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QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#547296 | #8211. Enumerating Substrings | rqoi031 | AC ✓ | 19ms | 5548kb | C++20 | 2.4kb | 2024-09-04 20:16:03 | 2024-09-04 20:16:05 |
Judging History
answer
#include<stdio.h>
#include<algorithm>
typedef unsigned int uint;
typedef unsigned long long ull;
constexpr uint mod{1000000007};
constexpr uint plus(const uint &x,const uint &y) {
if(x+y>=mod) {
return x+y-mod;
}
return x+y;
}
constexpr uint minus(const uint &x,const uint &y) {
if(x<y) {
return x-y+mod;
}
return x-y;
}
constexpr uint power(uint x,uint y) {
uint s(1);
while(y>0) {
if(y&1) {
s=ull(s)*x%mod;
}
x=ull(x)*x%mod;
y>>=1;
}
return s;
}
uint inv[2005],invk[4005];
uint fac[2005],ifac[2005],ifac2[2005];
uint powk[1000005];
int main() {
int n,m,k;
scanf("%d%d%d",&n,&m,&k);
if(k<<1<m) {
return puts("0"),0;
}
inv[0]=0,inv[1]=1;
for(int i=2;i<=m;i++) {
const int j(mod/i+1);
inv[i]=ull(j)*inv[i*j-mod]%mod;
}
for(int i=0;i<=m<<1&&i<=k;i++) {
invk[i]=power(k-i,mod-2);
}
fac[0]=1;
for(int i=1;i<=m;i++) {
fac[i]=ull(fac[i-1])*i%mod;
}
ifac[m]=power(fac[m],mod-2);
for(int i=m;i>=1;i--) {
ifac[i-1]=ull(ifac[i])*i%mod;
}
for(int i=0;i<=m;i++) {
ifac2[i]=ull(ifac[i])*ifac[i]%mod;
}
powk[0]=1;
for(int i=1;i<=n;i++) {
powk[i]=ull(powk[i-1])*k%mod;
}
const auto calc([&](const int &m,const int &k,const int &d)->uint {
int i(std::max(0,m-k));
if(i>k||i<<1>m) {
return 0;
}
uint res(0),coef(1);
for(int j=0;j!=m-(i<<1);j++) {
coef=ull(coef)*(k-i-j)%mod;
}
for(int j=0;j!=i;j++) {
coef=ull(coef)*(k-j)%mod*power(2,mod-2)%mod;
}
for(;i<=k&&i<<1<=m;i++) {
res=(res+ull(coef)*ifac[i]%mod*ifac[m-(i<<1)])%mod;
coef=ull(coef)*(k-i)%mod*invk[d+i]%mod*invk[d+m-i-1]%mod*power(2,mod-2)%mod;
}
res=ull(res)*fac[m]%mod;
return res;
});
uint ans(0);
uint coef(1),sum(calc(m,k,0));
for(int i=1;i<<1<=m;i++) {
coef=ull(coef)*(k-i+1)%mod;
const uint cnt(ull(coef)*(calc(m-(i<<1),k-i,i))%mod);
sum=minus(sum,cnt);
uint tmp(0);
for(int j=0,l=m;l<=n;j^=1,l+=m-i) {
tmp=(tmp+ull(j?mod-(n-l+1):n-l+1)*powk[n-l])%mod;
}
ans=(ans+ull(cnt)*tmp)%mod;
}
ans=(ans+ull(sum)*(n-m+1)%mod*powk[n-m])%mod;
printf("%u\n",ans);
return 0;
}
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Details
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Test #1:
score: 100
Accepted
time: 0ms
memory: 1632kb
input:
4 2 3
output:
228
result:
ok 1 number(s): "228"
Test #2:
score: 0
Accepted
time: 19ms
memory: 5548kb
input:
999999 1999 12345678
output:
52352722
result:
ok 1 number(s): "52352722"
Test #3:
score: 0
Accepted
time: 0ms
memory: 1620kb
input:
7 4 2
output:
182
result:
ok 1 number(s): "182"
Test #4:
score: 0
Accepted
time: 0ms
memory: 1660kb
input:
4 3 4
output:
480
result:
ok 1 number(s): "480"
Test #5:
score: 0
Accepted
time: 0ms
memory: 1656kb
input:
3 1 1
output:
3
result:
ok 1 number(s): "3"
Test #6:
score: 0
Accepted
time: 0ms
memory: 1344kb
input:
5 5 1
output:
0
result:
ok 1 number(s): "0"
Test #7:
score: 0
Accepted
time: 0ms
memory: 1560kb
input:
7 4 3
output:
5784
result:
ok 1 number(s): "5784"
Test #8:
score: 0
Accepted
time: 0ms
memory: 1556kb
input:
5 2 4
output:
3932
result:
ok 1 number(s): "3932"
Test #9:
score: 0
Accepted
time: 0ms
memory: 1664kb
input:
8 2 2
output:
1522
result:
ok 1 number(s): "1522"
Test #10:
score: 0
Accepted
time: 0ms
memory: 1632kb
input:
8 1 2
output:
2048
result:
ok 1 number(s): "2048"
Test #11:
score: 0
Accepted
time: 0ms
memory: 1620kb
input:
7 5 3
output:
2430
result:
ok 1 number(s): "2430"
Test #12:
score: 0
Accepted
time: 0ms
memory: 1600kb
input:
10 4 3
output:
272004
result:
ok 1 number(s): "272004"
Test #13:
score: 0
Accepted
time: 0ms
memory: 1472kb
input:
675978 614 2
output:
0
result:
ok 1 number(s): "0"
Test #14:
score: 0
Accepted
time: 0ms
memory: 1440kb
input:
244613 38 1
output:
0
result:
ok 1 number(s): "0"
Test #15:
score: 0
Accepted
time: 0ms
memory: 1392kb
input:
186293 1462 1
output:
0
result:
ok 1 number(s): "0"
Test #16:
score: 0
Accepted
time: 0ms
memory: 1496kb
input:
24867 886 1
output:
0
result:
ok 1 number(s): "0"
Test #17:
score: 0
Accepted
time: 0ms
memory: 1508kb
input:
976164 1014 2
output:
0
result:
ok 1 number(s): "0"
Test #18:
score: 0
Accepted
time: 1ms
memory: 2352kb
input:
179356 2 716844809
output:
577866092
result:
ok 1 number(s): "577866092"
Test #19:
score: 0
Accepted
time: 0ms
memory: 5408kb
input:
621001 130 310625363
output:
892869197
result:
ok 1 number(s): "892869197"
Test #20:
score: 0
Accepted
time: 3ms
memory: 4944kb
input:
678862 850 754662812
output:
582264789
result:
ok 1 number(s): "582264789"
Test #21:
score: 0
Accepted
time: 7ms
memory: 4400kb
input:
650845 978 348443366
output:
825425732
result:
ok 1 number(s): "825425732"
Test #22:
score: 0
Accepted
time: 5ms
memory: 4564kb
input:
669914 402 87448112
output:
318098088
result:
ok 1 number(s): "318098088"
Test #23:
score: 0
Accepted
time: 8ms
memory: 5536kb
input:
998593 530 681228665
output:
408255654
result:
ok 1 number(s): "408255654"
Test #24:
score: 0
Accepted
time: 14ms
memory: 4808kb
input:
369361 1954 125266115
output:
509912384
result:
ok 1 number(s): "509912384"
Test #25:
score: 0
Accepted
time: 12ms
memory: 5404kb
input:
900226 1378 424079373
output:
406320917
result:
ok 1 number(s): "406320917"
Test #26:
score: 0
Accepted
time: 9ms
memory: 2956kb
input:
334887 1506 17859926
output:
503264679
result:
ok 1 number(s): "503264679"
Test #27:
score: 0
Accepted
time: 7ms
memory: 5296kb
input:
936048 544 53978328
output:
548647866
result:
ok 1 number(s): "548647866"
Test #28:
score: 0
Accepted
time: 6ms
memory: 2228kb
input:
152789 1264 792983073
output:
839541707
result:
ok 1 number(s): "839541707"
Test #29:
score: 0
Accepted
time: 10ms
memory: 4424kb
input:
714493 1392 91796331
output:
721071046
result:
ok 1 number(s): "721071046"
Test #30:
score: 0
Accepted
time: 2ms
memory: 4544kb
input:
269571 816 830801077
output:
330064211
result:
ok 1 number(s): "330064211"
Test #31:
score: 0
Accepted
time: 9ms
memory: 5536kb
input:
845120 944 424581630
output:
348960190
result:
ok 1 number(s): "348960190"
Test #32:
score: 0
Accepted
time: 4ms
memory: 4608kb
input:
533990 368 163586376
output:
522092095
result:
ok 1 number(s): "522092095"
Test #33:
score: 0
Accepted
time: 10ms
memory: 2400kb
input:
181707 1792 462399634
output:
373795106
result:
ok 1 number(s): "373795106"
Test #34:
score: 0
Accepted
time: 13ms
memory: 4084kb
input:
417349 1920 761212891
output:
587051329
result:
ok 1 number(s): "587051329"
Test #35:
score: 0
Accepted
time: 9ms
memory: 4648kb
input:
526583 1344 500217637
output:
108767800
result:
ok 1 number(s): "108767800"
Test #36:
score: 0
Accepted
time: 5ms
memory: 5140kb
input:
867054 769 93998191
output:
239123369
result:
ok 1 number(s): "239123369"
Extra Test:
score: 0
Extra Test Passed