//~ while (clock()<=69*CLOCKS_PER_SEC)
//~ #pragma comment(linker, "/stack:200000000")
#pragma GCC optimize("O3")
//~ #pragma GCC optimize("Ofast")
//~ #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
//~ #pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
using namespace std;
template <typename T>
using ordered_set =
tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
#define sim template < class c
#define ris return * this
#define dor > debug & operator <<
#define eni(x) sim > typename \
enable_if<sizeof dud<c>(0) x 1, debug&>::type operator<<(c i) {
sim > struct rge { c b, e; };
sim > rge<c> range(c i, c j) { return rge<c>{i, j}; }
sim > auto dud(c* x) -> decltype(cerr << *x, 0);
sim > char dud(...);
struct debug {
#ifdef LOCAL
~debug() { cerr << endl; }
eni(!=) cerr << boolalpha << i; ris; }
eni(==) ris << range(begin(i), end(i)); }
sim, class b dor(pair < b, c > d) {
ris << "(" << d.first << ", " << d.second << ")";
}
sim dor(rge<c> d) {
*this << "[";
for (auto it = d.b; it != d.e; ++it)
*this << ", " + 2 * (it == d.b) << *it;
ris << "]";
}
#else
sim dor(const c&) { ris; }
#endif
};
#define imie(...) " [" << #__VA_ARGS__ ": " << (__VA_ARGS__) << "] "
#define shandom_ruffle random_shuffle
using ll=long long;
using pii=pair<int,int>;
using pll=pair<ll,ll>;
using vi=vector<int>;
using vll=vector<ll>;
const int nax=1007;
const int vax=13;
const int limit_na_k=10;
ll mod;
int n, k;
ll kom[nax][nax];
ll dp_prze[vax][nax];
ll dp_prze_s[vax][nax];
ll dp_pref[vax][nax];
ll dp_pref_s[vax][nax];
void dod(ll &a, ll b)
{
a=(a+b)%mod;
if (a<0)
a+=mod;
}
void ans(ll v)
{
printf("%lld\n", v);
exit(0);
}
int main()
{
scanf("%d%d%lld", &n, &k, &mod);
if (k>limit_na_k || n==1)
ans(0);
for (int i=0; i<=n; i++)
{
kom[i][0]=1;
for (int j=1; j<=i; j++)
kom[i][j]=(kom[i-1][j]+kom[i-1][j-1])%mod;
}
dp_prze[1][2]=dp_prze_s[1][2]=1;
for (int i=2; i<=k; i++)
{
for (int j=2; j<=n; j++)
{
for (int l=2; l<j; l++)
{
dod(dp_prze[i][j], dp_prze_s[i-1][l]*dp_prze[i][j-l+1]%mod*kom[j-3][l-2]*2);
dod(dp_prze[i][j], dp_prze[i-1][l]*dp_prze[i-1][j-l+1]%mod*kom[j-3][l-2]);
}
dp_prze_s[i][j]=(dp_prze_s[i-1][j]+dp_prze[i][j])%mod;
}
}
dp_pref[0][1]=dp_pref_s[0][1]=1;
for (int i=1; i<=k; i++)
{
dp_pref_s[i][1]=1;
for (int j=2; j<=n; j++)
{
for (int l=2; l<=j; l++)
dod(dp_pref_s[i][j], dp_prze_s[i][l]*dp_pref_s[i][j-l+1]%mod*kom[j-2][l-2]);
dp_pref[i][j]=(dp_pref_s[i][j]-dp_pref_s[i-1][j]+mod)%mod;
}
}
ll wyn=0;
for (int i=1; i<=n; i++)
dod(wyn, (dp_pref_s[k][i]*dp_pref_s[k][n-i+1]-dp_pref_s[k-1][i]*dp_pref_s[k-1][n-i+1])%mod*kom[n-1][i-1]);
ans(wyn);
return 0;
}
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 | //~ while (clock()<=69*CLOCKS_PER_SEC) //~ #pragma comment(linker, "/stack:200000000") #pragma GCC optimize("O3") //~ #pragma GCC optimize("Ofast") //~ #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native") //~ #pragma GCC optimize("unroll-loops") #include <bits/stdc++.h> #include <ext/pb_ds/assoc_container.hpp> #include <ext/pb_ds/tree_policy.hpp> using namespace __gnu_pbds; using namespace std; template <typename T> using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>; #define sim template < class c #define ris return * this #define dor > debug & operator << #define eni(x) sim > typename \ enable_if<sizeof dud<c>(0) x 1, debug&>::type operator<<(c i) { sim > struct rge { c b, e; }; sim > rge<c> range(c i, c j) { return rge<c>{i, j}; } sim > auto dud(c* x) -> decltype(cerr << *x, 0); sim > char dud(...); struct debug { #ifdef LOCAL ~debug() { cerr << endl; } eni(!=) cerr << boolalpha << i; ris; } eni(==) ris << range(begin(i), end(i)); } sim, class b dor(pair < b, c > d) { ris << "(" << d.first << ", " << d.second << ")"; } sim dor(rge<c> d) { *this << "["; for (auto it = d.b; it != d.e; ++it) *this << ", " + 2 * (it == d.b) << *it; ris << "]"; } #else sim dor(const c&) { ris; } #endif }; #define imie(...) " [" << #__VA_ARGS__ ": " << (__VA_ARGS__) << "] " #define shandom_ruffle random_shuffle using ll=long long; using pii=pair<int,int>; using pll=pair<ll,ll>; using vi=vector<int>; using vll=vector<ll>; const int nax=1007; const int vax=13; const int limit_na_k=10; ll mod; int n, k; ll kom[nax][nax]; ll dp_prze[vax][nax]; ll dp_prze_s[vax][nax]; ll dp_pref[vax][nax]; ll dp_pref_s[vax][nax]; void dod(ll &a, ll b) { a=(a+b)%mod; if (a<0) a+=mod; } void ans(ll v) { printf("%lld\n", v); exit(0); } int main() { scanf("%d%d%lld", &n, &k, &mod); if (k>limit_na_k || n==1) ans(0); for (int i=0; i<=n; i++) { kom[i][0]=1; for (int j=1; j<=i; j++) kom[i][j]=(kom[i-1][j]+kom[i-1][j-1])%mod; } dp_prze[1][2]=dp_prze_s[1][2]=1; for (int i=2; i<=k; i++) { for (int j=2; j<=n; j++) { for (int l=2; l<j; l++) { dod(dp_prze[i][j], dp_prze_s[i-1][l]*dp_prze[i][j-l+1]%mod*kom[j-3][l-2]*2); dod(dp_prze[i][j], dp_prze[i-1][l]*dp_prze[i-1][j-l+1]%mod*kom[j-3][l-2]); } dp_prze_s[i][j]=(dp_prze_s[i-1][j]+dp_prze[i][j])%mod; } } dp_pref[0][1]=dp_pref_s[0][1]=1; for (int i=1; i<=k; i++) { dp_pref_s[i][1]=1; for (int j=2; j<=n; j++) { for (int l=2; l<=j; l++) dod(dp_pref_s[i][j], dp_prze_s[i][l]*dp_pref_s[i][j-l+1]%mod*kom[j-2][l-2]); dp_pref[i][j]=(dp_pref_s[i][j]-dp_pref_s[i-1][j]+mod)%mod; } } ll wyn=0; for (int i=1; i<=n; i++) dod(wyn, (dp_pref_s[k][i]*dp_pref_s[k][n-i+1]-dp_pref_s[k-1][i]*dp_pref_s[k-1][n-i+1])%mod*kom[n-1][i-1]); ans(wyn); return 0; } |
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