#include <algorithm> #include <cstdio> #include <numeric> const int MAX_N = 1009; const int MAX_K = 1009; long long f[MAX_N]; void gen_fact(const long long p) { f[0] = 1LL; f[1] = 1LL; for(int i = 2; i < MAX_N; ++i) f[i] = (f[i-1] * i) % p; } long long fact(const long long n, const long long p) { return f[n]; } long long inv(const long long a, const long long p) { long long q; long long u = 1LL; long long w = a; long long x = 0LL; long long z = p; while(w) { if(w < z) { q = u; u = x; x = q; q = w; w = z; z = q; } q = w / z; u -= q * x; w -= q * z; } if(x < 0) x += p; return x; } long long b[MAX_N][MAX_K]; void gen_binom(const long long p) { b[0][0] = 1LL; b[1][0] = 1LL; b[1][1] = 1LL; for(int i = 2; i < MAX_N; ++i) { for(int j = 0; j < MAX_K; ++j) { if(j == 0) b[i][j] = 1LL; else b[i][j] = (b[i-1][j-1] + b[i-1][j]) % p; } } } long long binom(const long long n, long long k, const long long p) { k = std::min(k, n - k); return b[n][k]; } long long t1[MAX_N][MAX_K]; long long t1_sums[MAX_N][MAX_K]; void gen_t1(const long long p) { t1[2][1] = 1LL; t1[3][2] = 1LL; for(int j = 1; j < std::min(20, MAX_K); ++j) { t1_sums[2][j] = (t1_sums[2][j-1] + t1[2][j]) % p; t1_sums[3][j] = (t1_sums[3][j-1] + t1[3][j]) % p; } for(int i = 4; i < MAX_N; ++i) { for(int j = 2; j < MAX_K; ++j) { if(j == 2) { t1[i][j] = (2LL * t1[i-1][j]) % p; continue; } for(int len = 2; len < i; ++len) { const long long p1 = (t1[len][j] * t1_sums[i-len+1][j-1]) % p; const long long p2 = (t1[i-len+1][j] * t1_sums[len][j-1]) % p; const long long p3 = (t1[len][j-1] * t1[i-len+1][j-1]) % p; const long long to_add = (p1+p2+p3) % p; t1[i][j] = (t1[i][j] + to_add * binom(i-3, len-2, p)) % p; } if(t1[i][j] == 0LL) break; } for(int j = 1; j < std::min(20, MAX_K); ++j) t1_sums[i][j] = (t1_sums[i][j-1] + t1[i][j]) % p; } } long long t2[MAX_N][MAX_K]; long long t2_sums[MAX_N][MAX_K]; void gen_t2(const long long p) { t2[1][0] = 1LL; t2[2][1] = 1LL; for(int j = 1; j < std::min(20, MAX_K); ++j) { t2_sums[1][j] = (t2_sums[2][j-1] + t2[1][j]) % p; t2_sums[2][j] = (t2_sums[2][j-1] + t2[2][j]) % p; } for(int i = 3; i < MAX_N; ++i) { for(int j = 1; j < MAX_K; ++j) { if(j == 1) { t2[i][j] = 1LL; continue; } for(int len = 2; len < i; ++len) { const long long p1 = (t1[len][j] * t2_sums[i-len+1][j-1]) % p; const long long p2 = (t2[i-len+1][j] * t1_sums[len][j-1]) % p; const long long p3 = (t1[len][j] * t2[i-len+1][j]) % p; const long long to_add = (p1+p2+p3) % p; t2[i][j] = (t2[i][j] + to_add * binom(i-3, len-2, p)) % p; } if(t2[i][j] == 0LL) break; } for(int j = 1; j < std::min(20, MAX_K); ++j) t2_sums[i][j] = (t2_sums[i][j-1] + t2[i][j]) % p; } } long long t3[MAX_N][MAX_K]; void gen_t3(const long long p) { t3[1][0] = 1LL; t3[2][1] = 2LL; for(int i = 3; i < MAX_N; ++i) { for(int j = 1; j < MAX_K; ++j) { if(j == 1) { t3[i][j] = (2LL * t3[i-1][j]) % p; continue; } for(int len = 1; len <= i; ++len) { const long long p1 = (t2[len][j] * t2_sums[i-len+1][j-1]) % p; const long long p2 = (t2_sums[len][j-1] * t2[i-len+1][j]) % p; const long long p3 = (t2[len][j] * t2[i-len+1][j]) % p; const long long to_add = (p1+p2+p3) % p; t3[i][j] = (t3[i][j] + to_add * binom(i-3, len-2, p)) % p; } if(t3[i][j] == 0LL) break; } } } int main() { long long n, k, p; scanf("%lld%lld%lld", &n, &k, &p); gen_fact(p); gen_binom(p); gen_t1(p); gen_t2(p); gen_t3(p); for(int i = 3; i < (MAX_N-2); ++i) { for(int j = 2; j <= MAX_K; ++j) t3[i][j] = t3[i+2][j]; } printf("%lld\n", t3[n][k]); }
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 | #include <algorithm> #include <cstdio> #include <numeric> const int MAX_N = 1009; const int MAX_K = 1009; long long f[MAX_N]; void gen_fact(const long long p) { f[0] = 1LL; f[1] = 1LL; for(int i = 2; i < MAX_N; ++i) f[i] = (f[i-1] * i) % p; } long long fact(const long long n, const long long p) { return f[n]; } long long inv(const long long a, const long long p) { long long q; long long u = 1LL; long long w = a; long long x = 0LL; long long z = p; while(w) { if(w < z) { q = u; u = x; x = q; q = w; w = z; z = q; } q = w / z; u -= q * x; w -= q * z; } if(x < 0) x += p; return x; } long long b[MAX_N][MAX_K]; void gen_binom(const long long p) { b[0][0] = 1LL; b[1][0] = 1LL; b[1][1] = 1LL; for(int i = 2; i < MAX_N; ++i) { for(int j = 0; j < MAX_K; ++j) { if(j == 0) b[i][j] = 1LL; else b[i][j] = (b[i-1][j-1] + b[i-1][j]) % p; } } } long long binom(const long long n, long long k, const long long p) { k = std::min(k, n - k); return b[n][k]; } long long t1[MAX_N][MAX_K]; long long t1_sums[MAX_N][MAX_K]; void gen_t1(const long long p) { t1[2][1] = 1LL; t1[3][2] = 1LL; for(int j = 1; j < std::min(20, MAX_K); ++j) { t1_sums[2][j] = (t1_sums[2][j-1] + t1[2][j]) % p; t1_sums[3][j] = (t1_sums[3][j-1] + t1[3][j]) % p; } for(int i = 4; i < MAX_N; ++i) { for(int j = 2; j < MAX_K; ++j) { if(j == 2) { t1[i][j] = (2LL * t1[i-1][j]) % p; continue; } for(int len = 2; len < i; ++len) { const long long p1 = (t1[len][j] * t1_sums[i-len+1][j-1]) % p; const long long p2 = (t1[i-len+1][j] * t1_sums[len][j-1]) % p; const long long p3 = (t1[len][j-1] * t1[i-len+1][j-1]) % p; const long long to_add = (p1+p2+p3) % p; t1[i][j] = (t1[i][j] + to_add * binom(i-3, len-2, p)) % p; } if(t1[i][j] == 0LL) break; } for(int j = 1; j < std::min(20, MAX_K); ++j) t1_sums[i][j] = (t1_sums[i][j-1] + t1[i][j]) % p; } } long long t2[MAX_N][MAX_K]; long long t2_sums[MAX_N][MAX_K]; void gen_t2(const long long p) { t2[1][0] = 1LL; t2[2][1] = 1LL; for(int j = 1; j < std::min(20, MAX_K); ++j) { t2_sums[1][j] = (t2_sums[2][j-1] + t2[1][j]) % p; t2_sums[2][j] = (t2_sums[2][j-1] + t2[2][j]) % p; } for(int i = 3; i < MAX_N; ++i) { for(int j = 1; j < MAX_K; ++j) { if(j == 1) { t2[i][j] = 1LL; continue; } for(int len = 2; len < i; ++len) { const long long p1 = (t1[len][j] * t2_sums[i-len+1][j-1]) % p; const long long p2 = (t2[i-len+1][j] * t1_sums[len][j-1]) % p; const long long p3 = (t1[len][j] * t2[i-len+1][j]) % p; const long long to_add = (p1+p2+p3) % p; t2[i][j] = (t2[i][j] + to_add * binom(i-3, len-2, p)) % p; } if(t2[i][j] == 0LL) break; } for(int j = 1; j < std::min(20, MAX_K); ++j) t2_sums[i][j] = (t2_sums[i][j-1] + t2[i][j]) % p; } } long long t3[MAX_N][MAX_K]; void gen_t3(const long long p) { t3[1][0] = 1LL; t3[2][1] = 2LL; for(int i = 3; i < MAX_N; ++i) { for(int j = 1; j < MAX_K; ++j) { if(j == 1) { t3[i][j] = (2LL * t3[i-1][j]) % p; continue; } for(int len = 1; len <= i; ++len) { const long long p1 = (t2[len][j] * t2_sums[i-len+1][j-1]) % p; const long long p2 = (t2_sums[len][j-1] * t2[i-len+1][j]) % p; const long long p3 = (t2[len][j] * t2[i-len+1][j]) % p; const long long to_add = (p1+p2+p3) % p; t3[i][j] = (t3[i][j] + to_add * binom(i-3, len-2, p)) % p; } if(t3[i][j] == 0LL) break; } } } int main() { long long n, k, p; scanf("%lld%lld%lld", &n, &k, &p); gen_fact(p); gen_binom(p); gen_t1(p); gen_t2(p); gen_t3(p); for(int i = 3; i < (MAX_N-2); ++i) { for(int j = 2; j <= MAX_K; ++j) t3[i][j] = t3[i+2][j]; } printf("%lld\n", t3[n][k]); } |