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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#117847#6566. Power of DivisorsKlaus26AC ✓9ms9204kbC++202.6kb2023-07-02 11:09:282023-07-02 11:09:31

Judging History

你现在查看的是最新测评结果

  • [2023-08-10 23:21:45]
  • System Update: QOJ starts to keep a history of the judgings of all the submissions.
  • [2023-07-02 11:09:31]
  • 评测
  • 测评结果:AC
  • 用时:9ms
  • 内存:9204kb
  • [2023-07-02 11:09:28]
  • 提交

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'