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QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#117847 | #6566. Power of Divisors | Klaus26 | AC ✓ | 9ms | 9204kb | C++20 | 2.6kb | 2023-07-02 11:09:28 | 2023-07-02 11:09:31 |
Judging History
answer
#include <bits/stdc++.h>
using namespace std;
#ifdef LOCAL
#include "../debug.h"
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif
#define fst first
#define snd second
#define fore(i,a,b) for(int i=a,ThxDem=b;i<ThxDem;++i)
#define pb push_back
using ll = long long;
ll gcd(ll a, ll b){return a?gcd(b%a,a):b;}
ll mulmod(ll a, ll b, ll m) {
ll r=a*b-(ll)((long double)a*b/m+.5)*m;
return r<0?r+m:r;
}
ll expmod(ll b, ll e, ll m){
if(!e)return 1;
ll q=expmod(b,e/2,m);q=mulmod(q,q,m);
return e&1?mulmod(b,q,m):q;
}
bool is_prime_prob(ll n, int a){
if(n==a)return true;
ll s=0,d=n-1;
while(d%2==0)s++,d/=2;
ll x=expmod(a,d,n);
if((x==1)||(x+1==n))return true;
fore(_,0,s-1){
x=mulmod(x,x,n);
if(x==1)return false;
if(x+1==n)return true;
}
return false;
}
bool rabin(ll n){ // true iff n is prime
if(n==1)return false;
int ar[]={2,3,5,7,11,13,17,19,23};
fore(i,0,9)if(!is_prime_prob(n,ar[i]))return false;
return true;
}
// optimized version: replace rho and fact with the following:
const int MAXP=1e6+100; // sieve size
int sv[MAXP]; // sieve
ll add(ll a, ll b, ll m){return (a+=b)<m?a:a-m;}
ll rho(ll n){
static ll s[MAXP];
while(1){
ll x=rand()%n,y=x,c=rand()%n;
ll *px=s,*py=s,v=0,p=1;
while(1){
*py++=y=add(mulmod(y,y,n),c,n);
*py++=y=add(mulmod(y,y,n),c,n);
if((x=*px++)==y)break;
ll t=p;
p=mulmod(p,abs(y-x),n);
if(!p)return gcd(t,n);
if(++v==26){
if((p=gcd(p,n))>1&&p<n)return p;
v=0;
}
}
if(v&&(p=gcd(p,n))>1&&p<n)return p;
}
}
void init_sv(){
fore(i,2,MAXP)if(!sv[i])for(ll j=i;j<MAXP;j+=i)sv[j]=i;
}
void fact(ll n, map<ll,int>& f){ // call init_sv first!!!
for(auto&& p:f){
while(n%p.fst==0){
p.snd++;
n/=p.fst;
}
}
if(n<MAXP)while(n>1)f[sv[n]]++,n/=sv[n];
else if(rabin(n))f[n]++;
else {ll q=rho(n);fact(q,f);fact(n/q,f);}
}
const ll oo = 1e18+1;
ll x;
ll ans = 1e18+1;
void solve(int i, vector<pair<ll,int>>& v, ll p, ll num){
if(i == int(v.size())){
if(p <= 62){
bool ok = 1;
ll y = x;
while(p){
if(y < 1) break;
ok &= y%num==0;
y/=num;
p--;
}
if(ok && y == 1 && p == 0) ans = min(ans,num);
}
}else{
ll cur = 1;
for(ll j=0; j<=v[i].second; j++){
solve(i+1,v,p*(j+1),cur*num);
cur *= v[i].first;
}
}
}
int main(){
ios_base::sync_with_stdio(0); cin.tie(0);
cin>>x;
init_sv();
map<ll,int> f;
fact(x,f);
vector<pair<ll,int>> dv;
for(auto& [p,e] : f){
dv.push_back(make_pair(p,e));
}
solve(0,dv,1,1);
cout<<(ans == oo ? -1 : ans)<<'\n';
return 0;
}
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 8ms
memory: 8280kb
input:
15625
output:
25
result:
ok single line: '25'
Test #2:
score: 0
Accepted
time: 4ms
memory: 8516kb
input:
64000000
output:
20
result:
ok single line: '20'
Test #3:
score: 0
Accepted
time: 6ms
memory: 9032kb
input:
65536
output:
-1
result:
ok single line: '-1'
Test #4:
score: 0
Accepted
time: 8ms
memory: 8492kb
input:
1
output:
1
result:
ok single line: '1'
Test #5:
score: 0
Accepted
time: 8ms
memory: 8196kb
input:
10
output:
-1
result:
ok single line: '-1'
Test #6:
score: 0
Accepted
time: 9ms
memory: 7376kb
input:
100
output:
-1
result:
ok single line: '-1'
Test #7:
score: 0
Accepted
time: 4ms
memory: 8872kb
input:
10000
output:
10
result:
ok single line: '10'
Test #8:
score: 0
Accepted
time: 9ms
memory: 8752kb
input:
1000000000000000000
output:
100
result:
ok single line: '100'
Test #9:
score: 0
Accepted
time: 8ms
memory: 7836kb
input:
10372926089038969
output:
218089
result:
ok single line: '218089'
Test #10:
score: 0
Accepted
time: 8ms
memory: 7592kb
input:
10642944803293201
output:
10157
result:
ok single line: '10157'
Test #11:
score: 0
Accepted
time: 9ms
memory: 7380kb
input:
10646534823110209
output:
103182047
result:
ok single line: '103182047'
Test #12:
score: 0
Accepted
time: 4ms
memory: 8380kb
input:
1073741824
output:
32
result:
ok single line: '32'
Test #13:
score: 0
Accepted
time: 8ms
memory: 7568kb
input:
121
output:
11
result:
ok single line: '11'
Test #14:
score: 0
Accepted
time: 9ms
memory: 7984kb
input:
1296
output:
6
result:
ok single line: '6'
Test #15:
score: 0
Accepted
time: 9ms
memory: 7580kb
input:
16
output:
-1
result:
ok single line: '-1'
Test #16:
score: 0
Accepted
time: 8ms
memory: 7876kb
input:
16277421889
output:
127583
result:
ok single line: '127583'
Test #17:
score: 0
Accepted
time: 8ms
memory: 8444kb
input:
169
output:
13
result:
ok single line: '13'
Test #18:
score: 0
Accepted
time: 5ms
memory: 9004kb
input:
1985984
output:
-1
result:
ok single line: '-1'
Test #19:
score: 0
Accepted
time: 8ms
memory: 8240kb
input:
2
output:
-1
result:
ok single line: '-1'
Test #20:
score: 0
Accepted
time: 6ms
memory: 8700kb
input:
205891132094649
output:
243
result:
ok single line: '243'
Test #21:
score: 0
Accepted
time: 4ms
memory: 7880kb
input:
25
output:
5
result:
ok single line: '5'
Test #22:
score: 0
Accepted
time: 4ms
memory: 7540kb
input:
2626114239841
output:
1273
result:
ok single line: '1273'
Test #23:
score: 0
Accepted
time: 4ms
memory: 8920kb
input:
26269395104446321
output:
12731
result:
ok single line: '12731'
Test #24:
score: 0
Accepted
time: 8ms
memory: 7812kb
input:
3
output:
-1
result:
ok single line: '-1'
Test #25:
score: 0
Accepted
time: 8ms
memory: 7836kb
input:
3596345248055296
output:
88
result:
ok single line: '88'
Test #26:
score: 0
Accepted
time: 4ms
memory: 8460kb
input:
36
output:
-1
result:
ok single line: '-1'
Test #27:
score: 0
Accepted
time: 8ms
memory: 7932kb
input:
4
output:
2
result:
ok single line: '2'
Test #28:
score: 0
Accepted
time: 8ms
memory: 8672kb
input:
4096
output:
8
result:
ok single line: '8'
Test #29:
score: 0
Accepted
time: 8ms
memory: 8340kb
input:
49
output:
7
result:
ok single line: '7'
Test #30:
score: 0
Accepted
time: 8ms
memory: 7836kb
input:
5
output:
-1
result:
ok single line: '-1'
Test #31:
score: 0
Accepted
time: 8ms
memory: 8456kb
input:
576460752303423488
output:
-1
result:
ok single line: '-1'
Test #32:
score: 0
Accepted
time: 8ms
memory: 9204kb
input:
581431415926321
output:
24112889
result:
ok single line: '24112889'
Test #33:
score: 0
Accepted
time: 4ms
memory: 7920kb
input:
6
output:
-1
result:
ok single line: '-1'
Test #34:
score: 0
Accepted
time: 8ms
memory: 8464kb
input:
64
output:
4
result:
ok single line: '4'
Test #35:
score: 0
Accepted
time: 9ms
memory: 8028kb
input:
656100000000
output:
30
result:
ok single line: '30'
Test #36:
score: 0
Accepted
time: 9ms
memory: 9148kb
input:
7
output:
-1
result:
ok single line: '-1'
Test #37:
score: 0
Accepted
time: 4ms
memory: 8100kb
input:
729
output:
9
result:
ok single line: '9'
Test #38:
score: 0
Accepted
time: 4ms
memory: 9112kb
input:
8
output:
-1
result:
ok single line: '-1'
Test #39:
score: 0
Accepted
time: 8ms
memory: 8932kb
input:
81
output:
-1
result:
ok single line: '-1'
Test #40:
score: 0
Accepted
time: 8ms
memory: 7640kb
input:
8527674378686464
output:
452
result:
ok single line: '452'
Test #41:
score: 0
Accepted
time: 8ms
memory: 7956kb
input:
9
output:
3
result:
ok single line: '3'
Test #42:
score: 0
Accepted
time: 9ms
memory: 8660kb
input:
982134461213542729
output:
994009
result:
ok single line: '994009'
Test #43:
score: 0
Accepted
time: 8ms
memory: 8816kb
input:
9992002399680016
output:
9998
result:
ok single line: '9998'
Test #44:
score: 0
Accepted
time: 8ms
memory: 8788kb
input:
999269311525198921
output:
-1
result:
ok single line: '-1'
Test #45:
score: 0
Accepted
time: 9ms
memory: 8300kb
input:
999949000866995087
output:
-1
result:
ok single line: '-1'
Test #46:
score: 0
Accepted
time: 5ms
memory: 8576kb
input:
999995482005103081
output:
-1
result:
ok single line: '-1'
Test #47:
score: 0
Accepted
time: 9ms
memory: 8592kb
input:
999999969999997921
output:
-1
result:
ok single line: '-1'
Test #48:
score: 0
Accepted
time: 3ms
memory: 7456kb
input:
999999999999999989
output:
-1
result:
ok single line: '-1'
Test #49:
score: 0
Accepted
time: 9ms
memory: 9172kb
input:
999999999999999999
output:
-1
result:
ok single line: '-1'