#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define ar array
const int mxN=3e5;
int n, m, k, t, z, cnt[2*mxN+1];
ar<int, 2> cells[22];
vector<ar<int, 2>> pf;
ll f[2*mxN+1], iF[2*mxN+1], ways[22][22], dp1[22], dp2[22][22];
vector<ar<int, 2>> ans_set;
ll bp(ll b, int p, int M) {
ll r=1;
for (; p; p/=2, b=b*b%M)
if (p%2)
r=r*b%M;
return r;
}
ll C(int a, int b, ar<int, 2> prime, int pp) {
assert(0<=b&&b<=a&&a<=n+m);
int pwr=cnt[a]-cnt[b]-cnt[a-b];
assert(pwr>=0);
if (pwr>=prime[1])
return 0;
ll r=f[a]*iF[b]%pp*iF[a-b]%pp;
while(pwr--)
r=r*prime[0]%pp;
return r;
}
bool ord(int i, int j) {
return cells[i][0]<=cells[j][0]&&cells[i][1]<=cells[j][1];
}
void solve(ar<int, 2> prime) {
int pp=1;
for (int i=0; i<prime[1]; ++i)
pp*=prime[0];
f[0]=1, iF[0]=1;
for (int i=1; i<=n+m; ++i) {
int x=i;
cnt[i]=cnt[i-1];
while(x%prime[0]==0)
x/=prime[0], ++cnt[i];
f[i]=f[i-1]*x%pp;
iF[i]=bp(f[i], pp/prime[0]*(prime[0]-1)-1, pp);
}
auto Go=[&](int i, int j) {
assert(ord(i, j));
int x=cells[j][0]-cells[i][0];
int y=cells[j][1]-cells[i][1];
return C(x+y, x, prime, pp);
};
for (int i=0; i<k+2; ++i)
for (int j=i+1; j<k+2; ++j) {
assert(cells[i]!=cells[j]&&cells[i][0]<=cells[j][0]);
if (!ord(i, j)) {
ways[i][j]=0;
continue;
}
ways[i][j]=Go(i, j);
for (int a=i+1; a<j; ++a) {
if (ord(i, a)&&ord(a, j)) {
dp1[a]=Go(i, a);
for (int b=i+1; b<a; ++b)
if (ord(i, b)&&ord(b, a))
dp1[a]=(dp1[a]-dp1[b]*Go(b, a)%pp+pp)%pp;
ways[i][j]=(ways[i][j]-dp1[a]*Go(a, j)%pp+pp)%pp;
}
}
}
memset(dp2, 0, sizeof(dp2));
dp2[0][0]=1;
for (int i=1; i<k+2; ++i)
for (int j=1; j<k+2; ++j)
for (int a=0; a<i; ++a)
if (ord(a, i))
dp2[i][j]=(dp2[i][j]+dp2[a][j-1]*ways[a][i])%pp;
ll tot=0;
for (int i=0; i<=t+1; ++i)
tot=(tot+dp2[k+1][i])%pp;
//cout << tot << " " << pp << endl;
ans_set.push_back({(int)tot, pp});
}
ar<int, 2> mrg(ar<int, 2> a, ar<int, 2> b) {
assert(a[1]<b[1]);
ar<int, 2> c={b[0], a[1]*b[1]};
for (int i=1; i<a[1]; ++i) {
if (c[0]%a[1]==a[0])
break;
c[0]+=b[1];
}
assert(c[0]%a[1]==a[0]);
return c;
}
int main() {
ios::sync_with_stdio(0);
cin.tie(0);
cin >> n >> m >> k >> t >> z; // can hit <=t traps
t=min(t, k);
if (z==1) {
cout << 0;
return 0;
}
for (int i=2; i*i<=z; ++i) {
if (z%i==0) {
int c=0;
while(z%i==0)
z/=i, ++c;
pf.push_back({i, c});
}
}
if (z>1)
pf.push_back({z, 1});
for (int i=0; i<k; ++i)
cin >> cells[i][0] >> cells[i][1];
cells[k+1]={n, m};
sort(cells, cells+k+2);
for (ar<int, 2> prime : pf)
solve(prime);
sort(ans_set.begin(), ans_set.end(), [&](ar<int, 2> a, ar<int, 2> b) { return a[1]<b[1]; });
while(ans_set.size()>1) {
ar<int, 2> b=ans_set.back();
ans_set.pop_back();
ar<int, 2> a=ans_set.back();
ans_set.pop_back();
ans_set.push_back(mrg(a, b));
}
cout << ans_set[0][0];
return 0;
}
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
340 KB |
Output is correct |
| 2 |
Correct |
1 ms |
340 KB |
Output is correct |
| 3 |
Correct |
0 ms |
340 KB |
Output is correct |
| 4 |
Correct |
1 ms |
276 KB |
Output is correct |
| 5 |
Correct |
1 ms |
340 KB |
Output is correct |
| 6 |
Correct |
1 ms |
340 KB |
Output is correct |
| 7 |
Correct |
1 ms |
340 KB |
Output is correct |
| 8 |
Correct |
1 ms |
340 KB |
Output is correct |
| 9 |
Correct |
3 ms |
468 KB |
Output is correct |
| 10 |
Correct |
5 ms |
724 KB |
Output is correct |
| 11 |
Correct |
44 ms |
4152 KB |
Output is correct |
| 12 |
Correct |
132 ms |
12028 KB |
Output is correct |
| 13 |
Correct |
215 ms |
10104 KB |
Output is correct |
| 14 |
Correct |
79 ms |
4228 KB |
Output is correct |
| 15 |
Correct |
79 ms |
4236 KB |
Output is correct |
| 16 |
Correct |
227 ms |
11428 KB |
Output is correct |
| 17 |
Correct |
223 ms |
11080 KB |
Output is correct |
| 18 |
Correct |
231 ms |
12032 KB |
Output is correct |
| 19 |
Correct |
236 ms |
12052 KB |
Output is correct |
| 20 |
Correct |
243 ms |
12108 KB |
Output is correct |
