// Artur Kraska, II UWr
#include <algorithm>
#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <vector>
#include <cmath>
#include <list>
#include <set>
#include <map>
#define forr(i, n) for(int i=0; i<n; i++)
#define FOREACH(iter, coll) for(typeof(coll.begin()) iter = coll.begin(); iter != coll.end(); ++iter)
#define FOREACHR(iter, coll) for(typeof(coll.rbegin()) iter = coll.rbegin(); iter != coll.rend(); ++iter)
#define lbound(P,R,PRED) ({typeof(P) X=P,RRR=(R), PPP = P; while(PPP<RRR) {X = (PPP+(RRR-PPP)/2); if(PRED) RRR = X; else PPP = X+1;} PPP;})
#define testy() int _tests; scanf("%d", &_tests); FOR(_test, 1, _tests)
#define CLEAR(tab) memset(tab, 0, sizeof(tab))
#define CONTAIN(el, coll) (coll.find(el) != coll.end())
#define FOR(i, a, b) for(int i=a; i<=b; i++)
#define FORD(i, a, b) for(int i=a; i>=b; i--)
#define MP make_pair
#define PB push_back
#define deb(X) X;
#define M 1000000007
#define INF 1000000007
using namespace std;
int n, k, p, m, a;
long long zadne[1007][20], lewo[1007][20], obie[1007][20];
long long tr[1007][1007];
int LOG = 13;
void trojkat()
{
tr[0][0] = 1;
FOR(i, 1, 1000)
{
tr[i][0] = 1;
FOR(j, 1, i)
tr[i][j] = (tr[i-1][j-1] + tr[i-1][j]) % p;
}
}
int main()
{
cin >> n >> k >> p;
k++;
LOG = min(LOG, k);
trojkat();
FOR(i, 0, LOG)
{
zadne[0][i] = 1;
obie[0][i] = 1;
lewo[0][i] = 1;
}
FOR(i, 1, LOG)
{
zadne[1][i] = 1;
obie[1][i] = 1;
lewo[1][i] = 1;
}
FOR(i, 2, n)
{
FOR(j, 1, LOG)
{
zadne[i][j] = zadne[i][j-1];
obie[i][j] = obie[i][j-1];
lewo[i][j] = lewo[i][j-1];
FOR(x, 1, i)
{
obie[i][j] += ((obie[x-1][j-1] - obie[x-1][j-2]+p) * (obie[i-x][j-1] - obie[i-x][j-2]+p) +
(obie[x-1][j] - obie[x-1][j-1]+p) * obie[i-x][j-1] +
obie[x-1][j-1] * (obie[i-x][j] - obie[i-x][j-1]+p))%p * tr[i-1][x-1];
obie[i][j] %= p;
}
//obie[i][j] += 2*(obie[i-1][j] - obie[i-1][j-1] + p);
//obie[i][j] %= p;
FOR(x, 1, i)
{
lewo[i][j] += ((obie[x-1][j-1] - obie[x-1][j-2]+p) * lewo[i-x][j-1] +
obie[x-1][j-1] * (lewo[i-x][j] - lewo[i-x][j-1]+p))% p * tr[i-1][x-1];
lewo[i][j] %= p;
//cout << " lewo na " << x << " zwiekszone do " << lewo[i][j] << endl;
}
//lewo[i][j] += (lewo[i-1][j] - lewo[i-1][j-1] + p);
//lewo[i][j] %= p;
FOR(x, 1, i)
{
zadne[i][j] += (lewo[x-1][j-1]*lewo[i-x][j-1] - lewo[x-1][j-2]*lewo[i-x][j-2] + p)%p * tr[i-1][x-1];
zadne[i][j] %= p;
//cout << " zadne na " << x << " zwiekszone do " << zadne[i][j] << endl;
}
// if(obie[i][j] < 0 || lewo[i][j] < 0 || zadne[i][j] < 0)
// cout << "JAKAS UJEMNA WARTOSC!!!" << endl;
//cout << "dlugosc " << i << ", wynik " << j << " - obie: " << obie[i][j] << ", lewo: " << lewo[i][j] << ", zadne: " << zadne[i][j] << endl;
}
}
cout << (k > LOG ? 0 : ((zadne[n][k] - zadne[n][k-1]+p) % p)) << endl;
/*
long long rrr = 0;
FOR(i, 1, n)
FOR(j, 2, LOG)
rrr = (rrr + i*(j-1)*((zadne[i][j] - zadne[i][j-1]+p) % p))%p;
cout << "calosc: " << rrr << endl;
*/
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 | // Artur Kraska, II UWr #include <algorithm> #include <iostream> #include <cstdio> #include <cstdlib> #include <cstring> #include <vector> #include <cmath> #include <list> #include <set> #include <map> #define forr(i, n) for(int i=0; i<n; i++) #define FOREACH(iter, coll) for(typeof(coll.begin()) iter = coll.begin(); iter != coll.end(); ++iter) #define FOREACHR(iter, coll) for(typeof(coll.rbegin()) iter = coll.rbegin(); iter != coll.rend(); ++iter) #define lbound(P,R,PRED) ({typeof(P) X=P,RRR=(R), PPP = P; while(PPP<RRR) {X = (PPP+(RRR-PPP)/2); if(PRED) RRR = X; else PPP = X+1;} PPP;}) #define testy() int _tests; scanf("%d", &_tests); FOR(_test, 1, _tests) #define CLEAR(tab) memset(tab, 0, sizeof(tab)) #define CONTAIN(el, coll) (coll.find(el) != coll.end()) #define FOR(i, a, b) for(int i=a; i<=b; i++) #define FORD(i, a, b) for(int i=a; i>=b; i--) #define MP make_pair #define PB push_back #define deb(X) X; #define M 1000000007 #define INF 1000000007 using namespace std; int n, k, p, m, a; long long zadne[1007][20], lewo[1007][20], obie[1007][20]; long long tr[1007][1007]; int LOG = 13; void trojkat() { tr[0][0] = 1; FOR(i, 1, 1000) { tr[i][0] = 1; FOR(j, 1, i) tr[i][j] = (tr[i-1][j-1] + tr[i-1][j]) % p; } } int main() { cin >> n >> k >> p; k++; LOG = min(LOG, k); trojkat(); FOR(i, 0, LOG) { zadne[0][i] = 1; obie[0][i] = 1; lewo[0][i] = 1; } FOR(i, 1, LOG) { zadne[1][i] = 1; obie[1][i] = 1; lewo[1][i] = 1; } FOR(i, 2, n) { FOR(j, 1, LOG) { zadne[i][j] = zadne[i][j-1]; obie[i][j] = obie[i][j-1]; lewo[i][j] = lewo[i][j-1]; FOR(x, 1, i) { obie[i][j] += ((obie[x-1][j-1] - obie[x-1][j-2]+p) * (obie[i-x][j-1] - obie[i-x][j-2]+p) + (obie[x-1][j] - obie[x-1][j-1]+p) * obie[i-x][j-1] + obie[x-1][j-1] * (obie[i-x][j] - obie[i-x][j-1]+p))%p * tr[i-1][x-1]; obie[i][j] %= p; } //obie[i][j] += 2*(obie[i-1][j] - obie[i-1][j-1] + p); //obie[i][j] %= p; FOR(x, 1, i) { lewo[i][j] += ((obie[x-1][j-1] - obie[x-1][j-2]+p) * lewo[i-x][j-1] + obie[x-1][j-1] * (lewo[i-x][j] - lewo[i-x][j-1]+p))% p * tr[i-1][x-1]; lewo[i][j] %= p; //cout << " lewo na " << x << " zwiekszone do " << lewo[i][j] << endl; } //lewo[i][j] += (lewo[i-1][j] - lewo[i-1][j-1] + p); //lewo[i][j] %= p; FOR(x, 1, i) { zadne[i][j] += (lewo[x-1][j-1]*lewo[i-x][j-1] - lewo[x-1][j-2]*lewo[i-x][j-2] + p)%p * tr[i-1][x-1]; zadne[i][j] %= p; //cout << " zadne na " << x << " zwiekszone do " << zadne[i][j] << endl; } // if(obie[i][j] < 0 || lewo[i][j] < 0 || zadne[i][j] < 0) // cout << "JAKAS UJEMNA WARTOSC!!!" << endl; //cout << "dlugosc " << i << ", wynik " << j << " - obie: " << obie[i][j] << ", lewo: " << lewo[i][j] << ", zadne: " << zadne[i][j] << endl; } } cout << (k > LOG ? 0 : ((zadne[n][k] - zadne[n][k-1]+p) % p)) << endl; /* long long rrr = 0; FOR(i, 1, n) FOR(j, 2, LOG) rrr = (rrr + i*(j-1)*((zadne[i][j] - zadne[i][j-1]+p) % p))%p; cout << "calosc: " << rrr << endl; */ return 0; } |
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