結果

問題 No.3333 Consecutive Power Sum (Large)
コンテスト
ユーザー shobonvip
提出日時 2025-11-02 22:17:20
言語 PyPy3
(7.3.15)
結果
TLE  
実行時間 -
コード長 4,995 bytes
コンパイル時間 220 ms
コンパイル使用メモリ 82,884 KB
実行使用メモリ 499,044 KB
最終ジャッジ日時 2025-11-02 22:19:16
合計ジャッジ時間 114,691 ms
ジャッジサーバーID
（参考情報） 		judge1 / 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 * 3
other AC * 55 TLE * 2 -- * 6
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 # 

import os
import sys
from io import BytesIO, IOBase

BUFSIZE = 8192


class FastIO(IOBase):
	newlines = 0
	
	def __init__(self, file):
		self._fd = file.fileno()
		self.buffer = BytesIO()
		self.writable = "x" in file.mode or "r" not in file.mode
		self.write = self.buffer.write if self.writable else None
	
	def read(self):
		while True:
			b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
			if not b:
				break
			ptr = self.buffer.tell()
			self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
		self.newlines = 0
		return self.buffer.read()
	
	def readline(self):
		while self.newlines == 0:
			b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
			self.newlines = b.count(b"\n")+(not b)
			ptr = self.buffer.tell()
			self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
		self.newlines -= 1
		return self.buffer.readline()
	
	def flush(self):
		if self.writable:
			os.write(self._fd, self.buffer.getvalue())
			self.buffer.truncate(0), self.buffer.seek(0)


class IOWrapper(IOBase):
	def __init__(self, file):
		self.buffer = FastIO(file)
		self.flush = self.buffer.flush
		self.writable = self.buffer.writable
		self.write = lambda s:self.buffer.write(s.encode("ascii"))
		self.read = lambda:self.buffer.read().decode("ascii")
		self.readline = lambda:self.buffer.readline().decode("ascii")


sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda:sys.stdin.readline().rstrip("\r\n")


from collections import defaultdict

# https://qiita.com/Kiri8128/items/eca965fe86ea5f4cbb98
# このコードバグってるのかよ……
def gcd(a, b):
    while b: a, b = b, a % b
    return a
def isPrimeMR(n):
    d = n - 1
    d = d // (d & -d)
    L = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43]
    for a in L:
        t = d
        y = pow(a, t, n)
        if y == 1: continue
        while y != n - 1:
            y = (y * y) % n
            if y == 1 or t == n - 1: return 0
            t <<= 1
    return 1
def findFactorRho(n):
    m = 1 << n.bit_length() // 8
    for c in range(1, 99):
        f = lambda x: (x * x + c) % n
        y, r, q, g = 2, 1, 1, 1
        while g == 1:
            x = y
            for i in range(r):
                y = f(y)
            k = 0
            while k < r and g == 1:
                ys = y
                for i in range(min(m, r - k)):
                    y = f(y)
                    q = q * abs(x - y) % n
                g = gcd(q, n)
                k += m
            r <<= 1
        if g == n:
            g = 1
            while g == 1:
                ys = f(ys)
                g = gcd(abs(x - ys), n)
        if g < n:
            if isPrimeMR(g): return g
            elif isPrimeMR(n // g): return n // g
            return findFactorRho(g)
def primeFactor(n):
    i = 2
    ret = {}
    rhoFlg = 0
    while i*i <= n:
        k = 0
        while n % i == 0:
            n //= i
            k += 1
        if k: ret[i] = k
        i += 1 + i % 2
        if i == 101 and n >= 2 ** 20:
            while n > 1:
                if isPrimeMR(n):
                    ret[n], n = 1, 1
                else:
                    rhoFlg = 1
                    j = findFactorRho(n)
                    k = 0
                    while n % j == 0:
                        n //= j
                        k += 1
                    ret[j] = k

    if n > 1: ret[n] = 1
    if rhoFlg: ret = {x: ret[x] for x in sorted(ret)}
    return ret

n=int(input())

# e =1
# (r-l)(r+l+1) = 2n

pf2=list(primeFactor(2*n).items())
pf4=list(primeFactor(4*n).items())
pf6=list(primeFactor(6*n).items())

d2=[]
d4=[]
d6=[]

def dfs(i,x,d,pf):
	if i == len(pf):
		d.append(x)
		return
	for j in range(pf[i][1] + 1):
		dfs(i+1,x,d,pf)
		if j == pf[i][1]:break
		x *= pf[i][0]

dfs(0,1,d2,pf2)
dfs(0,1,d4,pf4)
dfs(0,1,d6,pf6)

ans=[]

# e = 1
for x in d2:
	y = 2*n//x
	x -= 1
	if (x+y)%2 != 0:
		continue
	r = (x+y)//2
	l = (x-y)//2
	if l >= r:
		continue
	if 1 <= l + 1:
		ans.append((1,l+1,r))

# e = 2
for s in d6:
	a = 6*n // s
	a -= 2*s*s
	a -= 1
	# a = s*(6*l+3) + 6*l*(l+1)
	if a < 0:
		continue

	# s*(6*t+3) + 6*t*(t+1) <= a ?
	lb = 0 # ok
	ub = 10 ** 12 + 1 # ng
	while ub - lb > 1:
		t = (ub + lb) // 2
		if s*(6*t+3) + 6*t*(t+1) <= a:
			lb = t
		else:
			ub = t
	
	if s*(6*lb+3) + 6*lb*(lb+1) == a:
		l = lb
		r = lb + s
		ans.append((2, l+1, r))

# e = 3
for s in d4:
	a = 4*n // s

	lb = 0 # ok
	ub = 10 ** 8 + 1 # ng
	while ub - lb > 1:
		t = (ub + lb) // 2
		v = t+s
		if (t+v+1)*(t*t+t+v*v+v) <= a:
			lb = t
		else:
			ub = t
	
	l = lb
	r = lb + s
	if (l+r+1)*(l*l+l+r*r+r) == a:
		ans.append((3, l+1, r))
	

for e in range(4,10**9):
	if 2**e > n:
		break 

	r=[0]
	for i in range(10**9):
		if (i+1)**e>n:break
		r.append((i+1)**e)
		r[-1] += r[-2]

	s = defaultdict(int)
	for i in range(len(r)):
		s[r[i]] = i

	for i in range(len(r)):
		if r[i]+n in s:
			ans.append((e,i+1,s[r[i]+n]))

ans.sort()

print(len(ans))
for e,l,r in ans:
	print(e,l,r)
0