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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#563740#7954. Special Numberssentheta#AC ✓7ms310840kbC++203.4kb2024-09-14 15:35:532024-09-14 15:35:53

Judging History

你现在查看的是最新测评结果

  • [2024-09-14 15:35:53]
  • 评测
  • 测评结果:AC
  • 用时:7ms
  • 内存:310840kb
  • [2024-09-14 15:35:53]
  • 提交

answer

#include<bits/stdc++.h>
using namespace std;

#define rep(i,a,b) for(int i=(int)a; i<(int)b; i++)
#define Int long long
#define int long long
#define V vector

void solve();
signed main(){
	solve();
}

const int MOD = 1e9+7;

int k;
int two, tri, fiv, svn;

V<int> fac;

int dp[22][68][43][30][25];

// #nonzero integer with nonzero digit product divisible by k
int f(string s){
	bool allZero = 1;
	for(char ch : s) allZero &= ch=='0';
	if(allZero) return 0;

	rep(i,0,s.size())
		rep(a,0,two+1) rep(b,0,tri+1) rep(c,0,fiv+1) rep(d,0,svn+1)
			dp[i][a][b][c][d] = 0;

	int sa=0, sb=0, sc=0, sd=0, zro=0;
	for(int i=0; i<s.size(); i++){
		// cerr << "i " << i << endl;
		int x = s[i]-'0';

		// prv(nonzero) + y
		// cerr << "prv + y" << endl;
		if(i>0) for(int y=1; y<=9; y++){
			rep(a,0,two+1) rep(b,0,tri+1) rep(c,0,fiv+1) rep(d,0,svn+1)
				(dp[i]
				[min(two,a+(y%2==0)+(y%4==0)+(y%8==0))]
				[min(tri,b+(y%3==0)+(y%9==0))]
				[min(fiv,c+(y%5==0))]
				[min(svn,d+(y%7==0))]
				+= dp[i-1][a][b][c][d] )%=MOD;
		}

		// pref(s) + y
		// cerr << "prefix + y" << endl;
		if(!zro) for(int y=1; y<x; y++){
			dp[i]
			[min(two,sa+(y%2==0)+(y%4==0)+(y%8==0))]
			[min(tri,sb+(y%3==0)+(y%9==0))]
			[min(fiv,sc+(y%5==0))]
			[min(svn,sd+(y%7==0))]
			+= 1;
		}
		zro |= x==0;
		sa += (x%2==0) + (x%4==0) + (x%8==0);
		sb += (x%3==0) + (x%9==0);
		sc += (x%5==0);
		sd += (x%7==0);

		// zeroes + y
		// cerr << "zeroes + y" << endl;
		if(i>0) for(int y=1; y<=9; y++){
			dp[i]
			[min(two,(int)(y%2==0)+(y%4==0)+(y%8==0))]
			[min(tri,(int)(y%3==0)+(y%9==0))]
			[min(fiv,(int)(y%5==0))]
			[min(svn,(int)(y%7==0))]
			++;
		}
	}

	// check s itself
	// cerr << "dp[last][last]... " << dp[s.size()-1][two][tri][fiv][svn] << '\n';
	int ret = dp[s.size()-1][two][tri][fiv][svn] + (!zro)*(sa>=two)*(sb>=tri)*(sc>=fiv)*(sd>=svn);
	return ret;
}

int dpg[22][2];
// #nonzero integer with zero digit product
int g(string s){
	bool allZero = 1;
	for(char ch : s) allZero &= ch=='0';
	if(allZero) return 0;

	rep(i,0,s.size())
		dpg[i][0] = dpg[i][1] = 0;

	int prod = 1;
	for(int i=0; i<s.size(); i++){
		int x = s[i]-'0';
		// cerr << "x: " << x << endl;

		// prv(nonzero) + y
		if(i>0) for(int y=0; y<=9; y++){
			(dpg[i][0] += dpg[i-1][0] )%=MOD;
			(dpg[i][(bool)(y)] += dpg[i-1][1] )%=MOD;
		}

		// pref(s) + y
		for(int y=(i==0?1:0); y<x; y++){
			dpg[i][prod&(bool)y]++;
		}
		prod &= (bool)x;

		// zeroes + y
		if(i>0) for(int y=1; y<=9; y++){
			dpg[i][1]++;
		}
	}

	// cerr << "g: dpg[last][0]: " << dpg[s.size()-1][0] << endl;
	// cerr << "prod " << prod << endl;
	int ret = dpg[s.size()-1][0] + (prod==0);
	return ret;
}


void solve(){
	string l, r;
	cin >> k >> l >> r;

	// substract 1 from l
	l.back()--;
	for(int i=l.size()-1; i>=0 && l[i]=='0'-1; i--){
		l[i] += 10;
		l[i-1]--;
	}
	while(l[0]=='0'){
		l = l.substr(1);
	}
	// cerr << l << " " << r << endl;

	// factorize k
	while(k%2==0){
		k/=2; two++;
	}
	while(k%3==0){
		k/=3; tri++;
	}
	while(k%5==0){
		k/=5; fiv++;
	}
	while(k%7==0){
		k/=7; svn++;
	}
	// cerr << k << endl;

	int ans = 0;

	if(k==1){
		// nonzero product
		(ans += f(r) )%=MOD;
		(ans -= f(l) )%=MOD;
	}
	// cerr << "f: " << ans << '\n';
	// zero product
	(ans += g(r) )%=MOD;
	(ans -= g(l) )%=MOD;
	// cerr << "f+g: " << ans << '\n';


	ans = (ans%MOD+MOD)%MOD;
	cout << ans << '\n';
}

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 1ms
memory: 5676kb

input:

5 1 20

output:

4

result:

ok single line: '4'

Test #2:

score: 0
Accepted
time: 1ms
memory: 7668kb

input:

5 50 100

output:

19

result:

ok single line: '19'

Test #3:

score: 0
Accepted
time: 1ms
memory: 5908kb

input:

15 11 19

output:

0

result:

ok single line: '0'

Test #4:

score: 0
Accepted
time: 0ms
memory: 14100kb

input:

1 100 100000

output:

99901

result:

ok single line: '99901'

Test #5:

score: 0
Accepted
time: 0ms
memory: 3568kb

input:

1 1 1

output:

1

result:

ok single line: '1'

Test #6:

score: 0
Accepted
time: 0ms
memory: 13880kb

input:

10 800 43021

output:

23570

result:

ok single line: '23570'

Test #7:

score: 0
Accepted
time: 3ms
memory: 310840kb

input:

1125899906842624 1 100000000000000000000

output:

555058180

result:

ok single line: '555058180'

Test #8:

score: 0
Accepted
time: 0ms
memory: 67048kb

input:

187500000 5941554024261918062 17356601866920567143

output:

679191360

result:

ok single line: '679191360'

Test #9:

score: 0
Accepted
time: 0ms
memory: 56884kb

input:

1555848 157165614890794026 49792374427566422833

output:

588832126

result:

ok single line: '588832126'

Test #10:

score: 0
Accepted
time: 3ms
memory: 77460kb

input:

53814924637488000 8378901287491856069 46225409092942057365

output:

964965504

result:

ok single line: '964965504'

Test #11:

score: 0
Accepted
time: 4ms
memory: 79460kb

input:

11814720750000000 8152927138245188051 35351923956338524619

output:

183963359

result:

ok single line: '183963359'

Test #12:

score: 0
Accepted
time: 3ms
memory: 108136kb

input:

6453888000000 4334845344448208535 35982793193772682339

output:

570114022

result:

ok single line: '570114022'

Test #13:

score: 0
Accepted
time: 0ms
memory: 61220kb

input:

90071357282285400 7893548167754114409 27099084703937108974

output:

869822186

result:

ok single line: '869822186'

Test #14:

score: 0
Accepted
time: 0ms
memory: 65196kb

input:

45571065750000 177160749596350425 98884377930460959454

output:

607698665

result:

ok single line: '607698665'

Test #15:

score: 0
Accepted
time: 0ms
memory: 147204kb

input:

1128443962982400 6338876482181492537 40931938533793596007

output:

881168270

result:

ok single line: '881168270'

Test #16:

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

input:

1 1 1

output:

1

result:

ok single line: '1'

Test #17:

score: 0
Accepted
time: 0ms
memory: 48816kb

input:

1412793457031250 2410155470167050095 99063185266833009818

output:

399813226

result:

ok single line: '399813226'

Test #18:

score: 0
Accepted
time: 4ms
memory: 132684kb

input:

67722117120000 8909573534349989418 73129289758235281558

output:

898227227

result:

ok single line: '898227227'

Test #19:

score: 0
Accepted
time: 3ms
memory: 138800kb

input:

472055808000 6809917603531307093 27494416416722163137

output:

379198478

result:

ok single line: '379198478'

Test #20:

score: 0
Accepted
time: 4ms
memory: 116404kb

input:

19353600000 8687492345912514346 24058039408337150852

output:

250715555

result:

ok single line: '250715555'

Test #21:

score: 0
Accepted
time: 0ms
memory: 65372kb

input:

47855420020225440 6150828649270625443 84863934988301168136

output:

665186711

result:

ok single line: '665186711'

Test #22:

score: 0
Accepted
time: 0ms
memory: 112308kb

input:

1382400000 9545797804645162278 70441077437727026904

output:

278230087

result:

ok single line: '278230087'

Test #23:

score: 0
Accepted
time: 0ms
memory: 90128kb

input:

816293376 2952089614708276156 10939708785225040670

output:

120954190

result:

ok single line: '120954190'

Test #24:

score: 0
Accepted
time: 3ms
memory: 44692kb

input:

4185097875 1348426133484952253 56617823359794500344

output:

773995224

result:

ok single line: '773995224'

Test #25:

score: 0
Accepted
time: 0ms
memory: 132600kb

input:

5828945117184 7777082394971366991 63470232991138132969

output:

678496908

result:

ok single line: '678496908'

Test #26:

score: 0
Accepted
time: 0ms
memory: 144956kb

input:

16184770560 3869053219872876321 94590086601168840932

output:

168181821

result:

ok single line: '168181821'

Test #27:

score: 0
Accepted
time: 1ms
memory: 5848kb

input:

2 1 12

output:

6

result:

ok single line: '6'

Test #28:

score: 0
Accepted
time: 0ms
memory: 42552kb

input:

30146484375 290228705524339176 51853415145287716863

output:

229436627

result:

ok single line: '229436627'

Test #29:

score: 0
Accepted
time: 0ms
memory: 167400kb

input:

2072513819443200 3726664558969607832 42501102605103061370

output:

947952932

result:

ok single line: '947952932'

Test #30:

score: 0
Accepted
time: 7ms
memory: 102632kb

input:

9920232000000000 4602219263214498291 80783137037024823899

output:

846877519

result:

ok single line: '846877519'

Test #31:

score: 0
Accepted
time: 0ms
memory: 124564kb

input:

97200000000000000 9310820760839688870 35322929083473756214

output:

936587432

result:

ok single line: '936587432'

Test #32:

score: 0
Accepted
time: 0ms
memory: 42484kb

input:

45209390625 5752361069878044328 64635325028527078951

output:

578047592

result:

ok single line: '578047592'

Test #33:

score: 0
Accepted
time: 0ms
memory: 95844kb

input:

54442233216000 2452030574225118723 90982734056131320662

output:

417646585

result:

ok single line: '417646585'

Test #34:

score: 0
Accepted
time: 0ms
memory: 87808kb

input:

1530550080000 7431421026778839808 84825282227911272129

output:

600103842

result:

ok single line: '600103842'

Test #35:

score: 0
Accepted
time: 0ms
memory: 136872kb

input:

13765147361280 4924477486471254843 10002324705150566233

output:

951883713

result:

ok single line: '951883713'

Test #36:

score: 0
Accepted
time: 6ms
memory: 53148kb

input:

59825698242187500 6303744363677706767 91410210495502213963

output:

774734375

result:

ok single line: '774734375'

Test #37:

score: 0
Accepted
time: 3ms
memory: 106228kb

input:

110658879959040 2133591391458550040 48494371567095341228

output:

103505650

result:

ok single line: '103505650'

Test #38:

score: 0
Accepted
time: 1ms
memory: 7888kb

input:

1 3 100

output:

98

result:

ok single line: '98'

Test #39:

score: 0
Accepted
time: 0ms
memory: 128844kb

input:

3160365465600 8968721517098518892 78444481529635953131

output:

364620926

result:

ok single line: '364620926'

Test #40:

score: 0
Accepted
time: 0ms
memory: 3628kb

input:

54838448056132899 4242999884713464056 92948071680698209741

output:

922087167

result:

ok single line: '922087167'

Test #41:

score: 0
Accepted
time: 0ms
memory: 3572kb

input:

78183771565555182 7823307199080715671 93466469990450000599

output:

635073629

result:

ok single line: '635073629'

Test #42:

score: 0
Accepted
time: 0ms
memory: 3512kb

input:

56555532446322947 2952925229100796893 35926880503684324113

output:

663547216

result:

ok single line: '663547216'

Test #43:

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

input:

15701121272683095 8633703383009071570 55273589042372583668

output:

253996413

result:

ok single line: '253996413'

Test #44:

score: 0
Accepted
time: 0ms
memory: 3628kb

input:

11914467542453704 2857068399817941722 83230805830740136213

output:

956698341

result:

ok single line: '956698341'

Test #45:

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

input:

28181999963152819 7948365158338416594 87742700746768593189

output:

720016372

result:

ok single line: '720016372'

Test #46:

score: 0
Accepted
time: 0ms
memory: 3600kb

input:

85409868208332321 3921672860136397259 55474188860042435613

output:

622329181

result:

ok single line: '622329181'

Test #47:

score: 0
Accepted
time: 0ms
memory: 3600kb

input:

14748052718175068 9293071633738211123 85443373435217434149

output:

38392129

result:

ok single line: '38392129'

Test #48:

score: 0
Accepted
time: 0ms
memory: 3572kb

input:

41002058985303228 6141335647135876923 78910335860595680506

output:

665823537

result:

ok single line: '665823537'

Test #49:

score: 0
Accepted
time: 0ms
memory: 9608kb

input:

4 3 123

output:

62

result:

ok single line: '62'

Test #50:

score: 0
Accepted
time: 3ms
memory: 134724kb

input:

100000000000000000 3 100000000000000000000

output:

302574822

result:

ok single line: '302574822'

Test #51:

score: 0
Accepted
time: 2ms
memory: 11996kb

input:

6 7 12034

output:

9505

result:

ok single line: '9505'

Test #52:

score: 0
Accepted
time: 2ms
memory: 12056kb

input:

7 8 43021

output:

25028

result:

ok single line: '25028'

Test #53:

score: 0
Accepted
time: 0ms
memory: 13812kb

input:

8 8 43021

output:

32619

result:

ok single line: '32619'

Test #54:

score: 0
Accepted
time: 0ms
memory: 11768kb

input:

9 800 43021

output:

30930

result:

ok single line: '30930'