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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#642011#4283. Power of XORdongyc666WA 17ms3884kbC++141.6kb2024-10-15 08:42:262024-10-15 08:42:27

Judging History

This is the latest submission verdict.

  • [2024-10-15 08:42:27]
  • Judged
  • Verdict: WA
  • Time: 17ms
  • Memory: 3884kb
  • [2024-10-15 08:42:26]
  • Submitted

answer

#pragma GCC optimize("Ofast,unroll-loops,-finline")
#include<bits/stdc++.h>
using namespace std;
#define int long long
const int MOD=1e9+7;
const int Inv2=5e8+4;
int n,k,a[60],c[100][100],cnt,f[100],ans[100];
void add(int &x,int y){x=(x+y)%MOD;}

int qpow(int x,int y){
	int res=1;
	while(y){
		if(y&1)res=res*x%MOD;
		x=x*x%MOD;y>>=1;
	}
	return res;
}

void insert(int x){
	for(int i=44;i>=0;i--)
		if((x>>i)&1){
			if(!a[i]){
				a[i]=x;
				cnt++;
				break;
			}
			x^=a[i];
		}
}

int arr[100],len;
void dfs(int col,int x){
	if(col==len+1){
		f[__builtin_popcountll(x)]++;
		return;
	}
	dfs(col+1,x);
	dfs(col+1,x^arr[col]);
}

signed main(){
	cin>>n>>k;
	for(int i=1,x;i<=n;i++)cin>>x,insert(x);
	if(!cnt){
		puts("0");
		return 0;
	}
	for(int i=0;i<=60;i++){
		c[i][0]=1;
		for(int j=1;j<=i;j++)c[i][j]=(c[i-1][j-1]+c[i-1][j])%MOD;
	}
	if(cnt<=22){
		for(int i=0;i<=44;i++)
			if(a[i])arr[++len]=a[i];
		dfs(1,0);
		int res=0;
		for(int i=0;i<=44;i++)add(res,f[i]*qpow(2,n-cnt)%MOD*qpow(i,k));
		cout<<res<<endl;
		return 0;
	}
	else{
		for(int i=43;i>=0;i--)
			if(!a[i]){
				int x=1ll<<i;
				for(int j=0;j<=44;j++)
					if((a[j]>>i)&1)x|=(1ll<<j);
				arr[++len]=x;
			}
		dfs(1,0);
		for(int i=0;i<=44;i++)f[i]=f[i]*qpow(Inv2,len)%MOD;
		for(int i=0;i<=44;i++)
			for(int j=0;j<=i;j++)
				for(int k=j;k-j<=44-i;k++)
					if(j&1)add(ans[k],-c[i][j]*c[44-i][k-j]%MOD*f[i]);
					else add(ans[k],c[i][j]*c[44-i][k-j]%MOD*f[i]);
		int res=0;
		for(int i=0;i<=44;i++)add(res,ans[i]*qpow(2,n-cnt)%MOD*qpow(i,k));
		cout<<(res+MOD)%MOD<<endl;
		return 0;
	}
}

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 0ms
memory: 3828kb

input:

3 2
1 2 3

output:

12

result:

ok 1 number(s): "12"

Test #2:

score: 0
Accepted
time: 0ms
memory: 3652kb

input:

2 1000000000
1 2

output:

140625003

result:

ok 1 number(s): "140625003"

Test #3:

score: 0
Accepted
time: 0ms
memory: 3516kb

input:

3 4
21 31 15

output:

1076

result:

ok 1 number(s): "1076"

Test #4:

score: 0
Accepted
time: 0ms
memory: 3616kb

input:

4 10
21 16 23 30

output:

3504120

result:

ok 1 number(s): "3504120"

Test #5:

score: 0
Accepted
time: 0ms
memory: 3656kb

input:

5 795325759
23 18 18 15 24

output:

398580583

result:

ok 1 number(s): "398580583"

Test #6:

score: 0
Accepted
time: 0ms
memory: 3548kb

input:

6 425010546
15190825693299 11021868218180 10853490476696 16489831131502 15731786397897 1859285400474

output:

226806798

result:

ok 1 number(s): "226806798"

Test #7:

score: 0
Accepted
time: 0ms
memory: 3880kb

input:

7 376524109
14035202899482 10047025581205 744778190838 10085364176616 17517303536898 10648638998430 4344258259221

output:

909089159

result:

ok 1 number(s): "909089159"

Test #8:

score: 0
Accepted
time: 0ms
memory: 3516kb

input:

8 849112677
12651182249229 2557626671152 16190796268614 7679451552477 1419165382365 16010747922241 1877804892046 6782866140038

output:

60890703

result:

ok 1 number(s): "60890703"

Test #9:

score: 0
Accepted
time: 0ms
memory: 3624kb

input:

9 874735099
10148022499611 4300816040299 6425463859799 11220407430827 16167481816769 5361425691648 9036180330515 1461806017525 5752555300268

output:

371891946

result:

ok 1 number(s): "371891946"

Test #10:

score: 0
Accepted
time: 0ms
memory: 3652kb

input:

10 466547903
14475814446599 10414899512095 8279261110485 15402964537241 12059977291235 14960757658011 15642794803423 176456760404 8544855584093 939455648117

output:

705005476

result:

ok 1 number(s): "705005476"

Test #11:

score: 0
Accepted
time: 0ms
memory: 3884kb

input:

11 587282176
2381973819369 7896756717881 3605049079058 3476202500557 8161539414084 4107261754597 4052905214220 13489145138694 14249896320133 4915388559035 946556082447

output:

221771132

result:

ok 1 number(s): "221771132"

Test #12:

score: 0
Accepted
time: 0ms
memory: 3584kb

input:

12 416671000
12040275816251 17062751464343 7135252213488 464175530141 1680797265108 8088672081270 15974373338891 2807308701611 10474875618229 14385428199760 7217460885705 14772837072591

output:

888526388

result:

ok 1 number(s): "888526388"

Test #13:

score: 0
Accepted
time: 0ms
memory: 3584kb

input:

13 555186260
16812780767710 10577402574202 14435021461484 7629604678144 2685467464476 6345623360274 243420234591 10035113157523 3422776077242 10218637237089 14851966122299 403170012001 9905420122107

output:

990043010

result:

ok 1 number(s): "990043010"

Test #14:

score: 0
Accepted
time: 0ms
memory: 3652kb

input:

14 509328299
8353561750434 10104176798819 6443583453798 16526745760567 11644429218948 7613211796505 14675590153019 16014035780673 8977332980184 8018462423140 10321575146167 3765866187251 951943560884 16567591980900

output:

554786244

result:

ok 1 number(s): "554786244"

Test #15:

score: 0
Accepted
time: 1ms
memory: 3588kb

input:

15 608613602
13478763858236 3740903255952 1077573334827 10777446313857 9164622625061 3532139720401 10581691792868 227725402800 1100326438302 11314744041629 5716533742148 13171916589439 3380813371904 4280184438172 3241608634862

output:

451055479

result:

ok 1 number(s): "451055479"

Test #16:

score: 0
Accepted
time: 1ms
memory: 3556kb

input:

16 940201087
10256426323317 3262426443677 11042930351118 9509672586143 6874576733055 17425354233945 44840572217 271060611230 5160013582892 940549858628 3460145241956 1911512043119 6262508016313 15998335209279 4331486722244 1174379722227

output:

609521624

result:

ok 1 number(s): "609521624"

Test #17:

score: 0
Accepted
time: 1ms
memory: 3644kb

input:

17 224938820
17119676032384 14016470814638 9555327895162 4956367760197 14164877522334 11840938437493 196922732084 1117964651219 15662255500985 6799149377748 2081570899516 8101318468846 6806038800783 8481897921532 14327689591834 3468429675406 707483765694

output:

952629882

result:

ok 1 number(s): "952629882"

Test #18:

score: 0
Accepted
time: 0ms
memory: 3652kb

input:

18 572144592
1034330548675 7466761131151 5479486866730 5805192559012 2072047969997 14094135393106 3957442001455 9636000453501 6359658906102 13786563194342 12655202300227 17497546480004 15210614567784 5757118085432 3507806179905 4092815624732 2831474245754 8905127237409

output:

711094061

result:

ok 1 number(s): "711094061"

Test #19:

score: 0
Accepted
time: 2ms
memory: 3540kb

input:

19 655059034
10160251337230 17368680333349 7582672215712 15170782424265 11091464398448 3468569802147 12985801017272 11885768849226 2042891901510 5816113601266 17200614913667 3230577285683 6122037312518 4476865090037 17458280591698 8087876238641 12295868407218 14891985681505 9046310739642

output:

444845559

result:

ok 1 number(s): "444845559"

Test #20:

score: 0
Accepted
time: 5ms
memory: 3876kb

input:

20 230956009
5657766305333 6062575310370 15139059764699 15999531683504 8700249448570 8496370986569 11931362029342 16808274736949 6582914043608 3148217142903 623248093777 2603754608083 16741237934194 11551777078922 17177864498497 147568049427 2693939410255 11977553059228 14614351055705 11790115139758

output:

618103113

result:

ok 1 number(s): "618103113"

Test #21:

score: 0
Accepted
time: 8ms
memory: 3592kb

input:

21 991001581
13505588614813 8588095735948 6076766289787 11667017057163 7602334689492 3100571431902 16456031754497 17012042226760 2298783364823 2292586959243 16484353107729 6379611127333 2309984518512 17222120007066 15742378844056 10137340715213 11581793910964 6058313717190 9891627922923 939856806688...

output:

340865032

result:

ok 1 number(s): "340865032"

Test #22:

score: 0
Accepted
time: 17ms
memory: 3588kb

input:

22 793915239
14683316686425 5162188247000 7429819452817 16611661938749 11084135813793 13856133740403 13108004035448 13856666274966 9461726048738 5612503807810 15177562338647 5006352927897 15216557346760 8527880141821 15843683785466 7692179013817 127553824751 5234432790248 6453714209319 1152804933059...

output:

669154856

result:

ok 1 number(s): "669154856"

Test #23:

score: -100
Wrong Answer
time: 9ms
memory: 3652kb

input:

23 46024280
7514210736994 16544433148860 5457306548546 5030077832970 10322997084235 5669909500374 8381456993928 10988407597025 8111544042162 10588037243918 12116378947678 13379626855924 10216405913667 9728737199159 12487637411090 11957321472850 15722206258699 17236861929685 15970454160165 2302405750...

output:

651896847

result:

wrong answer 1st numbers differ - expected: '560027727', found: '651896847'