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ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#806119 | #9782. NonZero PrefSuf Sums | ucup-team5008# | AC ✓ | 577ms | 419512kb | C++23 | 3.0kb | 2024-12-08 21:47:25 | 2024-12-08 21:47:25 |
Judging History
answer
#include<bits/stdc++.h>
using namespace std;
using ll=long long;
using vl=vector<ll>;
using vvl=vector<vl>;
using P=pair<ll,ll>;
using vp=vector<P>;
using vvp=vector<vp>;
const ll inf=LLONG_MAX/4;
#define rep2(i,j,k) for(ll i=ll(j);i<ll(k);i++)
#define rep(i,k) rep2(i,0,k)
#define rrep2(i,j,k) for(ll i=ll(j)-1;i>=ll(k);i--)
#define rrep(i,k) rrep2(i,k,0)
#define eb emplace_back
#define SZ(a) ll(a.size())
#define all(a) a.begin(),a.end()
template<class T>
bool chmin(T& a, T b){return a>b?a=b,1:0;}
template<class T>
bool chmax(T& a, T b){return a<b?a=b,1:0;}
int mod = 1;
struct mint {
int x;
mint(ll x = 0) : x((x%mod+mod)%mod) {}
mint &operator+=(const mint &a) { if((x += a.x) >= mod) x -= mod; return *this; }
mint &operator-=(const mint &a) { if((x += mod-a.x) >= mod) x -= mod; return *this; }
mint &operator*=(const mint &a) { x = (ll) x * a.x % mod; return *this; }
mint operator+(const mint &a) { return mint(*this) += a; }
mint operator-(const mint &a) { return mint(*this) -= a; }
mint operator*(const mint &a) { return mint(*this) *= a; }
mint pow(ll t) {
mint res(1), a(*this);
while(t) {
if(t&1) res *= a;
a *= a;
t >>= 1;
}
return res;
}
};
mint dp[101][101][10001];
mint sub[101][20001];
const int C = 100000;
mint fac[C+1], ifac[C+1];
mint binom(int n, int k) {
assert(n >= 0);
if(k < 0 or k > n) return 0;
return fac[n] * ifac[k] * ifac[n-k];
}
mint A[110][10010];
mint B[110][10010];
int main(){
cin.tie(0)->sync_with_stdio(0);
int n, m;
cin >> n >> m >> mod;
fac[0] = 1;
rep(i, C) fac[i+1] = fac[i] * (i+1);
ifac[C] = fac[C].pow(mod-2);
rrep(i, C) ifac[i] = ifac[i+1] * (i+1);
dp[0][0][0] = 1;
rep(i, n) {
rep(j, m+1) rep(k, (i+1)*j+1) A[j][k] = B[j][k] = 0;
rep(j, m+1) rep(k, i*j+1) {
A[j][k+1] += dp[i][j][k];
A[j][k+j+1] -= dp[i][j][k];
B[j+1][k+j+1] += dp[i][j][k];
// rep2(l, 1, m+1) dp[i+1][max(j,l)][k+l] += dp[i][j][k];
}
rep(j, m+1) rep(k, (i+1)*j+1) {
A[j][k+1] += A[j][k];
B[j+1][k+1] += B[j][k];
dp[i+1][j][k] += A[j][k];
dp[i+1][j][k] += B[j][k];
}
}
// rep2(i, 1, n+1) rep(k, i*m+1) {
// mint pre;
// rep2(j, 1, m+1) {
// mint now;
// if(i*j < k) continue;
// rep(l, i+1) {
// if(l*(j+1) > k) continue;
// mint tmp = binom(i, l) * binom(k-l*(j+1)+i-1, i-1);
// if(l&1) now -= tmp;
// else now += tmp;
// }
// assert((now-pre).x == dp[i][j][k].x);
// pre = now;
// }
// }
sub[0][0] = 1;
rep(i, n) rep(j, 2*m*i+1) rep(k, 2*m+1) if(k != m) sub[i+1][j+k] += sub[i][j];
mint ans;
rep(i, n+1) rep(j, m+1) rrep(k, n*m) dp[i][j][k] += dp[i][j][k+1];
rep2(i, 2, n+1) {
mint now;
rep2(a, 1, m+1) rep2(j, 1, i+1) rep(k, m/a+1) {
mint tmp;
int lb = max(0LL, j-k-1);
int ub = j;
assert(lb <= ub);
tmp += dp[i-j][k][lb];
tmp -= dp[i-j][k][ub];
//rep2(l, lb, ub) {
// tmp += dp[i-j][k][l];
//}
now += tmp * binom(i, j);
}
now *= 2;
now += sub[i][i*m];
mint cur = 1;
rep(_, i) cur *= 2*m;
cur -= now;
cur *= binom(n, i);
ans += cur;
}
cout << ans.x << endl;
}
Details
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Test #1:
score: 100
Accepted
time: 19ms
memory: 419452kb
input:
2 1 998244353
output:
2
result:
ok single line: '2'
Test #2:
score: 0
Accepted
time: 80ms
memory: 419444kb
input:
69 42 696969697
output:
378553557
result:
ok single line: '378553557'
Test #3:
score: 0
Accepted
time: 23ms
memory: 419368kb
input:
2 1 998244353
output:
2
result:
ok single line: '2'
Test #4:
score: 0
Accepted
time: 64ms
memory: 419392kb
input:
69 42 696969697
output:
378553557
result:
ok single line: '378553557'
Test #5:
score: 0
Accepted
time: 140ms
memory: 419448kb
input:
61 75 677323601
output:
34613998
result:
ok single line: '34613998'
Test #6:
score: 0
Accepted
time: 27ms
memory: 419360kb
input:
13 14 670577333
output:
41465431
result:
ok single line: '41465431'
Test #7:
score: 0
Accepted
time: 27ms
memory: 419460kb
input:
14 6 987686347
output:
37536510
result:
ok single line: '37536510'
Test #8:
score: 0
Accepted
time: 31ms
memory: 419396kb
input:
15 12 196428923
output:
29322522
result:
ok single line: '29322522'
Test #9:
score: 0
Accepted
time: 40ms
memory: 419512kb
input:
68 7 786815587
output:
149281835
result:
ok single line: '149281835'
Test #10:
score: 0
Accepted
time: 23ms
memory: 419460kb
input:
3 2 503002109
output:
82
result:
ok single line: '82'
Test #11:
score: 0
Accepted
time: 32ms
memory: 419508kb
input:
13 5 756093197
output:
415698676
result:
ok single line: '415698676'
Test #12:
score: 0
Accepted
time: 27ms
memory: 419392kb
input:
2 3 646574611
output:
30
result:
ok single line: '30'
Test #13:
score: 0
Accepted
time: 59ms
memory: 419392kb
input:
39 68 120037189
output:
43217507
result:
ok single line: '43217507'
Test #14:
score: 0
Accepted
time: 24ms
memory: 419456kb
input:
13 4 423132517
output:
360231790
result:
ok single line: '360231790'
Test #15:
score: 0
Accepted
time: 12ms
memory: 419392kb
input:
14 3 309713387
output:
94215386
result:
ok single line: '94215386'
Test #16:
score: 0
Accepted
time: 43ms
memory: 419512kb
input:
24 77 886983941
output:
211636479
result:
ok single line: '211636479'
Test #17:
score: 0
Accepted
time: 7ms
memory: 419460kb
input:
3 3 504388063
output:
270
result:
ok single line: '270'
Test #18:
score: 0
Accepted
time: 16ms
memory: 419392kb
input:
3 1 936205423
output:
8
result:
ok single line: '8'
Test #19:
score: 0
Accepted
time: 12ms
memory: 419392kb
input:
3 3 295983139
output:
270
result:
ok single line: '270'
Test #20:
score: 0
Accepted
time: 23ms
memory: 419448kb
input:
10 15 446169107
output:
149884328
result:
ok single line: '149884328'
Test #21:
score: 0
Accepted
time: 15ms
memory: 419400kb
input:
37 18 833753929
output:
592917251
result:
ok single line: '592917251'
Test #22:
score: 0
Accepted
time: 15ms
memory: 419388kb
input:
11 3 998773403
output:
860630017
result:
ok single line: '860630017'
Test #23:
score: 0
Accepted
time: 31ms
memory: 419452kb
input:
14 85 688036639
output:
347188409
result:
ok single line: '347188409'
Test #24:
score: 0
Accepted
time: 32ms
memory: 419468kb
input:
3 3 844621907
output:
270
result:
ok single line: '270'
Test #25:
score: 0
Accepted
time: 20ms
memory: 419392kb
input:
3 4 204335891
output:
620
result:
ok single line: '620'
Test #26:
score: 0
Accepted
time: 27ms
memory: 419384kb
input:
7 8 113007667
output:
58946097
result:
ok single line: '58946097'
Test #27:
score: 0
Accepted
time: 15ms
memory: 419460kb
input:
4 1 637268377
output:
22
result:
ok single line: '22'
Test #28:
score: 0
Accepted
time: 24ms
memory: 419464kb
input:
11 14 391637237
output:
303270280
result:
ok single line: '303270280'
Test #29:
score: 0
Accepted
time: 32ms
memory: 419460kb
input:
3 2 208286231
output:
82
result:
ok single line: '82'
Test #30:
score: 0
Accepted
time: 7ms
memory: 419412kb
input:
2 11 662696483
output:
462
result:
ok single line: '462'
Test #31:
score: 0
Accepted
time: 23ms
memory: 419396kb
input:
19 55 974135299
output:
887460557
result:
ok single line: '887460557'
Test #32:
score: 0
Accepted
time: 23ms
memory: 419448kb
input:
6 8 417027509
output:
23351024
result:
ok single line: '23351024'
Test #33:
score: 0
Accepted
time: 16ms
memory: 419436kb
input:
8 13 624006587
output:
353008442
result:
ok single line: '353008442'
Test #34:
score: 0
Accepted
time: 24ms
memory: 419396kb
input:
10 10 740294671
output:
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result:
ok single line: '79436611'
Test #35:
score: 0
Accepted
time: 7ms
memory: 419392kb
input:
11 10 394088657
output:
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result:
ok single line: '161476458'
Test #36:
score: 0
Accepted
time: 23ms
memory: 419512kb
input:
9 27 562853573
output:
135252259
result:
ok single line: '135252259'
Test #37:
score: 0
Accepted
time: 23ms
memory: 419448kb
input:
8 3 829129009
output:
5349034
result:
ok single line: '5349034'
Test #38:
score: 0
Accepted
time: 51ms
memory: 419468kb
input:
51 49 924010279
output:
815049368
result:
ok single line: '815049368'
Test #39:
score: 0
Accepted
time: 12ms
memory: 419468kb
input:
12 2 308466749
output:
223013998
result:
ok single line: '223013998'
Test #40:
score: 0
Accepted
time: 11ms
memory: 419480kb
input:
7 4 567557693
output:
4502296
result:
ok single line: '4502296'
Test #41:
score: 0
Accepted
time: 84ms
memory: 419388kb
input:
36 93 943780729
output:
13599465
result:
ok single line: '13599465'
Test #42:
score: 0
Accepted
time: 11ms
memory: 419388kb
input:
2 1 828681127
output:
2
result:
ok single line: '2'
Test #43:
score: 0
Accepted
time: 27ms
memory: 419456kb
input:
3 3 534160729
output:
270
result:
ok single line: '270'
Test #44:
score: 0
Accepted
time: 15ms
memory: 419436kb
input:
7 12 920925433
output:
453086694
result:
ok single line: '453086694'
Test #45:
score: 0
Accepted
time: 19ms
memory: 419448kb
input:
3 2 440546987
output:
82
result:
ok single line: '82'
Test #46:
score: 0
Accepted
time: 16ms
memory: 419468kb
input:
90 9 291269963
output:
72560304
result:
ok single line: '72560304'
Test #47:
score: 0
Accepted
time: 23ms
memory: 419444kb
input:
38 10 867575113
output:
165530481
result:
ok single line: '165530481'
Test #48:
score: 0
Accepted
time: 40ms
memory: 419384kb
input:
48 37 152663531
output:
135425620
result:
ok single line: '135425620'
Test #49:
score: 0
Accepted
time: 16ms
memory: 419396kb
input:
15 15 991731803
output:
102703562
result:
ok single line: '102703562'
Test #50:
score: 0
Accepted
time: 577ms
memory: 419464kb
input:
100 100 696969697
output:
313377809
result:
ok single line: '313377809'
Extra Test:
score: 0
Extra Test Passed