | |
| ユーザー |
 Keroru
|
| 提出日時 | 2022-06-10 22:20:22 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 11,842 bytes |
| コンパイル時間 | 280 ms |
| コンパイル使用メモリ | 82,508 KB |
| 実行使用メモリ | 118,772 KB |
| 最終ジャッジ日時 | 2024-09-21 06:29:54 |
| 合計ジャッジ時間 | 6,833 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 WA * 1 |
| other | AC * 1 WA * 10 TLE * 1 -- * 10 |
ソースコード
import sys
read=sys.stdin.buffer.read;readline=sys.stdin.buffer.readline;input=lambda:sys.stdin.readline().rstrip()
import bisect,string,math,time,functools,random,fractions
from bisect import*
from heapq import heappush,heappop,heapify
from collections import deque,defaultdict,Counter
from itertools import permutations,combinations,groupby
rep=range;R=range
def I():return int(input())
def LI():return [int(i) for i in input().split()]
def SLI():return sorted([int(i) for i in input().split()])
def LI_():return [int(i)-1 for i in input().split()]
def S_():return input()
def IS():return input().split()
def LS():return [i for i in input().split()]
def NI(n):return [int(input()) for i in range(n)]
def NI_(n):return [int(input())-1 for i in range(n)]
def NLI(n):return [[int(i) for i in input().split()] for i in range(n)]
def NLI_(n):return [[int(i)-1 for i in input().split()] for i in range(n)]
def StoLI():return [ord(i)-97 for i in input()]
def ItoS(n):return chr(n+97)
def LtoS(ls):return ''.join([chr(i+97) for i in ls])
def RLI(n=8,a=1,b=10):return [random.randint(a,b)for i in range(n)]
def RI(a=1,b=10):return random.randint(a,b)
def INP():
N=6
n=random.randint(1,N)
m=random.randint(1,N)
b=random.randint(1,n)
w=random.randint(1,m)
mn=0
mx=n
#a=[random.randint(mn,mx) for i in range(n)]
return n,m,b,w
def Rtest(T):
case,err=0,0
for i in range(T):
inp=INP()
a1=naive(*inp)
a2=solve(*inp)
if a1!=a2:
print(inp)
print('naive',a1)
print('solve',a2)
err+=1
case+=1
print('Tested',case,'case with',err,'errors')
def GI(V,E,ls=None,Directed=False,index=1):
org_inp=[];g=[[] for i in range(V)]
FromStdin=True if ls==None else False
for i in range(E):
if FromStdin:
inp=LI()
org_inp.append(inp)
else:
inp=ls[i]
if len(inp)==2:a,b=inp;c=1
else:a,b,c=inp
if index==1:a-=1;b-=1
aa=a,c,;bb=b,c,;g[a].append(bb)
if not Directed:g[b].append(aa)
return g,org_inp
def RE(E):
rt=[[]for i in range(len(E))]
for i in range(len(E)):
for nb,d in E[i]:
rt[nb]+=(i,d),
return rt
def GGI(h,w,search=None,replacement_of_found='.',mp_def={'#':1,'.':0},boundary=1):
#h,w,g,sg=GGI(h,w,search=['S','G'],replacement_of_found='.',mp_def={'#':1,'.':0},boundary=1) # sample usage
mp=[boundary]*(w+2);found={}
for i in R(h):
s=input()
for char in search:
if char in s:
found[char]=((i+1)*(w+2)+s.index(char)+1)
mp_def[char]=mp_def[replacement_of_found]
mp+=[boundary]+[mp_def[j] for j in s]+[boundary]
mp+=[boundary]*(w+2)
return h+2,w+2,mp,found
def TI(n):return GI(n,n-1)
def accum(ls):
rt=[0]
for i in ls:rt+=[rt[-1]+i]
return rt
def bit_combination(n,base=2):
rt=[]
for tb in R(base**n):s=[tb//(base**bt)%base for bt in R(n)];rt+=[s]
return rt
def gcd(x,y):
if y==0:return x
if x%y==0:return y
while x%y!=0:x,y=y,x%y
return y
def YN(x):print(['NO','YES'][x])
def Yn(x):print(['No','Yes'][x])
def show(*inp,end='\n'):
if show_flg:print(*inp,end=end)
mo=10**9+7
#mo=998244353
inf=float('inf')
FourNb=[(-1,0),(1,0),(0,1),(0,-1)];EightNb=[(-1,0),(1,0),(0,1),(0,-1),(1,1),(-1,-1),(1,-1),(-1,1)];compas=dict(zip('WENS',FourNb));cursol=dict(zip('LRUD',FourNb))
alp=[chr(ord('a')+i)for i in range(26)]
#sys.setrecursionlimit(10**7)
show_flg=False
show_flg=True
## Typical bug/TIPS
## modを取らなすぎ/取りすぎ
## listの1次元化で高速化
## Verified by Yukicoder 1073
## https://yukicoder.me/problems/no/1073
##
## Matrix Class supporting operators +, -, *, %, +=, -=, *=, %=
## *, *= allows int/float/complex
## ** or pow(self,p,mod) for the size N*N matrix is implemented by Repeated squaring. O(N^3*log(p))
##
## Constructor: matrix(array), where array is 1D or 2D array. 1-dimensional array X is modified as 2D array of [X].
##
## methods
## T(): returns transposed matrix
## resize((n,m),fill=0): changes the matrix instance into the new shape (n * m), missing entries are filled with "fill" (default value is zero).
class matrix:
class MulShapeError(Exception):
"mult is not applicable between the two matrices given"
pass
def __init__(self,arr_input,mod=10**9+7):
self.mod=mod
if hasattr(arr_input[0],"__getitem__"):
self.arr=arr_input
else:
self.arr=[arr_input]
self.shape=(len(self.arr),len(self.arr[0]))
def __getitem__(self,key):
return self.arr[key]
def __setitem__(self,key,value):
self.arr[key]=value
def __iter__(self):
return iter(self.arr)
def __add__(self,B):
if type(B)!=matrix:
return NotImplemented
if B.shape!=self.shape:
return NotImplemented
rt=[[0]*self.shape[1] for i in range(self.shape[0])]
for i in range(self.shape[0]):
for j in range(self.shape[1]):
rt[i][j]=self.arr[i][j]+B.arr[i][j]
return matrix(rt)
def __iadd__(self,B):
return self.__add__(B)
def __sub__(self,B):
if type(B)!=matrix:
return NotImplemented
if B.shape!=self.shape:
return NotImplemented
rt=[[0]*self.shape[1] for i in range(self.shape[0])]
for i in range(self.shape[0]):
for j in range(self.shape[1]):
rt[i][j]=self.arr[i][j]-B.arr[i][j]
return matrix(rt)
def __isub__(self,B):
return self.__sub__(B)
def __mul__(self,M):
if type(M) in [int,float,complex]:
M=matrix([[M*(i==j) for j in range(self.shape[1])] for i in range(self.shape[1])])
if type(M)!=matrix:
return NotImplemented
if M.shape[0]!=self.shape[1]:
raise matrix.MulShapeError("mult is not applicable between the matrices of shape "+str(self.shape)+" and "+str(M.shape))
ra,ca=self.shape
rb,cb=M.shape
c=[[0]*cb for i in range(ra)]
for i in range(ra):
for j in range(cb):
for k in range(ca):
c[i][j]+=self.arr[i][k]*M.arr[k][j]
return matrix(c)
def __imul__(self,M):
return self.__mul__(M)
def __rmul__(self,M):
if type(M) in [int,float,complex]:
M=matrix([[M*(i==j) for j in range(self.shape[1])] for i in range(self.shape[1])])
if type(M)!=matrix:
return NotImplemented
if M.shape[0]!=self.shape[1]:
raise matrix.MulShapeError("mult is not applicable between the matrix shape "+str(self.shape)+" and "+str(M.shape))
ra,ca=M.shape
rb,cb=self.shape
c=[[0]*cb for i in range(ra)]
for i in range(ra):
for j in range(cb):
for k in range(ca):
c[i][j]+=M.arr[i][k]*self.arr[k][j]
return matrix(c)
def __mod__(self,p):
if type(p)!=int:
return NotImplemented
c=[[0]*self.shape[1] for i in range(self.shape[0])]
for i in range(self.shape[0]):
for j in range(self.shape[1]):
c[i][j]=self.arr[i][j]%p
return matrix(c)
def __imod__(self,p):
return self.__mod__(p)
def __pow__(self,p):
if type(p)!=int or self.shape[0]!=self.shape[1]:
return NotImplemented
A=matrix(self.arr)
R=matrix([[1*(i==j) for j in range(self.shape[0])] for i in range(self.shape[0])])
while p>0:
if p&1:
R*=A
R%=self.mod
A*=A
A%=self.mod
p>>=1
return R
def __neg__(self):
return self.__mul__(-1)
def __str__(self):
rt='['
for i in self.arr:
rt=rt+str(i)+",\n"
return rt[:-2]+']'
def T(self):
rt=[[0]*self.shape[0] for i in range(self.shape[1])]
for i in range(self.shape[0]):
for j in range(self.shape[1]):
rt[j][i]=self.arr[i][j]
return matrix(rt)
def resize(self,new_shape,fill=0):
t_arr=[]
for i in self.arr:
t_arr+=i
t_arr.reverse()
n,m=new_shape
self.shape=(n,m)
self.arr=[[fill]*m for i in range(n)]
for i in range(self.shape[0]):
for j in range(self.shape[1]):
if t_arr:
self.arr[i][j]=t_arr.pop()
return
def view(self):
for i in self.arr:
print(i)
########################################################################################################################################################################
# Verified by
# https://yukicoder.me/problems/no/979
# https://atcoder.jp/contests/abc152/tasks/abc152_e
## return prime factors of N as dictionary {prime p:power of p}
## within 2 sec for N = 2*10**20+7
def primeFactor(N):
i,n=2,N
ret={}
d,sq=2,99
while i<=sq:
k=0
while n%i==0:
n,k,ret[i]=n//i,k+1,k+1
if k>0 or i==97:
sq=int(n**(1/2)+0.5)
if i<4:
i=i*2-1
else:
i,d=i+d,d^6
if n>1:
ret[n]=1
return ret
## return divisors of n as list
def divisors(n):
div=[1]
for i,j in primeFactor(n).items():
div=[(i**k)*d for d in div for k in range(j+1)]
return div
## return the array s such that s[q] = the minimum prime factor of q
def sieve(x):
s=[i for i in range(x+1)]
p=2
while p*p<=x:
if s[p]==p:
for q in range(2*p,x+1,p):
if s[q]==q:
s[q]=p
p+=1
return s
## return the list of prime numbers in [2,N], using eratosthenes sieve
## around 800 ms for N = 10**6 by PyPy3 (7.3.0) @ AtCoder
def PrimeNumSet(N):
M=int(N**0.5)
seachList=[i for i in range(2,N+1)]
primes=[]
while seachList:
if seachList[0]>M:
break
primes.append(seachList[0])
tmp=seachList[0]
seachList=[i for i in seachList if i%tmp!=0]
return primes+seachList
## retrun LCM of numbers in list b
## within 2sec for no of B = 10*5 and Bi < 10**6
def LCM(b,mo=10**9+7):
prs=PrimeNumSet(max(b))
M=dict(zip(prs,[0]*len(prs)))
for i in b:
dc=primeFactor(i)
for j,k in dc.items():
M[j]=max(M[j],k)
r=1
for j,k in M.items():
if k!=0:
r*=pow(j,k,mo)
r%=mo
return r
## return (a,b,gcd(x,y)) s.t. a*x+b*y=gcd(x,y)
def extgcd(x,y):
if y==0:
return 1,0
r0,r1,s0,s1 = x,y,1,0
while r1!= 0:
r0,r1,s0,s1=r1,r0%r1,s1,s0-r0//r1*s1
return s0,(r0-s0*x)//y,x*s0+y*(r0-s0*x)//y
## return x,LCM(mods) s.t. x = rem_i (mod_i), x = -1 if such x doesn't exist
## verified by ABC193E
## https://atcoder.jp/contests/abc193/tasks/abc193_e
def crt(rems,mods):
n=len(rems)
if n!=len(mods):
return NotImplemented
x,d=0,1
for r,m in zip(rems,mods):
a,b,g=extgcd(d,m)
x,d=(m*b*x+d*a*r)//g,d*(m//g)
x%=d
for r,m in zip(rems,mods):
if r!=x%m:
return -1,d
return x,d
## returns the maximum integer rt s.t. rt*rt<=x
## verified by ABC191D
## https://atcoder.jp/contests/abc191/tasks/abc191_d
def intsqrt(x):
if x<0:
return NotImplemented
rt=int(x**0.5)-1
while (rt+1)**2<=x:
rt+=1
return rt
ans=0
mo=10**9+7
n,m=LI()
dv=sorted(divisors(m))
r=len(dv)
D=matrix([0]*r*r,mod=mo)
D.resize([r,r])
for i in range(r):
for j in range(r):
if dv[i]*dv[j]<=m:
D[i][j]=1
x=matrix([1]*r)
x.resize([r,1])
for i in (D**(n-1))*x:
ans+=sum(i)
print(ans%mo)