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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#774081#9782. NonZero PrefSuf Sumsucup-team3555#AC ✓196ms31580kbC++203.4kb2024-11-23 11:38:522024-11-23 11:38:52

Judging History

你现在查看的是最新测评结果

  • [2024-11-23 11:38:52]
  • 评测
  • 测评结果:AC
  • 用时:196ms
  • 内存:31580kb
  • [2024-11-23 11:38:52]
  • 提交

answer

/*
I know this sky loves you
いずれ全て
変わってしまったって
空は青いだろうよ
*/

# include <bits/stdc++.h>
# define int long long

const int N=105,INF=0x3f3f3f3f,V=100;
int mod;

inline int read(void){
	int res,f=1;
	char c;
	while((c=getchar())<'0'||c>'9')
		if(c=='-') f=-1;
	res=c-48;
	while((c=getchar())>='0'&&c<='9')
		res=res*10+c-48;
	return res*f;
}

inline int adc(int a,int b){return (a+b>=mod)?(a+b-mod):(a+b);}
inline int dec(int a,int b){return (a<b)?(a-b+mod):(a-b);}
inline int mul(int a,int b){return 1ll*a*b%mod;}
inline void add(int &a,int b){a=adc(a,b);}
inline void del(int &a,int b){a=dec(a,b);}

inline int qpow(int d,int p){
//	printf("d = %d p = %d\n",d,p);	
	int ans=1;
	while(p){
		if(p&1) ans=1ll*ans*d%mod;
		d=1ll*d*d%mod,p>>=1;
	}
	return ans;
}

int dp[N][N][N];
int n,m;
int fac[N],finv[N];

int g[N][N];

inline void init(void){
	fac[0]=finv[0]=1;
	for(int i=1;i<=V;++i) fac[i]=mul(i,fac[i-1]),finv[i]=qpow(fac[i],mod-2);
	return;
}
inline int bi(int n,int m){
	if(n<m||n<0||m<0) return 0;
	return mul(mul(fac[n],finv[m]),finv[n-m]);
}

int pw_m[N];

// int arr[N][N][N]; // choosing i 

int suming[N][N*N*2];

const int Z=10005;

int h[N][N][N];

signed main(void){
//	freopen("in.txt","r",stdin);
	
	n=read(),m=read(),mod=read();
	
	pw_m[0]=1;
	for(int i=1;i<=n;++i) pw_m[i]=mul(pw_m[i-1],m);
	
	suming[0][Z]=1;
	for(int i=1;i<=n;++i){
		for(int s=-(i-1)*m;s<=(i-1)*m;++s){
			for(int d=-m;d<=m;++d) add(suming[i][s+d+Z],suming[i-1][s+Z]);
		}
	}
	
//	arr[0][0][0]=1;
	
	init();
	
	dp[0][0][0]=1;
	
//	std::cout<<finv[1]<<"A"<<std::endl;
	
	for(int v=1;v<=m;++v){
		memcpy(dp[v],dp[v-1],sizeof(dp[v]));
		for(int l=0;l<=n;++l){
			for(int sum=0;sum<=n;++sum){
				if(!dp[v-1][l][sum]) continue;
				for(int k=1;l+k<=n&&sum+k*v<=n;++k){
					add(dp[v][l+k][sum+k*v],mul(dp[v-1][l][sum],finv[k]));
					add(h[v][l+k][sum+k*v],mul(dp[v-1][l][sum],finv[k]));
				}
			}
		}
	}
	
//	printf("DEBUG = %d\n",dp[1][1][1]);
	
	for(int v=0;v<=m;++v){
		for(int l=0;l<=n;++l){
			for(int sum=1;sum<=n;++sum) add(h[v][l][sum],h[v][l][sum-1]);
		}
	}
	
//	printf("DEBUG = %d\n",dp[1][1][1]);
	
	int ans=qpow(2*m+1,n);
	
//	printf("ans = %d\n",ans);
	
	del(ans,mul(n,2*m)); // from 1 positive (negative)
	
//	printf("ans = %d\n",ans);
	
	del(ans,suming[n][Z]); // from sum = 0
	
//	printf("A = %d B = %d\n",mul(n,2*m),suming[n][Z]);
	
//	printf("ans = %d\n",ans);
	
	for(int zc=0;zc<=n;++zc){ // zero_counting
		for(int v=1;v<=m;++v){
			for(int po=1;po+zc<=n;++po){ // positive vs
				for(int ne=n-po-zc;ne==n-po-zc;++ne){
				for(int mx_ne=0;mx_ne<=m/v;++mx_ne){
					if(ne==0) continue;
					
					// IT IS VALID IFF: po >= mx_ne + sum + 2
					// sum <= po - mx_ne - 2
					
					// INVALID IFF: sum > po - mx_ne - 2
					
//					printf("v = %d zc = %d po = %d ne = %d\n",v,zc,po,ne);
					
					int ways=h[mx_ne][ne][po-1];
					if(po-mx_ne-2>=0) del(ways,h[mx_ne][ne][po-mx_ne-2]);
					
//					printf("lim = %d [%d,%d]\n",lim,slim+1,po-1);
					
					ways=mul(ways,fac[ne]);
					
//					ways=dec(pw_m[ne],ways);
//					printf("ways = %d\n",ways);
					
					int op=mul(mul(fac[n],finv[zc]),mul(finv[po],finv[ne]));
					del(ans,mul(mul(2,op),ways)); // positive & negative
					// calculating len = ne 
				}
				}
			}
		}
	}
	
	printf("%lld",ans);

	return 0;
}

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 1ms
memory: 7904kb

input:

2 1 998244353

output:

2

result:

ok single line: '2'

Test #2:

score: 0
Accepted
time: 21ms
memory: 16412kb

input:

69 42 696969697

output:

378553557

result:

ok single line: '378553557'

Test #3:

score: 0
Accepted
time: 1ms
memory: 7848kb

input:

2 1 998244353

output:

2

result:

ok single line: '2'

Test #4:

score: 0
Accepted
time: 25ms
memory: 16456kb

input:

69 42 696969697

output:

378553557

result:

ok single line: '378553557'

Test #5:

score: 0
Accepted
time: 46ms
memory: 22576kb

input:

61 75 677323601

output:

34613998

result:

ok single line: '34613998'

Test #6:

score: 0
Accepted
time: 2ms
memory: 8144kb

input:

13 14 670577333

output:

41465431

result:

ok single line: '41465431'

Test #7:

score: 0
Accepted
time: 0ms
memory: 8060kb

input:

14 6 987686347

output:

37536510

result:

ok single line: '37536510'

Test #8:

score: 0
Accepted
time: 0ms
memory: 10180kb

input:

15 12 196428923

output:

29322522

result:

ok single line: '29322522'

Test #9:

score: 0
Accepted
time: 0ms
memory: 8800kb

input:

68 7 786815587

output:

149281835

result:

ok single line: '149281835'

Test #10:

score: 0
Accepted
time: 2ms
memory: 9912kb

input:

3 2 503002109

output:

82

result:

ok single line: '82'

Test #11:

score: 0
Accepted
time: 2ms
memory: 9980kb

input:

13 5 756093197

output:

415698676

result:

ok single line: '415698676'

Test #12:

score: 0
Accepted
time: 1ms
memory: 8052kb

input:

2 3 646574611

output:

30

result:

ok single line: '30'

Test #13:

score: 0
Accepted
time: 18ms
memory: 17492kb

input:

39 68 120037189

output:

43217507

result:

ok single line: '43217507'

Test #14:

score: 0
Accepted
time: 0ms
memory: 10048kb

input:

13 4 423132517

output:

360231790

result:

ok single line: '360231790'

Test #15:

score: 0
Accepted
time: 2ms
memory: 10052kb

input:

14 3 309713387

output:

94215386

result:

ok single line: '94215386'

Test #16:

score: 0
Accepted
time: 3ms
memory: 18416kb

input:

24 77 886983941

output:

211636479

result:

ok single line: '211636479'

Test #17:

score: 0
Accepted
time: 1ms
memory: 7872kb

input:

3 3 504388063

output:

270

result:

ok single line: '270'

Test #18:

score: 0
Accepted
time: 1ms
memory: 7940kb

input:

3 1 936205423

output:

8

result:

ok single line: '8'

Test #19:

score: 0
Accepted
time: 1ms
memory: 7864kb

input:

3 3 295983139

output:

270

result:

ok single line: '270'

Test #20:

score: 0
Accepted
time: 0ms
memory: 10200kb

input:

10 15 446169107

output:

149884328

result:

ok single line: '149884328'

Test #21:

score: 0
Accepted
time: 4ms
memory: 10884kb

input:

37 18 833753929

output:

592917251

result:

ok single line: '592917251'

Test #22:

score: 0
Accepted
time: 0ms
memory: 7968kb

input:

11 3 998773403

output:

860630017

result:

ok single line: '860630017'

Test #23:

score: 0
Accepted
time: 6ms
memory: 17532kb

input:

14 85 688036639

output:

347188409

result:

ok single line: '347188409'

Test #24:

score: 0
Accepted
time: 0ms
memory: 7900kb

input:

3 3 844621907

output:

270

result:

ok single line: '270'

Test #25:

score: 0
Accepted
time: 1ms
memory: 7960kb

input:

3 4 204335891

output:

620

result:

ok single line: '620'

Test #26:

score: 0
Accepted
time: 1ms
memory: 7964kb

input:

7 8 113007667

output:

58946097

result:

ok single line: '58946097'

Test #27:

score: 0
Accepted
time: 1ms
memory: 7860kb

input:

4 1 637268377

output:

22

result:

ok single line: '22'

Test #28:

score: 0
Accepted
time: 0ms
memory: 10172kb

input:

11 14 391637237

output:

303270280

result:

ok single line: '303270280'

Test #29:

score: 0
Accepted
time: 2ms
memory: 9964kb

input:

3 2 208286231

output:

82

result:

ok single line: '82'

Test #30:

score: 0
Accepted
time: 2ms
memory: 9996kb

input:

2 11 662696483

output:

462

result:

ok single line: '462'

Test #31:

score: 0
Accepted
time: 0ms
memory: 15408kb

input:

19 55 974135299

output:

887460557

result:

ok single line: '887460557'

Test #32:

score: 0
Accepted
time: 0ms
memory: 8012kb

input:

6 8 417027509

output:

23351024

result:

ok single line: '23351024'

Test #33:

score: 0
Accepted
time: 2ms
memory: 10260kb

input:

8 13 624006587

output:

353008442

result:

ok single line: '353008442'

Test #34:

score: 0
Accepted
time: 0ms
memory: 8172kb

input:

10 10 740294671

output:

79436611

result:

ok single line: '79436611'

Test #35:

score: 0
Accepted
time: 1ms
memory: 8128kb

input:

11 10 394088657

output:

161476458

result:

ok single line: '161476458'

Test #36:

score: 0
Accepted
time: 2ms
memory: 10344kb

input:

9 27 562853573

output:

135252259

result:

ok single line: '135252259'

Test #37:

score: 0
Accepted
time: 1ms
memory: 7908kb

input:

8 3 829129009

output:

5349034

result:

ok single line: '5349034'

Test #38:

score: 0
Accepted
time: 14ms
memory: 15516kb

input:

51 49 924010279

output:

815049368

result:

ok single line: '815049368'

Test #39:

score: 0
Accepted
time: 0ms
memory: 10012kb

input:

12 2 308466749

output:

223013998

result:

ok single line: '223013998'

Test #40:

score: 0
Accepted
time: 1ms
memory: 10020kb

input:

7 4 567557693

output:

4502296

result:

ok single line: '4502296'

Test #41:

score: 0
Accepted
time: 19ms
memory: 19952kb

input:

36 93 943780729

output:

13599465

result:

ok single line: '13599465'

Test #42:

score: 0
Accepted
time: 0ms
memory: 7892kb

input:

2 1 828681127

output:

2

result:

ok single line: '2'

Test #43:

score: 0
Accepted
time: 1ms
memory: 7856kb

input:

3 3 534160729

output:

270

result:

ok single line: '270'

Test #44:

score: 0
Accepted
time: 2ms
memory: 10068kb

input:

7 12 920925433

output:

453086694

result:

ok single line: '453086694'

Test #45:

score: 0
Accepted
time: 1ms
memory: 7856kb

input:

3 2 440546987

output:

82

result:

ok single line: '82'

Test #46:

score: 0
Accepted
time: 6ms
memory: 9624kb

input:

90 9 291269963

output:

72560304

result:

ok single line: '72560304'

Test #47:

score: 0
Accepted
time: 3ms
memory: 10536kb

input:

38 10 867575113

output:

165530481

result:

ok single line: '165530481'

Test #48:

score: 0
Accepted
time: 11ms
memory: 12424kb

input:

48 37 152663531

output:

135425620

result:

ok single line: '135425620'

Test #49:

score: 0
Accepted
time: 1ms
memory: 10236kb

input:

15 15 991731803

output:

102703562

result:

ok single line: '102703562'

Test #50:

score: 0
Accepted
time: 196ms
memory: 31580kb

input:

100 100 696969697

output:

313377809

result:

ok single line: '313377809'

Extra Test:

score: 0
Extra Test Passed