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ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#709161 | #6566. Power of Divisors | tassei903 | AC ✓ | 16ms | 10764kb | Python3 | 1.2kb | 2024-11-04 12:28:34 | 2024-11-04 12:28:36 |
Judging History
answer
from math import floor
def kth_root_integer(a: int, k: int) -> int:
if a <= 1 or k == 1: return a
if 64 <= k: return 1
def check(n: int) -> bool:
x = 1; m = n
p = k
while p:
if p & 1: x *= m
p >>= 1
m *= m
return x <= a
n = int(pow(a, 1 / k))
while not check(n): n -= 1
while check(n + 1): n += 1
return n
def divisors(n):
a = []
i = 1
while i * i <= n:
if n % i == 0:
a.append(i)
if n // i != i:
a.append(n//i)
i += 1
return a
def solve():
n = int(input())
if n == 1:
print(1)
return
b, e = n, 1
for i in range(63, 1, -1):
x = kth_root_integer(n, i)
if x ** i != n:
continue
b, e = x, i
break
if e == 1:
print(-1)
return
ans = 10 ** 20
for j in sorted(divisors(e))[:-1]:
x = b ** j
if len(divisors(x)) == e // j:
print(x)
break
else:
print(-1)
solve()
# for _ in range(int(input())):
# solve()
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 11ms
memory: 10556kb
input:
15625
output:
25
result:
ok single line: '25'
Test #2:
score: 0
Accepted
time: 11ms
memory: 10588kb
input:
64000000
output:
20
result:
ok single line: '20'
Test #3:
score: 0
Accepted
time: 15ms
memory: 10684kb
input:
65536
output:
-1
result:
ok single line: '-1'
Test #4:
score: 0
Accepted
time: 8ms
memory: 10540kb
input:
1
output:
1
result:
ok single line: '1'
Test #5:
score: 0
Accepted
time: 12ms
memory: 10648kb
input:
10
output:
-1
result:
ok single line: '-1'
Test #6:
score: 0
Accepted
time: 6ms
memory: 10548kb
input:
100
output:
-1
result:
ok single line: '-1'
Test #7:
score: 0
Accepted
time: 14ms
memory: 10724kb
input:
10000
output:
10
result:
ok single line: '10'
Test #8:
score: 0
Accepted
time: 14ms
memory: 10688kb
input:
1000000000000000000
output:
100
result:
ok single line: '100'
Test #9:
score: 0
Accepted
time: 14ms
memory: 10764kb
input:
10372926089038969
output:
218089
result:
ok single line: '218089'
Test #10:
score: 0
Accepted
time: 10ms
memory: 10596kb
input:
10642944803293201
output:
10157
result:
ok single line: '10157'
Test #11:
score: 0
Accepted
time: 15ms
memory: 10748kb
input:
10646534823110209
output:
103182047
result:
ok single line: '103182047'
Test #12:
score: 0
Accepted
time: 7ms
memory: 10756kb
input:
1073741824
output:
32
result:
ok single line: '32'
Test #13:
score: 0
Accepted
time: 9ms
memory: 10724kb
input:
121
output:
11
result:
ok single line: '11'
Test #14:
score: 0
Accepted
time: 11ms
memory: 10652kb
input:
1296
output:
6
result:
ok single line: '6'
Test #15:
score: 0
Accepted
time: 7ms
memory: 10684kb
input:
16
output:
-1
result:
ok single line: '-1'
Test #16:
score: 0
Accepted
time: 9ms
memory: 10600kb
input:
16277421889
output:
127583
result:
ok single line: '127583'
Test #17:
score: 0
Accepted
time: 10ms
memory: 10764kb
input:
169
output:
13
result:
ok single line: '13'
Test #18:
score: 0
Accepted
time: 4ms
memory: 10748kb
input:
1985984
output:
-1
result:
ok single line: '-1'
Test #19:
score: 0
Accepted
time: 16ms
memory: 10684kb
input:
2
output:
-1
result:
ok single line: '-1'
Test #20:
score: 0
Accepted
time: 11ms
memory: 10600kb
input:
205891132094649
output:
243
result:
ok single line: '243'
Test #21:
score: 0
Accepted
time: 14ms
memory: 10664kb
input:
25
output:
5
result:
ok single line: '5'
Test #22:
score: 0
Accepted
time: 14ms
memory: 10688kb
input:
2626114239841
output:
1273
result:
ok single line: '1273'
Test #23:
score: 0
Accepted
time: 14ms
memory: 10608kb
input:
26269395104446321
output:
12731
result:
ok single line: '12731'
Test #24:
score: 0
Accepted
time: 14ms
memory: 10728kb
input:
3
output:
-1
result:
ok single line: '-1'
Test #25:
score: 0
Accepted
time: 7ms
memory: 10648kb
input:
3596345248055296
output:
88
result:
ok single line: '88'
Test #26:
score: 0
Accepted
time: 14ms
memory: 10608kb
input:
36
output:
-1
result:
ok single line: '-1'
Test #27:
score: 0
Accepted
time: 7ms
memory: 10664kb
input:
4
output:
2
result:
ok single line: '2'
Test #28:
score: 0
Accepted
time: 6ms
memory: 10700kb
input:
4096
output:
8
result:
ok single line: '8'
Test #29:
score: 0
Accepted
time: 11ms
memory: 10612kb
input:
49
output:
7
result:
ok single line: '7'
Test #30:
score: 0
Accepted
time: 12ms
memory: 10616kb
input:
5
output:
-1
result:
ok single line: '-1'
Test #31:
score: 0
Accepted
time: 7ms
memory: 10700kb
input:
576460752303423488
output:
-1
result:
ok single line: '-1'
Test #32:
score: 0
Accepted
time: 11ms
memory: 10664kb
input:
581431415926321
output:
24112889
result:
ok single line: '24112889'
Test #33:
score: 0
Accepted
time: 14ms
memory: 10548kb
input:
6
output:
-1
result:
ok single line: '-1'
Test #34:
score: 0
Accepted
time: 15ms
memory: 10660kb
input:
64
output:
4
result:
ok single line: '4'
Test #35:
score: 0
Accepted
time: 9ms
memory: 10600kb
input:
656100000000
output:
30
result:
ok single line: '30'
Test #36:
score: 0
Accepted
time: 14ms
memory: 10600kb
input:
7
output:
-1
result:
ok single line: '-1'
Test #37:
score: 0
Accepted
time: 10ms
memory: 10652kb
input:
729
output:
9
result:
ok single line: '9'
Test #38:
score: 0
Accepted
time: 15ms
memory: 10508kb
input:
8
output:
-1
result:
ok single line: '-1'
Test #39:
score: 0
Accepted
time: 11ms
memory: 10724kb
input:
81
output:
-1
result:
ok single line: '-1'
Test #40:
score: 0
Accepted
time: 14ms
memory: 10580kb
input:
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output:
452
result:
ok single line: '452'
Test #41:
score: 0
Accepted
time: 11ms
memory: 10684kb
input:
9
output:
3
result:
ok single line: '3'
Test #42:
score: 0
Accepted
time: 12ms
memory: 10700kb
input:
982134461213542729
output:
994009
result:
ok single line: '994009'
Test #43:
score: 0
Accepted
time: 11ms
memory: 10700kb
input:
9992002399680016
output:
9998
result:
ok single line: '9998'
Test #44:
score: 0
Accepted
time: 16ms
memory: 10660kb
input:
999269311525198921
output:
-1
result:
ok single line: '-1'
Test #45:
score: 0
Accepted
time: 9ms
memory: 10704kb
input:
999949000866995087
output:
-1
result:
ok single line: '-1'
Test #46:
score: 0
Accepted
time: 16ms
memory: 10612kb
input:
999995482005103081
output:
-1
result:
ok single line: '-1'
Test #47:
score: 0
Accepted
time: 10ms
memory: 10580kb
input:
999999969999997921
output:
-1
result:
ok single line: '-1'
Test #48:
score: 0
Accepted
time: 15ms
memory: 10576kb
input:
999999999999999989
output:
-1
result:
ok single line: '-1'
Test #49:
score: 0
Accepted
time: 8ms
memory: 10764kb
input:
999999999999999999
output:
-1
result:
ok single line: '-1'