#include <bits/stdc++.h> using namespace std; const int maxn = 1100; typedef long long ll; typedef pair<int, int> Pii; typedef vector<Pii> vpii; typedef vector<int> vi; typedef vector<vi> vvi; typedef vector<ll> vll; #define pb push_back #define fst first #define snd second ll N, K, p; ll dp[maxn][16][3]; ll binom[maxn][maxn]; bool ok[maxn][16][3]; ll dp2[maxn][16][3]; bool ok2[maxn][16][3]; ll jebaj(int n, int k, int type); ll sumka(int n, int k, int type) { if(k == 0) return jebaj(n,k,type); if(!ok2[n][k][type]) { if(k > 0) dp2[n][k][type] = (jebaj(n,k,type) + sumka(n,k-1,type)) % p; else dp2[n][k][type] = jebaj(n,k,type); ok2[n][k][type] = true; } return dp2[n][k][type]; } ll jebaj(int n, int k, int type) { if(!ok[n][k][type]) { ll res = 0; if(type == 0) { if(k == 0) return n == 1; //if(n == 1) return k == 0; for(int i = 0; i < n; ++i) { ll res2 = jebaj(i, k, 1) * jebaj(n-i-1, k, 1); //res += binom[n-1][i] * jebaj(i, k, 1) % p * jebaj(n-i-1, k, 1) % p; //for(int j = 0; j < k; ++j) { ///res += binom[n-1][i] * jebaj(i, k, 1) % p * jebaj(n-i-1, j, 1) % p; res2 += jebaj(i, k, 1) * sumka(n-i-1, k-1, 1); ///res += binom[n-1][i] * jebaj(i, j, 1) % p * jebaj(n-i-1, k, 1) % p; res2 += sumka(i, k-1, 1) * jebaj(n-i-1, k, 1); } res += res2 % p * binom[n-1][i] % p; } } if(type == 1) { if(k == 0) return n == 0; if(n == 1) return k == 1; for(int i = 0; i < n; ++i) { //res += binom[n-1][i] * jebaj(i, k - 1, 2) % p * jebaj(n-i-1, k-1, 1) % p; //for(int j = 0; j < k; ++j) { //res += binom[n-1][i] * jebaj(i, k - 1 , 2) % p * jebaj(n-i-1, j, 1) % p; ll res2 = jebaj(i, k - 1 , 2) * sumka(n-i-1, k-1, 1); //res += binom[n-1][i] * jebaj(i, k - 1 , 2) % p * sumka(n-i-1, k-1, 1) % p; //res += binom[n-1][i] * jebaj(i, j, 2) % p * jebaj(n-i-1, k, 1) % p; res2 += sumka(i, k-1, 2) * jebaj(n-i-1, k, 1); res += res2 % p * binom[n-1][i] % p; } } } if(type == 2) // obie strony { if(k == 0) return n == 0; if(n == 1) return k == 1; for(int i = 0; i < n; ++i) { ll res2 = jebaj(i, k-1, 2) * jebaj(n-i-1, k-1, 2); //for(int j = 0; j < k; ++j) { //res += binom[n-1][i] * jebaj(i, k, 2) % p * jebaj(n-i-1, j, 2) % p; res2 += jebaj(i, k, 2) * sumka(n-i-1, k-1, 2); //res += binom[n-1][i] * jebaj(i, j, 2) % p * jebaj(n-i-1, k, 2) % p; res2 += sumka(i, k-1, 2) * jebaj(n-i-1, k, 2); res += res2 % p * binom[n-1][i] % p; } } } dp[n][k][type] = res % p; ok[n][k][type] = true; } return dp[n][k][type]; } void init() { for(int i = 0; i < maxn; ++i) binom[i][0] = 1; for(int i = 1; i < maxn; ++i) for(int j = 1; j <= i; ++j) { binom[i][j] = (binom[i-1][j] + binom[i-1][j-1]); if(binom[i][j] > p) binom[i][j] -= p; } } int main() { scanf("%lld%lld%lld", &N, &K, &p); //N = 1000; K = 15; p = 100000007; init(); //~ ll sum = 0; //~ for(int i = 1; i <= 1000; ++i) //~ for(int j = 1; j < 11; ++j) //~ sum += i * j * jebaj(i,j,0) % p; //~ printf("suma = %lld\n", sum % p); if(K >= 11) puts("0"); else printf("%lld\n", jebaj(N, K, 0)); return 0; //~ for(int i = 1; i < 1001; ++i) //~ { //~ for(int j = 1; j < 11; ++j) //~ printf("%lld ", jebaj(i, j, 0)); //~ puts(""); //~ } }
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 | #include <bits/stdc++.h> using namespace std; const int maxn = 1100; typedef long long ll; typedef pair<int, int> Pii; typedef vector<Pii> vpii; typedef vector<int> vi; typedef vector<vi> vvi; typedef vector<ll> vll; #define pb push_back #define fst first #define snd second ll N, K, p; ll dp[maxn][16][3]; ll binom[maxn][maxn]; bool ok[maxn][16][3]; ll dp2[maxn][16][3]; bool ok2[maxn][16][3]; ll jebaj(int n, int k, int type); ll sumka(int n, int k, int type) { if(k == 0) return jebaj(n,k,type); if(!ok2[n][k][type]) { if(k > 0) dp2[n][k][type] = (jebaj(n,k,type) + sumka(n,k-1,type)) % p; else dp2[n][k][type] = jebaj(n,k,type); ok2[n][k][type] = true; } return dp2[n][k][type]; } ll jebaj(int n, int k, int type) { if(!ok[n][k][type]) { ll res = 0; if(type == 0) { if(k == 0) return n == 1; //if(n == 1) return k == 0; for(int i = 0; i < n; ++i) { ll res2 = jebaj(i, k, 1) * jebaj(n-i-1, k, 1); //res += binom[n-1][i] * jebaj(i, k, 1) % p * jebaj(n-i-1, k, 1) % p; //for(int j = 0; j < k; ++j) { ///res += binom[n-1][i] * jebaj(i, k, 1) % p * jebaj(n-i-1, j, 1) % p; res2 += jebaj(i, k, 1) * sumka(n-i-1, k-1, 1); ///res += binom[n-1][i] * jebaj(i, j, 1) % p * jebaj(n-i-1, k, 1) % p; res2 += sumka(i, k-1, 1) * jebaj(n-i-1, k, 1); } res += res2 % p * binom[n-1][i] % p; } } if(type == 1) { if(k == 0) return n == 0; if(n == 1) return k == 1; for(int i = 0; i < n; ++i) { //res += binom[n-1][i] * jebaj(i, k - 1, 2) % p * jebaj(n-i-1, k-1, 1) % p; //for(int j = 0; j < k; ++j) { //res += binom[n-1][i] * jebaj(i, k - 1 , 2) % p * jebaj(n-i-1, j, 1) % p; ll res2 = jebaj(i, k - 1 , 2) * sumka(n-i-1, k-1, 1); //res += binom[n-1][i] * jebaj(i, k - 1 , 2) % p * sumka(n-i-1, k-1, 1) % p; //res += binom[n-1][i] * jebaj(i, j, 2) % p * jebaj(n-i-1, k, 1) % p; res2 += sumka(i, k-1, 2) * jebaj(n-i-1, k, 1); res += res2 % p * binom[n-1][i] % p; } } } if(type == 2) // obie strony { if(k == 0) return n == 0; if(n == 1) return k == 1; for(int i = 0; i < n; ++i) { ll res2 = jebaj(i, k-1, 2) * jebaj(n-i-1, k-1, 2); //for(int j = 0; j < k; ++j) { //res += binom[n-1][i] * jebaj(i, k, 2) % p * jebaj(n-i-1, j, 2) % p; res2 += jebaj(i, k, 2) * sumka(n-i-1, k-1, 2); //res += binom[n-1][i] * jebaj(i, j, 2) % p * jebaj(n-i-1, k, 2) % p; res2 += sumka(i, k-1, 2) * jebaj(n-i-1, k, 2); res += res2 % p * binom[n-1][i] % p; } } } dp[n][k][type] = res % p; ok[n][k][type] = true; } return dp[n][k][type]; } void init() { for(int i = 0; i < maxn; ++i) binom[i][0] = 1; for(int i = 1; i < maxn; ++i) for(int j = 1; j <= i; ++j) { binom[i][j] = (binom[i-1][j] + binom[i-1][j-1]); if(binom[i][j] > p) binom[i][j] -= p; } } int main() { scanf("%lld%lld%lld", &N, &K, &p); //N = 1000; K = 15; p = 100000007; init(); //~ ll sum = 0; //~ for(int i = 1; i <= 1000; ++i) //~ for(int j = 1; j < 11; ++j) //~ sum += i * j * jebaj(i,j,0) % p; //~ printf("suma = %lld\n", sum % p); if(K >= 11) puts("0"); else printf("%lld\n", jebaj(N, K, 0)); return 0; //~ for(int i = 1; i < 1001; ++i) //~ { //~ for(int j = 1; j < 11; ++j) //~ printf("%lld ", jebaj(i, j, 0)); //~ puts(""); //~ } } |