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#include <bits/stdc++.h> using namespace std; long long n, d, mod, ans, f[20], g[20], dp[1010][20][1010]; inline long long read() { long long x = 0, f = 1; char c = getchar(); while (c < '0' || c > '9') { if (c == '-') f = -1; c = getchar(); } while (c >= '0' && c <= '9') { x = (x << 3) + (x << 1) + (c ^ '0'); c = getchar(); } return x * f; } long long Pow(long long x, long long k) { long long res = mod != 1; x %= mod; while (k) { if (k & 1) res = res * x % mod; x = x * x % mod; k >>= 1; } return res; } long long C(long long n, long long m) { if (n < m) return 0; long long res = 1; for (long long i = 1; i <= m; i++) res = res * (n - i + 1) % mod; return res * g[m] % mod; } int main() { n = read(); d = read(); mod = read(); f[0] = g[0] = 1; for (long long i = 1; i <= 10; i++) f[i] = f[i - 1] * i % mod; g[10] = Pow(f[10], mod - 2); for (long long i = 9; i; i--) g[i] = g[i + 1] * (i + 1) % mod; if (n <= 2) { puts("1"); return 0; } for (long long i = 0; i <= n; i++) dp[1][0][i] = 1; for (long long i = 2; i <= n; i++) for (long long j = 1; j <= min(i - 1, d); j++) for (long long k = 1; k <= n; k++) { dp[i][j][k] = dp[i][j][k - 1]; for (long long t = 1; i - t * k > 0 && j - t >= 0; t++) { if (k != 1) dp[i][j][k] = (dp[i][j][k] + dp[i - t * k][j - t][k - 1] * C(dp[k][d - 1][k - 1] + t - 1, t) % mod) % mod; else dp[i][j][k] = (dp[i][j][k] + dp[i - t * k][j - t][k - 1] * C(dp[k][0][k - 1] + t - 1, t) % mod) % mod; } } if (n & 1) ans = dp[n][d][n / 2]; else ans = (dp[n][d][n / 2] - C(dp[n / 2][d - 1][n / 2 - 1], 2) + mod) % mod; printf("%lld", ans); return 0; }
#include <bits/stdc++.h> using namespace std; template <class T, class S> ostream& operator<<(ostream& os, const pair<T, S>& v) { return os << "(" << v.first << ", " << v.second << ")"; } template <class T> ostream& operator<<(ostream& os, const vector<T>& v) { os << "["; for (int i = int(0); i <= int((static_cast<int>((v).size())) - 1); ++i) { if (i) os << ", "; os << v[i]; } return os << "]"; } template <class T> bool setmax(T& _a, T _b) { if (_b > _a) { _a = _b; return true; } return false; } template <class T> bool setmin(T& _a, T _b) { if (_b < _a) { _a = _b; return true; } return false; } template <class T> T gcd(T _a, T _b) { return _b == 0 ? _a : gcd(_b, _a % _b); } const int N = 1010; const int D = 11; long long f[N][D][N]; long long inv[D]; int main() { int n, d; long long mod; cin >> n >> d >> mod; const auto power = [mod](long long a, long long b) { long long c = 1; for (; b > 0; b >>= 1, a = a * a % mod) if (b & 1) c = c * a % mod; return c; }; for (int i = int(1); i <= int(D - 1); ++i) inv[i] = power(i, mod - 2); memset(f, 0, sizeof(f)); for (int j = int(0); j <= int(d); ++j) for (int k = int(0); k <= int(n); ++k) f[1][j][k] = 1; for (int i = int(2); i <= int(n); ++i) for (int j = int(0); j <= int(d); ++j) for (int k = int(1); k <= int(n); ++k) { long long cur = 1, p = f[k][d - 1][k - 1]; long long ans = 0; for (int t = int(0); t <= int(min(j, (i - 1) / k)); ++t) { if (i - t * k != 1 || (i - t * k == 1 && j == t)) { ans += f[i - t * k][j - t][k - 1] * cur; } (cur *= p + t) %= mod; (cur *= inv[t + 1]) %= mod; } f[i][j][k] = ans % mod; } long long ans = f[n][d][(n - 1) / 2]; if (n % 2 == 0) { long long tmp = f[n / 2][d - 1][n / 2 - 1]; (ans += tmp * (tmp + 1) / 2) %= mod; } cout << ans << endl; return 0; }
#include <bits/stdc++.h> using namespace std; int dp[1100], n, d, mo, num[1100][11], A[1100], w[11], B[11][11], nI[11]; int quick(int k1, int k2) { int k3 = 1; while (k2) { if (k2 & 1) k3 = 1ll * k3 * k1 % mo; k2 >>= 1; k1 = 1ll * k1 * k1 % mo; } return k3; } int main() { scanf("%d%d%d", &n, &d, &mo); nI[0] = 1; for (int i = 1; i <= d; i++) nI[i] = 1ll * nI[i - 1] * quick(i, mo - 2) % mo; dp[1] = 1; num[1][0] = 1; B[0][0] = 1; for (int i = 1; i <= d; i++) for (int j = 1; j <= i; j++) for (int k = 1; k <= i; k++) B[i][j] = (B[i][j] + B[i - k][j - 1]) % mo; for (int i = 1; i <= n / 2; i++) { dp[i] = num[i][d - 1]; int pre = 1; if (i == 1) dp[i]++; if (i * 2 == n) continue; if (dp[i] == 0) continue; memset(w, 0x00, sizeof w); for (int j = 1; j <= d; j++) { pre = 1ll * pre * (dp[i] - j + 1) % mo; for (int k = j; k <= d; k++) w[k] = (w[k] + 1ll * pre * nI[j] % mo * B[k][j]) % mo; } for (int a = d; a; a--) { for (int b = 1, si = i; b <= a; b++, si += i) for (int k = si + 1; k <= n; k++) num[k][a] = (num[k][a] + 1ll * w[b] * num[k - si][a - b]) % mo; } } int ans = 0; if (n % 2 == 0) ans = 1ll * dp[n / 2] * (dp[n / 2] + 1) % mo * nI[2] % mo; ans = (ans + num[n][d]) % mo; if (n == 1) ans = (ans + 1) % mo; cout << (ans + mo) % mo << endl; return 0; }
#include <bits/stdc++.h> using namespace std; int mod = 1000000000 + 7; int addm(int& a, int b) { return (a += b) < mod ? (a < 0 ? a += mod : a) : a -= mod; } int addm2(int a, int b) { return addm(a, b); } template <class T, class U> bool smin(T& a, U b) { return a > b ? (a = b, 1) : 0; } template <class T, class U> bool smax(T& a, U b) { return a < b ? (a = b, 1) : 0; } int n, d, dp[1001][11][1001], cs[1001][11][1002]; int a, b, g; void gcd(int m, int n) { if (n == 0) { a = 1; b = 0; g = m; return; } gcd(n, m % n); int t = a - b * (m / n); a = b; b = t; } int inv(int a, int mod) { gcd(mod, a); return g > 0 ? b : -b; } int iv[1001]; int main() { ios::sync_with_stdio(0); cin.tie(0); cin >> n >> d >> mod; dp[0][0][0] = 1; for (int i = 1; i <= 1000; i++) iv[i] = inv(i, mod); for (int i = 1; i < 1002; i++) for (int j = 0; j <= d; j++) cs[0][j][i] = addm2(cs[0][j][i - 1], dp[0][j][i - 1]); for (int i = 1; i < n; i++) for (int j = 1; j <= d; j++) for (int k = 1; k < n; k++) { long long f = 1; for (int l = 1; l * k <= i && l <= j && (k == 1 || cs[k - 1][d - 1][k]); l++) { f = f * ((k == 1 ? 1 : cs[k - 1][d - 1][k]) + l - 1) % mod * iv[l] % mod; if (cs[i - l * k][j - l][k]) addm(cs[i][j][k + 1], (long long)cs[i - l * k][j - l][k] * f % mod); } addm(cs[i][j][k + 1], cs[i][j][k]); } int ans = cs[n - 1][d][(n + 1) / 2]; addm(ans, cs[n - 1][0][(n + 1) / 2]); if (n % 2 == 0) { long long v = cs[n / 2 - 1][d - 1][n / 2] + cs[n / 2 - 1][0][n / 2]; addm(ans, v * (v + 1) / 2 % mod); } if (ans < 0) ans += mod; cout << ans << endl; }
#include <bits/stdc++.h> const int N = 1010; int n, d, mod, f[N][20][N], fac[20], Inv[20]; int ksm(int a, int b) { int ans = 1; while (b) { if (b & 1) ans = 1LL * ans * a % mod; a = 1LL * a * a % mod; b >>= 1; } return ans; } int C(int n, int m) { if (m > n) return 0; int ans = 1; for (int i = n - m + 1; i <= n; i++) ans = 1LL * ans * i % mod; ans = 1LL * ans * Inv[m] % mod; return ans; } int main() { scanf("%d%d%d", &n, &d, &mod); if (n == 1 || n == 2) { puts("1"); return 0; } fac[0] = Inv[0] = 1; for (int i = 1; i <= d; i++) fac[i] = 1LL * fac[i - 1] * i % mod; Inv[d] = ksm(fac[d], mod - 2); for (int i = d - 1; i >= 1; i--) Inv[i] = 1LL * Inv[i + 1] * (i + 1) % mod; for (int i = 0; i <= n; i++) f[1][0][i] = 1; for (int i = 2; i <= n; i++) { for (int j = 1; j <= std::min(d, i - 1); j++) { for (int k = 1; k <= n; k++) { f[i][j][k] = f[i][j][k - 1]; for (int t = 1; t <= j; t++) { if (i >= t * k && j >= t && k - 1 >= 0) { if (k > 1) f[i][j][k] = (f[i][j][k] + 1LL * f[i - t * k][j - t][k - 1] * C(f[k][d - 1][k - 1] + t - 1, t) % mod) % mod; else { f[i][j][k] = (f[i][j][k] + 1LL * f[i - t * k][j - t][k - 1] * C(f[k][0][k - 1] + t - 1, t) % mod) % mod; } } } } } } int res; if (n & 1) res = f[n][d][n / 2]; else res = (f[n][d][n / 2] - C(f[n / 2][d - 1][n / 2 - 1], 2) + mod) % mod; printf("%d", res); return 0; }
#include <bits/stdc++.h> const int N = 1e3 + 100; const int D = 12; int n; int d; int mod; void init() { std::cin >> n; std::cin >> d; std::cin >> mod; } int inverse(int x, int mod) { if (x == 1) { return 1; } else { return (long long)(mod - mod / x) * inverse(mod % x, mod) % mod; } } int comb(int r, int k) { static int inv[D]; int result = 1; for (int i = 1; i <= k; i++) { result = (long long)result * (r - i + 1) % mod; if (inv[i] == 0) { inv[i] = inverse(i, mod); } result = (long long)result * inv[i] % mod; } return result; } void update(int &x, int y) { x = (x + y) % mod; } void work() { if (n <= 2) { std::cout << 1 % mod << std::endl; return; } static int f[N][D][N]; std::memset(f, 0, sizeof(f)); f[1][0][0] = 1; for (int i = 1; i <= n; i++) { for (int j = 0; j <= d; j++) { for (int k = 0; k <= n / 2; k++) { if (k > 0) { update(f[i][j][k], f[i][j][k - 1]); for (int t = 1; t * k < i && t <= j; t++) { if (k == 1) { update(f[i][j][k], f[i - t * k][j - t][k - 1]); } else { update(f[i][j][k], (long long)f[i - t * k][j - t][k - 1] * comb(f[k][d - 1][k - 1] + t - 1, t) % mod); } } } } } } int answer = f[n][d][(n - 1) / 2]; if (n % 2 == 0) { answer += comb(f[n / 2][d - 1][n / 2 - 1] + 1, 2); answer %= mod; } std::cout << answer << std::endl; } int main() { init(); work(); return 0; }
#include <bits/stdc++.h> using namespace std; int n, d; long long mod, dp[1005][25][1005], f[1005], g[1005], ans; long long Pow(long long a, long long b) { long long rec = 1; for (; b; b >>= 1, a = a * a % mod) if (b & 1) rec = a * rec % mod; return rec; } int C(int n, int m) { if (n < m) return 0; long long ans = 1; for (int i = 1; i <= m; i++) ans = ans * (long long)(n - i + 1) % mod; return ans * g[m] % mod; } int main() { scanf("%d%d%lld", &n, &d, &mod); f[0] = g[0] = 1; for (int i = 1; i <= n; i++) f[i] = f[i - 1] * i % mod; g[n] = Pow(f[n], mod - 2); for (int i = n - 1; i; i--) g[i] = g[i + 1] * (i + 1) % mod; if (n <= 2) return puts("1"), 0; for (int i = 0; i <= n; i++) dp[1][0][i] = 1; for (int i = 2; i <= n; i++) for (int j = 1; j <= min(i - 1, d); j++) for (int k = 1; k <= n; k++) { dp[i][j][k] = dp[i][j][k - 1]; for (int t = 1; i - t * k > 0 && j - t >= 0; t++) if (k != 1) dp[i][j][k] = (dp[i][j][k] + dp[i - t * k][j - t][k - 1] * C(dp[k][d - 1][k - 1] + t - 1, t)) % mod; else dp[i][j][k] = (dp[i][j][k] + dp[i - t * k][j - t][k - 1] * C(dp[k][0][k - 1] + t - 1, t) % mod) % mod; } if (n & 1) ans = dp[n][d][n / 2]; else ans = (dp[n][d][n / 2] - C(dp[n / 2][d - 1][n / 2 - 1], 2) + mod) % mod; printf("%lld\n", ans); }
#include <bits/stdc++.h> using namespace std; int n, d, Md, f2[1010][1010][11], ny[1010], f[1010]; int Quick(int a, int b) { int Now = a, ret = 1; for (; b; b >>= 1, Now = 1LL * Now * Now % Md) if (b & 1) ret = 1LL * ret * Now % Md; return ret; } int main() { cin >> n >> d >> Md; if (n <= 2) { printf("1"); return 0; } for (int i = 1; i <= 1000; i++) ny[i] = Quick(i, Md - 2); f[1] = 1; f2[0][0][0] = 1; for (int(W) = (0); (W) <= (d); (W)++) f2[1][W][W] = 1; for (int i = 2; i * 2 <= n; i++) { f[i] = f2[i - 1][i - 1][d - 1]; for (int(k) = (0); (k) <= (d); (k)++) for (int(j) = (0); (j) <= (n); (j)++) if (f2[i - 1][j][k]) { int Now = f2[i - 1][j][k]; for (int l = 0; j + l * i <= n && l + k <= d && Now; l++) { f2[i][j + l * i][l + k] += Now; if (f2[i][j + l * i][l + k] >= Md) f2[i][j + l * i][l + k] -= Md; Now = 1LL * Now * (f[i] + l) % Md * ny[l + 1] % Md; } } } if (n & 1) printf("%d\n", f2[n >> 1][n - 1][d]); else { int ans = f2[(n >> 1) - 1][n - 1][d], Now = f[n >> 1]; Now = 1LL * (Now + 1) * Now % Md * ny[2] % Md; ans = (ans + Now) % Md; printf("%d\n", ans); } return 0; }
#include <bits/stdc++.h> using namespace std; const int maxn = 1009; int f[maxn][12][maxn / 2], n, d, mod; int inv[maxn], fac[maxn]; inline void pls(int &x, int y) { x = (x + y >= mod ? x + y - mod : x + y); } inline int dec(int &x, int y) { return (x - y < 0 ? x - y + mod : x - y); } void init() { inv[1] = 1; for (int i = 2; i < maxn; i++) inv[i] = (long long)(mod - mod / i) * inv[mod % i] % mod; for (int i = 2; i < maxn; i++) inv[i] = (long long)inv[i - 1] * inv[i] % mod; } inline int C(int n, int m) { if (m > n) return 0; int res = 1; for (int i = n - m + 1; i <= n; i++) res = (long long)res * i % mod; return (long long)res * inv[m] % mod; } int main() { scanf("%d%d%d", &n, &d, &mod); if (n <= 2) { puts("1"); return 0; } init(); for (int i = 0; i <= n / 2; i++) f[1][0][i] = 1; f[1][d - 1][0] = 1; for (int i = 2; i <= n; i++) for (int j = 1; j <= min(d, i - 1); j++) for (int k = 1; k <= n / 2; k++) { f[i][j][k] = f[i][j][k - 1]; for (int t = 1; t * k <= i && t <= j; t++) pls(f[i][j][k], (long long)f[i - t * k][j - t][k - 1] * C(f[k][d - 1][k - 1] + t - 1, t) % mod); } if (n & 1) printf("%d", f[n][d][n / 2]); else printf("%d", dec(f[n][d][n / 2], C(f[n / 2][d - 1][n / 2 - 1], 2))); return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 1111; const int D = 11; int n, mod, d; int f[N][D][N], g[N][D], iv[N]; template <typename T> inline void chkmin(T &x, T y) { x = min(x, y); } template <typename T> inline void chkmax(T &x, T y) { x = max(x, y); } template <typename T> inline void read(T &x) { T f = 1; x = 0; char c = getchar(); for (; !isdigit(c); c = getchar()) if (c == '-') f = -f; for (; isdigit(c); c = getchar()) x = (x << 3) + (x << 1) + c - '0'; x *= f; } inline int power(int a, int n) { int res = 1, b = a; while (n > 0) { if (n & 1) res = 1ll * res * b % mod; b = 1ll * b * b % mod; n >>= 1; } return res; } inline int inv(int x) { return power(x, mod - 2); } inline void add(int &x, int y) { x += y; while (x >= mod) x -= mod; } inline void sub(int &x, int y) { x -= y; if (x < 0) x += mod; } int main() { read(n); read(d); read(mod); for (int i = 0; i <= n; ++i) f[1][0][i] = 1; for (int i = 1; i <= d; ++i) g[1][i] = 1; for (int i = 1; i <= d; ++i) iv[i] = inv(i); for (int i = 2; i <= n; ++i) { for (int j = 1; j <= d; ++j) { for (int k = 1; k < i; ++k) for (int l = 1; l <= j && l * k <= i; ++l) add(f[i][j][k], 1ll * f[i - l * k][j - l][k - 1] * g[k][l] % mod); for (int k = 1; k <= n; ++k) add(f[i][j][k], f[i][j][k - 1]); } g[i][1] = f[i][d - 1][n]; for (int j = 2; j <= d; ++j) g[i][j] = 1ll * g[i][j - 1] * (f[i][d - 1][n] + j - 1) % mod * iv[j] % mod; } int ans = 0; if (n <= 2) ans = 1; else ans = f[n][d][n >> 1]; if (n > 2 && (n % 2 == 0)) sub(ans, 1ll * (f[n / 2][d - 1][n / 2] - 1) * f[n / 2][d - 1][n / 2] % mod * iv[2] % mod); printf("%d\n", ans); return 0; }
#include <bits/stdc++.h> using namespace std; const int maxn = 1005; const int maxd = 11; long long n, d, mod, dp[maxn][maxd], pd[maxn][maxd], f, t[maxd]; inline long long ksm(long long x, long long n) { long long ret = 1; while (n) { if (n & 1) ret = ret * x % mod; n >>= 1; x = x * x % mod; } return ret; } inline long long solve() { dp[1][0] = 1; for (int i = 1; i <= n / 2; ++i) if ((i - 1) % (d - 1) == 0) { f = (i == 1) ? 1 : dp[i][d - 1]; for (int j = 1; j <= n; ++j) for (int k = 0; k <= d; ++k) pd[j][k] = 0; t[0] = 1; for (int j = 1; j <= d; ++j) t[j] = t[j - 1] * (f + j - 1) % mod * ksm(j, mod - 2) % mod; for (int j = 0; j <= d; ++j) for (int k = 0; k <= d; ++k) if (j + k <= d) for (int l = 1; l <= n; ++l) if (l + i * k <= n) pd[l + i * k][j + k] = (pd[l + i * k][j + k] + dp[l][j] * t[k]) % mod; for (int j = 0; j <= n; ++j) for (int k = 0; k <= d; ++k) dp[j][k] = pd[j][k]; } long long ret = dp[n][d]; if (n % 2 == 0) ret = ((ret - dp[n / 2][d - 1] * (dp[n / 2][d - 1] - 1) / 2) % mod + mod) % mod; return ret; } int main() { scanf("%I64d%I64d%I64d", &n, &d, &mod); printf("%I64d\n", n <= 2 ? 1 : solve()); return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 1002, D = 12; int n, d, mod, inv, C[D], dp[D][N], res[D][N]; long long pow(long long x, long long y, long long mod) { return (!y ? 1 : pow(x * x % mod, y / 2, mod) * (y & 1 ? x : 1)) % mod; } int main() { cin >> n >> d >> mod; dp[0][1] = 1; inv = mod / 2 + 1; if (n < 3) return cout << 1, 0; for (int i = 1; i < (n + 1) / 2; i++) { int num = max(dp[d - 1][i], int(i == 1)); C[0] = 1; for (int i = 1; i < D; i++) C[i] = 1ll * C[i - 1] * pow(i, mod - 2, mod) % mod * (num + i - 1) % mod; for (int j = n - i; j >= 1; j--) for (int k = 1; k * i + j <= n; k++) for (int o = 0; o < d + 1; o++) if (o + k < D) dp[o + k][j + k * i] = (dp[o + k][j + k * i] + 1ll * dp[o][j] * C[k] % mod) % mod; } cout << (dp[d][n] + ((n + 1) & 1) * (1ll * dp[d - 1][n / 2] * (dp[d - 1][n / 2] + 1) % mod * inv % mod)) % mod; }
#include <bits/stdc++.h> using namespace std; const int maxn = 1005; const int maxd = 11; long long n, d, mod, dp[maxn][maxd], pd[maxn][maxd], f, t[maxd]; inline long long ksm(long long x, long long n) { long long ret = 1; while (n) { if (n & 1) ret = ret * x % mod; n >>= 1; x = x * x % mod; } return ret; } inline long long solve() { dp[1][0] = 1; for (int i = 1; i <= n / 2; ++i) { f = (i == 1) ? 1 : dp[i][d - 1]; for (int j = 1; j <= n; ++j) for (int k = 0; k <= d; ++k) pd[j][k] = 0; t[0] = 1; for (int j = 1; j <= d; ++j) t[j] = t[j - 1] * (f + j - 1) % mod * ksm(j, mod - 2) % mod; for (int j = 0; j <= d; ++j) for (int k = 0; k <= d; ++k) if (j + k <= d) for (int l = 1; l <= n; ++l) if (l + i * k <= n) pd[l + i * k][j + k] = (pd[l + i * k][j + k] + dp[l][j] * t[k]) % mod; for (int j = 0; j <= n; ++j) for (int k = 0; k <= d; ++k) dp[j][k] = pd[j][k]; } long long ret = dp[n][d]; if (n % 2 == 0) ret = ((ret - dp[n / 2][d - 1] * (dp[n / 2][d - 1] - 1) / 2) % mod + mod) % mod; return ret; } int main() { scanf("%I64d%I64d%I64d", &n, &d, &mod); if (n <= 2) puts("1"); else printf("%I64d\n", solve()); return 0; }
#include <bits/stdc++.h> using namespace std; const int M = 1e3 + 5; long long int dp[M][12][M], inv[M], n, d, mod; long long int pw(long long int a, long long int b) { if (b == 0) return 1ll; long long int p = pw(a, b / 2ll); if (b % 2ll) return p * p % mod * a % mod; else return p * p % mod; } int main() { cin >> n >> d >> mod; for (long long int i = 1; i <= n; i++) inv[i] = pw(i, mod - 2ll); dp[1][0][0] = 1; for (int i = 2; i <= n; i++) for (int j = 1; j <= d; j++) for (int k = (i - 1) / j; k <= i - 1; k++) { dp[i][j][k] = dp[i][j][k - 1]; long long int cur = 1, buf = dp[k][d - 1][k - 1]; for (int t = 1; t <= j && t * k <= i - 1; t++) { cur = cur * buf++ % mod * inv[t] % mod; (dp[i][j][k] += dp[i - t * k][j - t][min(k - 1, i - t * k - 1)] * (cur + (k == 1))) %= mod; } } long long int ans = dp[n][d][(n - 1) / 2]; if (n % 2 == 0) (ans += dp[n / 2][d - 1][n / 2 - 1] * (dp[n / 2][d - 1][n / 2 - 1] + 1) % mod * inv[2]) %= mod; cout << (n <= 2 ? 1 : ans) << endl; }
#include <bits/stdc++.h> using namespace std; const int MAXN = 1111; int inv[11], dp[MAXN][11][MAXN], n, D, MOD; inline int Fpw(int x, int K, int MOD) { int ret = 1; for (; K; K >>= 1) { if (K & 1) ret = (long long)ret * x % MOD; x = (long long)x * x % MOD; } return ret; } int main() { scanf("%d%d%d", &n, &D, &MOD); for (int i = 1; i <= D; ++i) inv[i] = Fpw(i, MOD - 2, MOD); dp[1][D - 1][0] = 1; dp[1][0][0] = 1; for (int i = 1; i <= n; ++i) { for (int j = 0; j <= D; ++j) for (int k = 1; k <= n; ++k) { dp[i][j][k] = dp[i][j][k - 1]; if (!dp[k][D - 1][k - 1] || i == 1) continue; int tmp = 1; for (int t = 1; t <= j && t * k <= i; ++t) { tmp = (long long)tmp * (dp[k][D - 1][k - 1] + t - 1) % MOD * inv[t] % MOD; dp[i][j][k] = ((long long)tmp * dp[i - t * k][j - t][k - 1] + dp[i][j][k]) % MOD; } } } int ans = 0; if (n & 1) ans = dp[n][D][n / 2]; else { int tmp = dp[n / 2][D - 1][n / 2 - 1]; ans = (dp[n][D][n / 2 - 1] + (long long)tmp * (tmp + 1) / 2) % MOD; } if (n == 1) ans = 1; if (ans < 0) ans += MOD; cout << ans << endl; }
#include <bits/stdc++.h> using namespace std; int n, d, mod, ans, tr[15]; int f[1005], inv[15]; int g[15][1005]; int main() { scanf("%d%d%d", &n, &d, &mod); if (n == 1) return puts("1"), 0; for (int i = (int)(0); i <= (int)(d); i++) g[i][i] = 1; f[1] = inv[0] = inv[1] = 1; for (int i = (int)(2); i <= (int)(d); i++) inv[i] = 1ll * inv[mod % i] * (mod - mod / i) % mod; for (int i = (int)(2); i <= (int)(n / 2); i++) { f[i] = g[d - 1][i - 1]; tr[0] = 1; for (int j = (int)(1); j <= (int)(d); j++) tr[j] = 1ll * tr[j - 1] * inv[j] % mod * (f[i] + j - 1) % mod; for (int j = (int)(d); j >= (int)(0); j--) for (int k = (int)(1); k <= (int)(d - j); k++) for (int l = (int)(0); l <= (int)(n - k * i); l++) g[j + k][l + k * i] = (g[j + k][l + k * i] + 1ll * g[j][l] * tr[k]) % mod; if (i == (n - 1) / 2) ans = g[d][n - 1]; } if (n % 2 == 0) ans = (ans + 1ll * f[n / 2] * (f[n / 2] + 1) / 2) % mod; printf("%d\n", ans); }
#include <bits/stdc++.h> using namespace std; long long n, d, mod, f[1100][11], jc[11]; inline long long read() { long long x = 0, f = 1; char ch = getchar(); while (ch < '0' || ch > '9') { if (ch == '-') f = -1; ch = getchar(); } while (ch >= '0' && ch <= '9') { x = (x << 1) + (x << 3) + ch - 48; ch = getchar(); } return x * f; } inline long long ksm(long long a, long long b) { long long ans = 1; while (b) { if (b & 1) ans = (ans * a) % mod; a = (a * a) % mod; b >>= 1; } return ans % mod; } int main() { n = read(); d = read(); mod = read(); if (n <= 2) { cout << 1; return 0; } f[1][d - 1] = f[1][0] = jc[1] = 1; for (int i = 2; i <= d; i++) jc[i] = jc[i - 1] * i; for (int i = 2; i <= d; i++) jc[i] = ksm(jc[i], mod - 2); for (int k = 1; k <= n / 2; k++) { if (!f[k][d - 1]) continue; long long tmp = f[k][d - 1], cs = 0; for (int i = n; i >= k + 1; i--) { for (int j = 1; j <= d; j++) { tmp = f[k][d - 1]; cs = 0; for (int t = 1; t <= j && t * k <= i; t++) { if (t != 1) tmp *= (++cs + f[k][d - 1]), tmp %= mod; f[i][j] += (f[i - k * t][j - t] * tmp % mod) * jc[t] % mod; f[i][j] %= mod; } } } } if (n % 2) cout << f[n][d] % mod; else { f[n][d] -= f[n / 2][d - 1] * (f[n / 2][d - 1] - 1) % mod * jc[2] % mod; cout << (f[n][d] + mod) % mod; } }
#include <bits/stdc++.h> using namespace std; int mod = 1000000000 + 7; int addm(int& a, int b) { return (a += b) < mod ? (a < 0 ? a += mod : a) : a -= mod; } int addm2(int a, int b) { return addm(a, b); } template <class T, class U> bool smin(T& a, U b) { return a > b ? (a = b, 1) : 0; } template <class T, class U> bool smax(T& a, U b) { return a < b ? (a = b, 1) : 0; } int n, d, dp[1001][11][1001], cs[1001][11][1002]; int a, b, g; void gcd(int m, int n) { if (n == 0) { a = 1; b = 0; g = m; return; } gcd(n, m % n); int t = a - b * (m / n); a = b; b = t; } int inv(int a, int mod) { gcd(mod, a); return g > 0 ? b : -b; } int iv[1001]; int main() { ios::sync_with_stdio(0); cin.tie(0); cin >> n >> d >> mod; dp[0][0][0] = 1; for (int i = 1; i <= 1000; i++) iv[i] = inv(i, mod); for (int i = 1; i < 1002; i++) for (int j = 0; j <= d; j++) cs[0][j][i] = addm2(cs[0][j][i - 1], dp[0][j][i - 1]); for (int i = 1; i < n; i++) for (int j = 1; j <= d; j++) for (int k = 1; k < n; k++) { long long f = 1; for (int l = 1; l * k <= i && l <= j && (k == 1 || cs[k - 1][d - 1][k]); l++) { f = f * ((k == 1 ? 1 : cs[k - 1][d - 1][k]) + l - 1) % mod * iv[l] % mod; addm(cs[i][j][k + 1], (long long)cs[i - l * k][j - l][k] * f % mod); } addm(cs[i][j][k + 1], cs[i][j][k]); } int ans = cs[n - 1][d][(n + 1) / 2]; addm(ans, cs[n - 1][0][(n + 1) / 2]); if (n % 2 == 0) { long long v = cs[n / 2 - 1][d - 1][n / 2] + cs[n / 2 - 1][0][n / 2]; addm(ans, v * (v + 1) / 2 % mod); } if (ans < 0) ans += mod; cout << ans << endl; }
#include <bits/stdc++.h> using namespace std; long long n, d, P, inv[15], f[1100][15][1100]; long long C(long long n, long long m) { long long res = 1; for (long long i = n; i > n - m; i--) res = res * i % P; for (long long j = 1; j <= m; j++) res = res * inv[j] % P; return res; } signed main() { scanf("%lld %lld %lld", &n, &d, &P); if (n <= 2) return puts("1"), 0; inv[1] = 1; for (long long i = 2; i <= d; i++) inv[i] = (P - P / i) * inv[P % i] % P; for (long long i = 0; i <= n; i++) f[1][0][i] = 1; for (long long i = 2; i <= n; i++) for (long long j = 1; j <= min(d, i - 1); j++) for (long long k = 1; k <= n; k++) { f[i][j][k] = f[i][j][k - 1]; for (long long t = 1; t <= j && k * t <= i; t++) { if (k == 1) (f[i][j][k] += f[i - t * k][j - t][k - 1] * C(f[k][0][k - 1] + t - 1, t)) %= P; else (f[i][j][k] += f[i - t * k][j - t][k - 1] * C(f[k][d - 1][k - 1] + t - 1, t)) %= P; } } if (n & 1) printf("%lld\n", f[n][d][n / 2]); else printf("%lld\n", (f[n][d][n / 2] - C(f[n / 2][d - 1][n / 2 - 1], 2) + P) % P); return 0; }
#include <bits/stdc++.h> using namespace std; int Mod, inv[1005]; inline void add(int &x, int y) { if ((x += y) >= Mod) x -= Mod; if (x < 0) x += Mod; } inline int fp(int a, int k) { int res = 1; while (k) { if (k & 1) res = 1LL * res * a % Mod; a = 1LL * a * a % Mod; k >>= 1; } return res; } int dp[1005][15]; int main() { int n, d; scanf("%d%d%d", &n, &d, &Mod); if (n <= 2) return 0 * printf("1"); for (int i = 1; i <= n; i++) inv[i] = fp(i, Mod - 2); dp[1][0] = 1; int res = 0; for (int k = 1; k <= n; k++) for (int i = n; i >= 2; i--) for (int j = d; j >= 1; j--) { int sum = 0, now = 1, cnt = (k > 1 ? dp[k][d - 1] : 1); for (int t = 0; t <= j && t * k < i; t++) { add(sum, 1LL * now * dp[i - t * k][j - t] % Mod); now = 1LL * now * (cnt + t) % Mod * inv[t + 1] % Mod; } dp[i][j] = sum; if (k == n / 2 && i == n && j == d) add(res, dp[i][j]); } if (n % 2 == 0) add(res, -1LL * dp[n / 2][d - 1] * (dp[n / 2][d - 1] - 1) / 2 % Mod); printf("%d\n", res); return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 1e3 + 10; const int D = 11; int mod; long long mul(long long a, long long b) { return (a * b) % mod; } long long bin_pow(long long b, long long p) { long long res = 1; for (long long j = 1, pw = b; j <= p; j <<= 1, pw = mul(pw, pw)) if (p & j) res = mul(res, pw); return res; } long long inv(long long x) { return bin_pow(x, mod - 2); } long long nCr(long long n, long long r) { long long res = 1; for (int i = 0; i < r; i++) { res = mul(res, mul(n - i, inv(i + 1))); } return res; } long long dp[N][N][D]; long long ct[N][D]; int main() { ios::sync_with_stdio(0); cin.tie(0); cout.tie(0); int n, d; cin >> n >> d >> mod; if (n <= 2) return cout << "1\n", 0; fill(ct[1], ct[1] + D, 1); for (int i = 0; i < N; i++) dp[1][i][0] = 1; for (int i = 2; i <= n; i++) { for (int j = 1; j <= n; j++) { for (int k = 0; k <= d; k++) { dp[i][j][k] = dp[i][j - 1][k]; for (int cnt = 1; cnt <= k && cnt * j < i; cnt++) { dp[i][j][k] += dp[i - cnt * j][j - 1][k - cnt] * ct[j][cnt]; dp[i][j][k] %= mod; } } } ct[i][0] = 1; ct[i][1] = dp[i][i - 1][d - 1]; for (int j = 2; j <= d; j++) { ct[i][j] = nCr(ct[i][1] + j - 1, j); } } long long ans = dp[n][(n - 1) / 2][d]; if (n % 2 == 0) { long long x = dp[n / 2][(n / 2) - 1][d - 1]; ans += x; ans += mul(mul(x, x - 1), inv(2)); } cout << ans % mod << '\n'; return 0; }
#include <bits/stdc++.h> using namespace std; int n, d, modulo; int inv[99]; const int N(1111); int dp[N][N][15]; int f(int i, int j, int k) { if (dp[i][j][k] != -1) { return dp[i][j][k]; } else if (i == 0 && j == 0 && k == 0) { return 1; } else if (j == 0) { return 0; } else if (dp[i][j][k] != -1) { return dp[i][j][k]; } else { int& res(dp[i][j][k]); res = 0; int x(j == 1 ? 1 : f(j - 1, j - 1, d)); int lst(1); for (int o(0); o * j <= i && o <= k; o++) { res = (res + (long long)f(i - o * j, j - 1, k - o) * lst) % modulo; lst = (long long)lst * (x + o + modulo) % modulo * inv[o + 1] % modulo; } return res; } } int pw(int x, int n) { int res(1); while (n) { if (n & 1) { res = (long long)res * x % modulo; } x = (long long)x * x % modulo; n /= 2; } return res; } int main() { scanf("%d%d%d", &n, &d, &modulo); d--; if (d == 1 || n <= 2) { printf("1\n"); return 0; } for (int i(1); i <= d + 1; i++) { inv[i] = pw(i, modulo - 2); } memset(dp, -1, sizeof(dp)); dp[0][0][0] = 1; f(n - 1, n - 1, d + 1); for (int i(0); i <= n - 1; i++) { f(i, i, d + 1); f(i, i, d); } int ans(dp[n - 1][n - 1][d + 1]); dp[0][0][d] = 0; for (int i(1); i <= n - i; i++) { ans = (ans - (long long)dp[i - 1][i - 1][d] * dp[n - i - 1][n - i - 1][d] % modulo + modulo) % modulo; } if (n % 2 == 0) { ans = (ans + (long long)(dp[n / 2 - 1][n / 2 - 1][d]) * (dp[n / 2 - 1][n / 2 - 1][d] + 1) / 2) % modulo; } printf("%d\n", ans); }
#include <bits/stdc++.h> using namespace std; const int N = 1005, maxn = 15; int n, d, mod; long long ans, fac[maxn], inv[maxn], f[N][maxn][N]; long long fpow(long long a, long long b) { long long res = 1; while (b) { if (b & 1) { res = (res * a) % mod; } a = (a * a) % mod; b >>= 1; } return res % mod; } inline long long C(int n, int m) { if (n < m || n < 0 || m < 0) { return 0; } long long res = 1; for (int i = n; i >= n - m + 1; i--) { res = (res * i) % mod; } return (res * inv[m]) % mod; } int main() { scanf("%d%d%d", &n, &d, &mod); if (n <= 2) { printf("1\n"); return 0; } fac[0] = inv[0] = 1; for (int i = 1; i <= d; i++) { fac[i] = (fac[i - 1] * i) % mod; inv[i] = fpow(fac[i], mod - 2); } for (int k = 0; k <= n / 2; k++) { f[1][0][k] = 1; } for (int i = 2; i <= n; i++) { for (int j = 1; j <= min(i - 1, d); j++) { for (int k = 1; k <= n / 2; k++) { f[i][j][k] = f[i][j][k - 1]; for (int t = 1; t <= j && t * k < i; t++) { if (k == 1) { f[i][j][k] = (f[i][j][k] + C(f[k][0][k - 1] + t - 1, t) * f[i - t * k][j - t][k - 1] % mod) % mod; } else { f[i][j][k] = (f[i][j][k] + C(f[k][d - 1][k - 1] + t - 1, t) * f[i - t * k][j - t][k - 1] % mod) % mod; } } } } } if (n & 1) { ans = f[n][d][n / 2]; } else { ans = (f[n][d][n / 2] - C(f[n / 2][d - 1][n / 2 - 1], 2) + mod) % mod; } printf("%lld\n", ans); return 0; }
#include <bits/stdc++.h> using namespace std; inline long long read() { long long x = 0, f = 1; char ch = getchar(); while (ch < '0' || ch > '9') { if (ch == '-') f = -1; ch = getchar(); } while (ch >= '0' && ch <= '9') { x = x * 10 + (ch ^ 48); ch = getchar(); } return x * f; } const long long N = 1010; long long n, d, mod, f[N][11][N >> 1], fac[N], inv[N]; inline long long fpow(long long x, long long p) { long long ans = 1; for (; p; p >>= 1, x = x * x % mod) if (p & 1) ans = ans * x % mod; return ans; } inline void initfac(long long n) { fac[0] = 1; for (long long i = 1; i <= n; ++i) fac[i] = fac[i - 1] * i % mod; inv[n] = fpow(fac[n], mod - 2); for (long long i = n - 1; ~i; --i) inv[i] = inv[i + 1] * (i + 1) % mod; } inline long long C(long long n, long long m) { if (n < m) return 0; long long ans = 1; for (long long i = n; i >= n - m + 1; --i) ans = ans * i % mod; return ans * inv[m] % mod; } signed main() { n = read(); d = read(); mod = read(); if (n <= 2) return puts("1") & 0; initfac(N - 10); for (long long i = 0; i <= n / 2; ++i) f[1][0][i] = 1; f[1][d - 1][0] = 1; for (long long i = 2; i <= n; ++i) { for (long long j = 1; j <= min(d, i - 1); ++j) { for (long long k = 1; k <= n / 2; ++k) { f[i][j][k] = f[i][j][k - 1]; for (long long l = 1; l * k <= i && l <= j; ++l) { f[i][j][k] = (f[i][j][k] + f[i - l * k][j - l][k - 1] * C(f[k][d - 1][k - 1] + l - 1, l) % mod) % mod; } } } } if (n & 1) return printf("%lld", f[n][d][n / 2]) & 0; return printf( "%lld", (f[n][d][n / 2] - C(f[n / 2][d - 1][n / 2 - 1], 2) + mod) % mod) & 0; }
#include <bits/stdc++.h> int md; int vv[10 + 1]; void init() { int i; for (i = 1; i <= 10; i++) vv[i] = i == 1 ? 1 : (long long)vv[i - md % i] * (md / i + 1) % md; } int main() { static int dp[1000 + 1], dq[1000 + 1]; int n, d, i, j, k, ans; scanf("%d%d%d", &n, &d, &md), init(); if (n == 1 || d == 2) { printf("1\n"); return 0; } if ((n - 1) % (d - 1) != 1) { printf("0\n"); return 0; } dp[1] = 1, dq[1] = 1; for (i = 1; i * 2 < n; i++) { int x = dp[i]; if (i % (d - 1) != 1 || x == 0) continue; for (j = n / 2 - 1; j > 0; j--) { int y = dp[j], z = 1, k_ = (j - 2) % (d - 1) + 1; for (k = 1; (j + i * k) * 2 <= n && k_ + k < d && z != 0; k++) { z = (long long)z * (x + k - 1) % md * vv[k] % md; dp[j + i * k] = (dp[j + i * k] + (long long)y * z) % md; } } for (j = n - 1; j > 0; j--) { int y = dq[j], z = 1, k_ = (j - 2) % (d - 1) + 1; for (k = 1; j + i * k <= n && (k_ + k < d || k_ + k == d && j + i * k == n) && z != 0; k++) { z = (long long)z * (x + k - 1) % md * vv[k] % md; dq[j + i * k] = (dq[j + i * k] + (long long)y * z) % md; } } } ans = dq[n]; if (n % 2 == 0 && n / 2 % (d - 1) == 1) ans = (ans + (long long)dp[n / 2] * (dp[n / 2] + 1) % md * vv[2]) % md; printf("%d\n", ans); return 0; }
#include <bits/stdc++.h> using namespace std; int n, d, mod; int f[1010][11][1010], g[1010][11], iv[11]; inline int add(int a, int b) { if ((a += b) >= mod) a -= mod; return a; } inline int mult(int a, int b) { long long t = 1ll * a * b; if (t >= mod) t %= mod; return t; } inline int power(int a, int b) { int out = 1; while (b) { if (b & 1) out = mult(out, a); a = mult(a, a); b >>= 1; } return out; } int main() { scanf("%d%d%d", &n, &d, &mod); for (int i = 0; i <= n; i++) f[1][0][i] = 1; for (int i = 1; i <= d; i++) g[1][i] = 1; for (int i = 1; i <= d; i++) iv[i] = power(i, mod - 2); for (int i = 2; i <= n; i++) { for (int j = 1; j <= d; j++) { for (int k = 1; k < i; k++) { for (int l = 1; l <= j && l * k <= i; l++) { f[i][j][k] = add(f[i][j][k], mult(f[i - l * k][j - l][k - 1], g[k][l])); } } for (int k = 1; k <= n; k++) f[i][j][k] = add(f[i][j][k], f[i][j][k - 1]); } g[i][1] = f[i][d - 1][n]; for (int j = 2; j <= d; j++) g[i][j] = mult(mult(g[i][j - 1], (f[i][d - 1][n] + j - 1)), iv[j]); } int ans; if (n <= 2) ans = 1; else ans = f[n][d][n / 2]; if (n > 2 && !(n & 1)) ans = (ans - mult(mult((f[n / 2][d - 1][n / 2] - 1), f[n / 2][d - 1][n / 2]), iv[2]) + mod) % mod; printf("%d\n", ans); return 0; }
#include <bits/stdc++.h> using namespace std; const int maxn = 2010; int n, m, mod; int inv[maxn], f[maxn][12][maxn >> 1]; inline void read(int &k) { int f = 1; k = 0; char c = getchar(); while (c < '0' || c > '9') c == '-' && (f = -1), c = getchar(); while (c <= '9' && c >= '0') k = k * 10 + c - '0', c = getchar(); k *= f; } inline int power(int a, int b) { int ans = 1; for (; b; b >>= 1, a = 1ll * a * a % mod) if (b & 1) ans = 1ll * ans * a % mod; return ans; } int main() { read(n); read(m); read(mod); if (n <= 2) return puts("1"), 0; for (int i = 1; i <= n; i++) inv[i] = power(i, mod - 2); for (int i = 0; i <= n / 2; i++) f[1][0][i] = 1; for (int i = 2; i <= n; i++) { for (int j = 1; j <= m; j++) { for (int k = 1; k <= n / 2; k++) { f[i][j][k] = f[i][j][k - 1]; for (int l = 1, tmp = 1; l <= j && k * l <= i; l++) { tmp = 1ll * tmp * (f[k][(k == 1) ? 0 : m - 1][k - 1] + l - 1) % mod * inv[l] % mod; f[i][j][k] = (f[i][j][k] + 1ll * f[i - k * l][j - l][k - 1] * tmp) % mod; } } } } int ans = f[n][m][n >> 1]; if ((n & 1) == 0) { int t = f[n >> 1][m - 1][(n >> 1) - 1]; ans = (ans - 1ll * t * (t - 1) / 2 % mod + mod) % mod; } printf("%d\n", ans); }
#include <bits/stdc++.h> using namespace std; inline void rd(int &x) { char ch; x = 0; bool fl = false; while (!isdigit(ch = getchar())) (ch == '-') && (fl = true); for (x = (ch ^ '0'); isdigit(ch = getchar()); x = x * 10 + (ch ^ '0')) ; (fl == true) && (x = -x); } namespace Miracle { const int N = 1005; int mod, n, d; int f[N][11][N]; int jie[11], inv[11]; int qm(int x, int y) { int ret = 1; while (y) { if (y & 1) ret = (long long)ret * x % mod; x = (long long)x * x % mod; y >>= 1; } return ret; } int dp(int i, int j, int k) { if (f[i][j][k] != -1) return f[i][j][k]; if (i == 1) { if (j == 0) return f[i][j][k] = 1; else if (k == 0) return f[i][j][k] = 1; return f[i][j][k] = 0; } if (i == 0) { if (k == 0 && j == 0) return f[i][j][k] = 1; else return f[i][j][k] = 0; } if (j > i - 1) return f[i][j][k] = 0; if (i > 1 && k == 0) return f[i][j][k] = 0; int C = 1; int ret = 0; int tmp = dp(k, d - 1, k - 1); for (register int m = 0; m <= j && m * k <= i - 1; ++m) { ret = (ret + (long long)dp(i - m * k, j - m, k - 1) * C % mod * inv[m] % mod) % mod; C = (long long)C * (tmp - 1 + m + 1) % mod; } return f[i][j][k] = ret; } int main() { rd(n); rd(d); rd(mod); if (n <= 2) { puts("1"); return 0; } memset(f, -1, sizeof f); jie[0] = 1; for (register int i = 1; i <= 10; ++i) jie[i] = (long long)jie[i - 1] * i % mod; inv[10] = qm(jie[10], mod - 2); for (register int i = 9; i >= 0; --i) inv[i] = (long long)inv[i + 1] * (i + 1) % mod; long long ans = 0; ans = (ans + dp(n, d, (n - 1) / 2)); if (n % 2 == 0) { long long tmp = 0; tmp = dp(n / 2, d - 1, n / 2 - 1); ans = (ans + (tmp * (tmp + 1) / 2 % mod)) % mod; } printf("%I64d", ans); return 0; } } // namespace Miracle signed main() { Miracle::main(); return 0; }
#include <bits/stdc++.h> int f[1005][11][1005], g[1005][11], ine[11], n, d, mo; int inv(int x) { int i = 1, y = mo - 2; for (; y; y >>= 1, x = 1ll * x * x % mo) if (y & 1) i = 1ll * i * x % mo; return i; } int main() { scanf("%d%d%d\n", &n, &d, &mo); for (int i = 0; i <= n; i++) f[1][0][i] = 1; for (int i = 1; i <= d; i++) g[1][i] = 1; for (int i = 1; i <= d; i++) ine[i] = inv(i); for (int i = 2; i <= n; i++) { for (int j = 1; j <= d; j++) { for (int k = 1; k < i; k++) for (int l = 1; l <= j && l * k <= i; l++) f[i][j][k] = (f[i][j][k] + 1ll * f[i - l * k][j - l][k - 1] * g[k][l]) % mo; for (int k = 1; k <= n; k++) f[i][j][k] = (f[i][j][k] + f[i][j][k - 1]) % mo; } g[i][1] = f[i][d - 1][n]; for (int j = 2; j <= d; j++) g[i][j] = 1ll * g[i][j - 1] * (f[i][d - 1][n] + j - 1) % mo * ine[j] % mo; } int ans; if (n <= 2) ans = 1; else ans = f[n][d][n / 2]; if (n > 2 && !(n & 1)) ans = (ans - 1ll * (f[n / 2][d - 1][n / 2] - 1) * f[n / 2][d - 1][n / 2] % mo * ine[2] % mo + mo) % mo; printf("%d\n", ans); }
#include <bits/stdc++.h> int mod, inv[10 + 1], dp[1000 + 1], d[1000 + 1][1000 + 1][10 + 1]; inline int lgput(int a, int n) { int r = 1; while (n) { if (n % 2) r = 1LL * r * a % mod; n /= 2; a = 1LL * a * a % mod; } return r; } int main() { int n, D; fscanf(stdin, "%d%d%d", &n, &D, &mod); if (D == 2 || n <= 2) { fprintf(stdout, "1\n"); return 0; } for (int i = 1; i <= D; i++) inv[i] = lgput(i, mod - 2); for (int j = 0; j <= n; j++) d[1][j][0] = 1; dp[1] = 1; for (int i = 2; i <= n; i++) { for (int j = 1; j <= n; j++) { for (int g = 0; g <= D; g++) { d[i][j][g] = d[i][j - 1][g]; int r = 1; for (int p = 1; p <= g && i - p * j > 0; p++) { r = 1LL * r * (dp[j] + p - 1) % mod * inv[p] % mod; d[i][j][g] = (d[i][j][g] + 1LL * r * d[i - p * j][j - 1][g - p]) % mod; } } } dp[i] = d[i][n][D - 1]; } int ans = d[n][(n - 1) / 2][D]; if (n % 2 == 0) ans = (ans + 1LL * d[n / 2][n][D - 1] * (d[n / 2][n][D - 1] + 1) / 2) % mod; fprintf(stdout, "%d\n", ans); fclose(stdin); fclose(stdout); return 0; }
#include <bits/stdc++.h> using namespace std; const double pi = acos(-1.0); const int N = 1005; int P; inline int Pow(int a, int b) { int c = 1; for (; b; b >>= 1, a = a * 1ll * a % P) if (b & 1) c = c * 1ll * a % P; return c; } inline void add(int &a, int b) { a += b; if (a >= P) a -= P; } inline void dec(int &a, int b) { a -= b; if (a < 0) a += P; } int n, d; int fac[N], inv[N]; int f[N][11]; int ji(int a, int b) { int res = 1; for (int i = (int)0; i <= (int)b - 1; i++) res = res * 1ll * (a + i) % P; return res; } int main() { scanf("%d%d%d", &n, &d, &P); if (n <= 2) { printf("1"); return 0; } fac[0] = 1; for (int i = (int)1; i <= (int)n; i++) fac[i] = fac[i - 1] * 1ll * i % P; inv[n] = Pow(fac[n], P - 2); for (int i = (int)n - 1; i >= (int)0; i--) inv[i] = inv[i + 1] * 1ll * (i + 1) % P; for (int k = (int)0; k <= (int)d; k++) f[1 + k][k] = 1; for (int i = (int)1; i <= (int)(n - 1) / 2; i++) { int way = f[i][d - 1]; for (int j = (int)n; j >= (int)1; j--) for (int k = (int)0; k <= (int)d - 1; k++) if (f[j][k]) { int rest = n - j; int dd = way; for (int use = (int)1; use <= (int)rest / i; use++) { if (k + use > d) break; add(f[j + use * i][k + use], (f[j][k] * 1ll * dd % P) * 1ll * inv[use] % P); dd = dd * 1ll * (way + use) % P; } } } if (n % 2 == 0) { int ans = f[n / 2][d - 1]; add(ans, (f[n / 2][d - 1] * 1ll * (f[n / 2][d - 1] - 1) / 2) % P); add(ans, f[n][d]); printf("%d\n", ans); } else { printf("%d\n", f[n][d]); } return 0; }
#include <bits/stdc++.h> using namespace std; inline int read() { int t = 1, sum = 0; char ch = getchar(); while (ch < '0' || ch > '9') { if (ch == '-') t = -1; ch = getchar(); } while (ch >= '0' && ch <= '9') sum = sum * 10 + ch - '0', ch = getchar(); return t * sum; } const int Max = 1e3 + 10; int g[Max], f[Max][15], inv[Max], n, d, mod, ans; void get_ready() { inv[0] = inv[1] = true; int i; for (i = 2; i <= n; i++) inv[i] = 1LL * (mod - mod / i) * inv[mod % i] % mod; for (i = 1; i <= n; i++) inv[i] = 1LL * inv[i - 1] * inv[i] % mod; } inline void up(int &x, int y) { x += y; if (x >= mod) x -= mod; } void solve() { int i, j, k, l, w; g[1] = 1; f[0][0] = 1; for (i = 1; i <= n / 2; i++) { for (j = n - i; ~j; j--) for (k = 0; k < d; k++) if (f[j][k]) for (w = 1, l = 1; k + l <= d && j + i * l <= n; l++) w = 1LL * w * (g[i] + l - 1) % mod, up(f[j + i * l][k + l], 1LL * f[j][k] * w % mod * inv[l] % mod); g[i + 1] = f[i][d - 1]; } ans = f[n - 1][d]; if (!(n & 1)) up(ans, mod - 1LL * g[n >> 1] * (g[n >> 1] - 1) / 2 % mod); printf("%d\n", ans); } int main() { n = read(); d = read(); mod = read(); if (n <= 2) return printf("1\n"), 0; if ((n - 2) % (d - 1) != 0) return printf("0\n"), 0; get_ready(); solve(); return 0; }
#include <bits/stdc++.h> using namespace std; bool debug = 0; int n, m, k; int dx[4] = {0, 1, 0, -1}, dy[4] = {1, 0, -1, 0}; string direc = "RDLU"; long long ln, lk, lm; void etp(bool f = 0) { puts(f ? "YES" : "NO"); exit(0); } void addmod(int &x, int y, int mod = 1000000007) { x += y; if (x >= mod) x -= mod; assert(x >= 0 && x < mod); } void et() { puts("-1"); exit(0); } long long fastPow(long long x, long long y, int mod = 1000000007) { long long ans = 1; while (y > 0) { if (y & 1) ans = (x * ans) % mod; x = x * x % mod; y >>= 1; } return ans; } int mod, d; int dp[1005][12][1005]; int inv[20]; void fmain() { scanf("%d%d%d", &n, &d, &mod); dp[1][0][0] = 1; dp[1][d - 1][0] = 1; inv[0] = 1; for (int(i) = 1; (i) <= (int)(15); (i)++) inv[i] = fastPow(i, mod - 2, mod); if (n <= 2) { puts("1"); return; } for (int i = 2; i <= n; i++) { for (int j = 1; j <= d; j++) { for (int k = 1; k < i; k++) { dp[i][j][k] = dp[i][j][k - 1]; int r = dp[k][d - 1][k - 1] - 1, c = 1; for (int t = 1; t * k < i && t <= j; t++) { int z = dp[i - t * k][j - t][min(k - 1, i - t * k - 1)]; c = (long long)c * (++r) % mod * inv[t] % mod; addmod(dp[i][j][k], (long long)z * c % mod, mod); } } } } int ans = dp[n][d][(n + 1) / 2 - 1]; if (n % 2 == 0) { addmod(ans, (long long)dp[n / 2][d - 1][n / 2 - 1] * (dp[n / 2][d - 1][n / 2 - 1] + 1) / 2 % mod, mod); } printf("%d\n", ans); } int main() { int t = 1; for (int(i) = 1; (i) <= (int)(t); (i)++) { fmain(); } return 0; }
#include <bits/stdc++.h> using namespace std; long long n, d, mod, dp[((long long)1010)][((long long)1010)][((long long)11)], tvn[((long long)11)]; long long tavan(long long x, long long y) { long long res = 1; while (y) { res *= (y % 2) ? x : 1; res %= mod; x *= x; x %= mod; y /= 2; } return res; } long long C(long long x, long long y) { if (x < y) return 0; long long res = 1; for (long long i = x; i > x - y; i--) res *= i, res %= mod; for (long long i = 1; i <= y; i++) res *= tvn[i], res %= mod; return res; } int main() { ios_base::sync_with_stdio(0); cin.tie(0); cin >> n >> d >> mod; for (int i = 1; i < ((long long)11); i++) tvn[i] = tavan(i, mod - 2); if (n <= 2) return cout << "1\n", 0; dp[1][0][d - 1] = dp[1][0][0] = 1; for (int i = 2; i <= n; i++) for (int j = 1; j <= i - 1; j++) for (int k = 1; k <= d; k++) { dp[i][j][k] = dp[i][j - 1][k]; for (int p = 1; p * j <= i - 1 && p <= k; p++) if (i - p * j != 1 || min(j - 1, i - p * j - 1) != 0 || k - p != d - 1) dp[i][j][k] += (dp[i - p * j][min(j - 1, i - p * j - 1)][k - p] * C(dp[j][j - 1][d - 1] + p - 1, p)) % mod, dp[i][j][k] %= mod; } long long res = dp[n][n / 2][d]; if (n % 2 == 0) res -= C(dp[n / 2][n / 2 - 1][d - 1], 2), res %= mod, res += mod, res %= mod; cout << res << "\n"; ; return 0; }
#include <bits/stdc++.h> using namespace std; char c; inline void read(long long& a) { a = 0; do c = getchar(); while (c < '0' || c > '9'); while (c <= '9' && c >= '0') a = (a << 3) + (a << 1) + c - '0', c = getchar(); } long long n, d, Mod, F[1001], G[11][1001], Rev[10]; inline long long C(long long x, long long y) { long long r = Rev[y]; for (long long i = x; i < x + y; i++) r = r * i % Mod; return r; } int main() { read(n), read(d), read(Mod); if (n == 1) return puts("1"), 0; if ((n - 2) % (d - 1)) return puts("0"), 0; n = (n - 2) / (d - 1); Rev[0] = Rev[1] = 1; for (int i = 2; i <= d; i++) Rev[i] = (Mod - Mod / i) * Rev[Mod % i] % Mod; for (int i = 2; i <= d; i++) Rev[i] = Rev[i] * Rev[i - 1] % Mod; F[0] = 1; for (int i = 0; i <= d; i++) G[i][0] = 1; for (int i = 1; i <= n >> 1; i++) { F[i] = G[d - 1][i - 1]; if (i + i < n) for (int j = d; j; j--) for (int l = i; l <= n; l++) for (int k = 1; k <= j && i * k <= l; k++) G[j][l] = (G[j][l] + G[j - k][l - i * k] * C(F[i], k)) % Mod; } cout << (G[d][n - 1] + (n & 1 ? 0 : C(F[n >> 1], 2))) % Mod << endl; return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 1e3 + 7; const int D = 12; int MOD; int f[N][D], g[N]; int n, d, rev[N]; int power(int a, int n) { int ret = 1; for (int i = 1; i <= n; i <<= 1) { if (n & i) { ret = 1LL * ret * a % MOD; } a = 1LL * a * a % MOD; } return ret; } void add(int &a, int b) { if ((a += b) >= MOD) { a -= MOD; } } int comb(int n, int m) { assert(n <= MOD && m <= MOD); int ret = 1; for (int i = 1; i <= m; i++) { ret = 1LL * ret * ((n - i + 1 + MOD) % MOD) % MOD; ret = 1LL * ret * rev[i] % MOD; } return ret; } int main() { scanf("%d %d %d", &n, &d, &MOD); if (n <= 2) { printf("1\n"); return 0; } rev[0] = 1; for (int i = 1; i <= d; i++) { rev[i] = power(i, MOD - 2) % MOD; } f[1][0] = 1; for (int i = 1; i <= n / 2; i++) { if (i == 1) { g[1] = 1; } else { g[i] = f[i][d - 1]; } if (g[i] == 0) continue; if ((i - 1) % (d - 1) != 0) assert(g[i] == 0); for (int j = n; j >= 1; j--) { for (int k = 0; k <= d; k++) { if (f[j][k] == 0) { continue; } for (int l = 1; k + l <= d && j + l * i <= n; l++) { add(f[j + l * i][k + l], 1LL * f[j][k] * comb(g[i] + l - 1, l) % MOD); } } } } int ans = f[n][d]; if (n % 2 == 0) { ans += MOD - comb(f[n / 2][d - 1], 2); ans %= MOD; } printf("%d\n", ans); return 0; }
#include <bits/stdc++.h> const int MAXN = 1026; std::map<std::pair<long long, long long>, long long> M; long long MOD; long long qpow(long long a, long long p) { long long ans = 1; while (p > 0) { if (p & 1) ans = (ans * a) % MOD; a = a * a % MOD; p >>= 1; } return ans; } int N, D; long long dp[MAXN][11][MAXN]; long long inv[200]; long long C(long long n, long long k) { std::map<std::pair<long long, long long>, long long>::iterator it = M.find(std::pair<long long, long long>(n, k)); if (it != M.end()) return it->second; n %= MOD; long long ans = 1; for (long long i = 0; i < k; i++) { ans = (ans * (n - i + MOD)) % MOD; } ans = ans * inv[k] % MOD; return M[std::pair<long long, long long>(n, k)] = ans; } int main() { std::cin >> N >> D >> MOD; if (N == 1) { puts("1"); return 0; } inv[0] = 1; for (int i = 1; i <= 20; i++) { inv[i] = inv[i - 1] * qpow(i, MOD - 2) % MOD; } for (int i = 0; i <= N; i++) { dp[1][D - 1][i] = 1; dp[1][0][i] = 1; } for (int i = 2; i <= N; i++) { for (int j = 1; j <= D; j++) { for (int k = 1; k <= N; k++) { dp[i][j][k] = dp[i][j][k - 1]; for (int t = 1; t * k <= i && t <= j; t++) { dp[i][j][k] += dp[i - k * t][j - t][k - 1] * C(dp[k][D - 1][k - 1] + t - 1, t) % MOD; if (dp[i][j][k] >= MOD) dp[i][j][k] -= MOD; } } } } long long ans = dp[N][D][(N + 1) / 2 - 1]; long long x = dp[N / 2][D - 1][N / 2 - 1]; if (N % 2 == 0) ans += (x * x % MOD + x) % MOD * inv[2] % MOD; ans %= MOD; std::cout << ans << std::endl; return 0; }
#include <bits/stdc++.h> const int MAXN = 1000, MAXD = 20; int n, d, Mod; int Add(int x, int y) { x += y; return x >= Mod ? x - Mod : x; } int Sub(int x, int y) { x -= y; return x < 0 ? x + Mod : x; } int Quick_pow(int x, int po) { int Ans = 1; for (; po; po >>= 1, x = 1ll * x * x % Mod) if (po & 1) Ans = 1ll * Ans * x % Mod; return Ans; } int Inverse(int x) { return Quick_pow(x, Mod - 2); } int Fac[MAXD + 5], Inv[MAXD + 5]; void Init() { Fac[0] = 1; for (int i = 1; i <= MAXD; i++) Fac[i] = 1ll * Fac[i - 1] * i % Mod; Inv[MAXD] = Inverse(Fac[MAXD]); for (int i = MAXD; i >= 1; i--) Inv[i - 1] = 1ll * Inv[i] * i % Mod; } int C(int n, int m) { int Ans = 1; for (int i = n; i >= n - m + 1; i--) Ans = 1ll * Ans * i % Mod; return 1ll * Ans * Inv[m] % Mod; } int dp[MAXN + 5][MAXD + 1][MAXN / 2 + 5]; int dfs(int Sz, int nowd, int MaxSz) { if (dp[Sz][nowd][MaxSz] != -1) return dp[Sz][nowd][MaxSz]; if (Sz == 1) return dp[Sz][nowd][MaxSz] = nowd == 0; if (MaxSz == 1) return dp[Sz][nowd][MaxSz] = Sz == nowd + 1; if (!nowd || !MaxSz || nowd >= Sz) return dp[Sz][nowd][MaxSz] = 0; int Ans = 0; for (int t = 0; t * MaxSz < Sz && t <= nowd; t++) Ans = Add(Ans, 1ll * C(dfs(MaxSz, d - 1, MaxSz - 1) + t - 1, t) * dfs(Sz - t * MaxSz, nowd - t, MaxSz - 1) % Mod); return dp[Sz][nowd][MaxSz] = Ans; } int main() { scanf("%d %d %d", &n, &d, &Mod); if (n == 1 || n == 2) return printf("1\n") & 0; Init(); memset(dp, -1, sizeof(dp)); if (n & 1) printf("%d\n", dfs(n, d, n / 2)); else printf("%d\n", Sub(dfs(n, d, n / 2), C(dfs(n / 2, d - 1, n / 2 - 1), 2))); return 0; }
#include <bits/stdc++.h> using namespace std; int n, m, mod; inline int mul(int x, int y) { return (long long)x * y % mod; } inline void add(int &x, int y) { y += x; x = y >= mod ? y - mod : y; } inline int inc(int x, int y) { x += y; return x >= mod ? x - mod : x; } inline int qpow(int x, int y) { int res = 1; for (; y; y >>= 1, x = mul(x, x)) if (y & 1) res = mul(res, x); return res; } const int maxn = 1005; int f[maxn][12][maxn >> 1], inv[maxn]; int main() { cin >> n >> m >> mod; if (n <= 2) return puts("1"), 0; for (int i = 1; i <= n; i++) inv[i] = qpow(i, mod - 2); for (int i = 0; i <= n / 2; i++) f[1][0][i] = 1; for (int i = 2; i <= n; i++) for (int j = 1; j <= m; j++) for (int k = 1; k <= n / 2; k++) { f[i][j][k] = f[i][j][k - 1]; for (int l = 1, coef = 1; l <= j && k * l <= i; l++) { coef = mul(coef, mul(f[k][k == 1 ? 0 : m - 1][k - 1] + l - 1, inv[l])); add(f[i][j][k], mul(f[i - l * k][j - l][k - 1], coef)); } } int ans = f[n][m][n >> 1]; if (!(n & 1)) { int v = f[n >> 1][m - 1][(n >> 1) - 1]; add(ans, mod - (long long)v * (v - 1) / 2ll % mod); } printf("%d\n", ans); return 0; }
#include <bits/stdc++.h> using namespace std; const int MAXN = 1010; const int MAXD = 22; int n, d, mod; long long dp[MAXN][MAXD][MAXN], inv[MAXD]; long long quick_pow(long long a, long long b) { long long ret = 1; while (b) { if (b & 1) ret = ret * a % mod; a = a * a % mod; b >>= 1; } return ret; } long long DFS(int n, int m, int k) { k = min(k, n - 1); long long& ret = dp[n][m][k]; if (~ret) return ret; if ((n == 1 && m == 0) || (n == 1 && m == d - 1)) return ret = 1; if (n == 1 || k == 0) return ret = 0; ret = DFS(n, m, k - 1); long long t = DFS(k, d - 1, k), tmp = 1; for (int i = 1; i * k < n && i <= m; ++i) { tmp = tmp * (i + t - 1) % mod * inv[i] % mod; ret = (ret + tmp * DFS(n - i * k, m - i, k - 1)) % mod; } return ret; } int main() { scanf("%d%d%d", &n, &d, &mod); inv[0] = inv[1] = 1; for (int i = 2; i < MAXD; ++i) inv[i] = quick_pow(i, mod - 2); memset(dp, -1, sizeof(dp)); if (n == 1 || n == 2) { puts("1"); return 0; } if ((n - 2) % (d - 1)) { puts("0"); return 0; } long long ans = DFS(n, d, n / 2); if (n % 2 == 0) { long long b = DFS(n / 2, d - 1, n / 2); ans = ((ans - (b - 1) * b / 2) % mod + mod) % mod; } printf("%I64d\n", ans); return 0; }
#include <bits/stdc++.h> using namespace std; template <typename T> void read(T &x) { x = 0; bool f = 0; char c = getchar(); for (; !isdigit(c); c = getchar()) if (c == '-') f = 1; for (; isdigit(c); c = getchar()) x = x * 10 + (c ^ 48); if (f) x = -x; } template <typename F> inline void write(F x, char ed = '\n') { static short st[30]; short tp = 0; if (x < 0) putchar('-'), x = -x; do st[++tp] = x % 10, x /= 10; while (x); while (tp) putchar('0' | st[tp--]); putchar(ed); } template <typename T> inline void Mx(T &x, T y) { x < y && (x = y); } template <typename T> inline void Mn(T &x, T y) { x > y && (x = y); } const int N = 1050; int n, d, P; long long inv[N], dp[N]; long long C(long long n, int m) { long long res = inv[m]; while (m) res = res * n % P, --n, --m; return res; } long long f[12][N][N]; int main() { read(n), read(d), read(P); if (n == 1 || n == 2) return write(1), 0; inv[0] = inv[1] = dp[1] = 1; for (int i = 2; i <= d; i++) inv[i] = (P - P / i) * inv[P % i] % P; for (int i = 2; i <= d; i++) inv[i] = inv[i - 1] * inv[i] % P; for (int i = 0; i <= n; i++) f[0][1][i] = 1; for (int i = 2; i <= n; i++) { int lim = min(d, i - 1); for (int j = 1; j <= lim; j++) { f[j][i][1] = i == j + 1; for (int k = 2; k + k <= n; k++) { f[j][i][k] = f[j][i][k - 1]; for (int t = 1; t <= j && t * k < i; t++) f[j][i][k] = (f[j][i][k] + f[j - t][i - t * k][k - 1] * C(dp[k] + t - 1, t) % P) % P; } } dp[i] = f[d - 1][i][i - 1]; } long long ans = 0; if (n & 1) ans = f[d][n][n / 2]; else ans = (f[d][n][n / 2 - 1] + C(dp[n / 2] + 1, 2)) % P; write(ans); return 0; }
#include <bits/stdc++.h> using namespace std; long long read() { char c = getchar(); long long flag = 1, ans = 0; while (c < '0' || c > '9') { if (c == '-') flag = -flag; c = getchar(); } while (c >= '0' && c <= '9') { ans = ans * 10 + c - '0'; c = getchar(); } return ans * flag; } const long long MAXN = 1005; long long dp[MAXN][12][MAXN], inv[MAXN], fac[MAXN]; long long n, d, mod; inline long long add(long long a, long long b) { return (a + b >= mod) ? (a + b - mod) : (a + b); } inline long long sub(long long a, long long b) { return (a < b) ? (a + mod - b) : (a - b); } inline long long mul(long long a, long long b) { return a * b % mod; } long long qpow(long long b, long long k) { long long ans = 1; while (k) { if (k & 1) ans = mul(ans, b); b = mul(b, b); k >>= 1; } return ans; } void init() { fac[0] = 1; for (long long i = 1; i <= n; ++i) fac[i] = mul(fac[i - 1], i); inv[n] = qpow(fac[n], mod - 2); for (long long i = n - 1; i + 1; --i) inv[i] = mul(inv[i + 1], i + 1); } long long C(long long n, long long m) { if (n < 0 || m < 0 || n < m) return 0; long long ans = 1; for (long long i = 0; i < m; ++i) ans = mul(ans, (n - i)); return mul(ans, inv[m]); } int main() { n = read(), d = read(), mod = read(); if (n <= 2) { puts("1"); return 0; } init(); for (long long i = 0; i <= n; ++i) dp[1][0][i] = 1ll; for (long long i = 2; i <= n; ++i) for (long long j = 1; j <= min(d, i - 1); ++j) for (long long k = 1; k <= n; ++k) { dp[i][j][k] = dp[i][j][k - 1]; for (long long t = 1; t <= j && t * k <= i; ++t) dp[i][j][k] = add(dp[i][j][k], mul(C(dp[k][(k > 1) ? (d - 1) : 0][k - 1] + t - 1, t), dp[i - t * k][j - t][k - 1])); } long long ans = dp[n][d][n / 2]; if (!(n & 1)) ans = sub(ans, C(dp[n / 2][d - 1][n / 2 - 1], 2)); printf("%lld\n", ans); return 0; }
#include <bits/stdc++.h> using namespace std; int fac[1010], inv[1010], mod; int ksm(int a, int b = mod - 2) { int r = 1; for (; b; b >>= 1) { if (b & 1) r = 1ll * r * a % mod; a = 1ll * a * a % mod; } return r; } int C(int a, int b) { int r = inv[b]; for (b--; b >= 0; b--) r = 1ll * r * (a - b) % mod; return r; } int f[1010][12][1010]; int main() { int n, d; scanf("%d%d%d", &n, &d, &mod); if (n <= 2) { puts("1"); return 0; } fac[0] = 1; for (int i = 1; i <= n; i++) fac[i] = 1ll * fac[i - 1] * i % mod; inv[n] = ksm(fac[n]); for (int i = n - 1; i >= 0; i--) inv[i] = 1ll * inv[i + 1] * (i + 1) % mod; for (int i = 0; i <= n; i++) f[1][0][i] = 1; for (int i = 2; i <= n; i++) for (int j = 1; j <= min(d, i - 1); j++) for (int k = 1; k <= n; k++) { f[i][j][k] = f[i][j][k - 1]; for (int t = 1; t * k <= i && t <= j; t++) f[i][j][k] = (f[i][j][k] + 1ll * f[i - t * k][j - t][k - 1] * (k == 1 ? 1 : C(f[k][d - 1][k - 1] + t - 1, t)) % mod) % mod; } printf("%d\n", (f[n][d][n / 2] - ((n & 1) ? 0 : C(f[n / 2][d - 1][n / 2 - 1], 2)) + mod) % mod); return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 1010, M = 15; int n, d, mod, f[N][M][N], inv[M], ans; void upd(int &x, int y) { x += y; x -= x >= mod ? mod : 0; } int ksm(int x, int y) { int s = 1; for (; y; y >>= 1, x = (long long)x * x % mod) if (y & 1) s = (long long)s * x % mod; return s; } int C(int n, int m) { int mi = 1; for (int i = (n - m + 1); i <= (n); i++) mi = (long long)mi * i % mod; return (long long)mi * inv[m] % mod; } int main() { scanf("%d%d%d", &n, &d, &mod); if (n <= 2) return puts("1"), 0; inv[0] = 1; for (int i = (1); i <= (d); i++) inv[i] = inv[i - 1] * i; inv[d] = ksm(inv[d], mod - 2); for (int i = d - 1; i; i--) inv[i] = (long long)inv[i + 1] * (i + 1) % mod; for (int i = (0); i <= (n); i++) f[1][0][i] = 1; for (int i = (2); i <= (n); i++) for (int j = (1); j <= (min(i - 1, d)); j++) for (int k = (1); k <= (n); k++) { upd(f[i][j][k], f[i][j][k - 1]); for (int t = 1; t <= j && t * k < i; t++) { if (k > 1) upd(f[i][j][k], (long long)f[i - t * k][j - t][k - 1] * C(f[k][d - 1][k - 1] + t - 1, t) % mod); else upd(f[i][j][k], (long long)f[i - t * k][j - t][k - 1] * C(f[k][0][k - 1] + t - 1, t) % mod); } } upd(ans, f[n][d][n / 2]); if (!(n & 1)) upd(ans, mod - C(f[n / 2][d - 1][n / 2], 2)); printf("%d\n", ans); return 0; }
#include <bits/stdc++.h> using namespace std; template <typename T, typename U> void chkmax(T& x, U y) { if (x < y) x = y; } template <typename T, typename U> void chkmin(T& x, U y) { if (y < x) x = y; } const int MAXN = 1111; int N, D, MOD; int dp[12][MAXN]; int r[MAXN], C[MAXN]; int main() { cin >> N >> D >> MOD; r[1] = 1; for (int i = 2; i < MAXN; i++) { r[i] = (long long)(MOD - r[MOD % i]) * (MOD / i) % MOD; } if (D == 2) { puts("1"); return 0; } int M = N / 2; D--, dp[D][1] = dp[D + 1][1] = 1; dp[0][1] = 1; for (int i = 1; i <= M; i++) { int cur = dp[D][i]; C[0] = 1; for (int k = 1; k <= D + 1; k++) C[k] = (long long)C[k - 1] * (cur + k - 1) % MOD * r[k] % MOD; for (int k = D + 1; k > 0; k--) { for (int j = N; j > i; j--) { for (int l = k - 1; l >= 0; l--) { if (j >= i * (k - l)) dp[k][j] = (dp[k][j] + (long long)dp[l][j - i * (k - l)] * C[k - l]) % MOD; } } } } int ans = dp[D + 1][N]; if (N + 1 & 1) ans = (ans + (long long)(MOD - dp[D][M]) * (dp[D][M] - 1) % MOD * r[2]) % MOD; cout << ans << endl; return 0; }
#include <bits/stdc++.h> using namespace std; inline int read() { int x = 0, f = 1; char c = getchar(); while (c < '0' || c > '9') { if (c == '-') f = -1; c = getchar(); } while (c >= '0' && c <= '9') x = (x << 3) + (x << 1) + (c ^ '0'), c = getchar(); return x * f; } const int N = 1e3 + 5, M = 15; int mod; inline int inc(int x, int y) { x += y - mod; return x + (x >> 31 & mod); } inline int del(int x, int y) { x -= y; return x + (x >> 31 & mod); } inline int mul(int x, int y) { return 1ll * x * y % mod; } inline void Inc(int &x, int y) { x = inc(x, y); } inline void Del(int &x, int y) { x = del(x, y); } inline void Mul(int &x, int y) { x = mul(x, y); } inline long long Pow(long long x, int k) { long long res = 1; while (k) { if (k & 1) res = res * x % mod; k >>= 1; x = x * x % mod; } return res; } bool st; int fac[M], inv[M]; inline void init(int n) { fac[0] = inv[0] = 1; for (int i = 1; i <= n; i++) fac[i] = 1ll * fac[i - 1] * i % mod; inv[n] = Pow(fac[n], mod - 2); for (int i = n - 1; i >= 1; i--) inv[i] = 1ll * inv[i + 1] * (i + 1) % mod; } int n, d, f[N][M][N]; inline int C(int n, int m) { if (n < m) return 0; int res = 1; for (int i = n - m + 1; i <= n; i++) res = 1ll * res * i % mod; return 1ll * res * inv[m] % mod; } bool ed; int main() { n = read(), d = read(), mod = read(); const int m = n / 2; if (n <= 2) return puts("1"), 0; init(10); for (int i = 0; i <= n; i++) f[1][0][i] = 1; f[1][d - 1][0] = 1; for (int i = 2; i <= n; i++) for (int j = 1; j <= min(i - 1, d); j++) for (int k = 1; k <= m; k++) { f[i][j][k] = f[i][j][k - 1]; for (int t = 1; t <= j && i - t * k > 0; t++) Inc(f[i][j][k], mul(f[i - t * k][j - t][k - 1], C(f[k][d - 1][k - 1] + t - 1, t))); } if (n & 1) printf("%d\n", f[n][d][m]); else printf("%d\n", del(f[n][d][m], C(f[m][d - 1][m - 1], 2))); return 0; }
#include <bits/stdc++.h> using namespace std; inline int read() { int x = 0, f = 1; char c = getchar(); while (c < '0' || c > '9') { if (c == '-') f = -1; c = getchar(); } while (c >= '0' && c <= '9') x = (x << 3) + (x << 1) + (c ^ '0'), c = getchar(); return x * f; } const int N = 1e3 + 5, M = 15; int mod; inline int inc(int x, int y) { x += y - mod; return x + (x >> 31 & mod); } inline int del(int x, int y) { x -= y; return x + (x >> 31 & mod); } inline int mul(int x, int y) { return 1ll * x * y % mod; } inline void Inc(int &x, int y) { x = inc(x, y); } inline void Del(int &x, int y) { x = del(x, y); } inline void Mul(int &x, int y) { x = mul(x, y); } inline long long Pow(long long x, int k) { long long res = 1; while (k) { if (k & 1) res = res * x % mod; k >>= 1; x = x * x % mod; } return res; } bool st; int fac[M], inv[M]; inline void init(int n) { fac[0] = inv[0] = 1; for (int i = 1; i <= n; i++) fac[i] = 1ll * fac[i - 1] * i % mod; inv[n] = Pow(fac[n], mod - 2); for (int i = n - 1; i >= 1; i--) inv[i] = 1ll * inv[i + 1] * (i + 1) % mod; } int n, d, f[N][M][N]; inline int C(int n, int m) { if (n < m) return 0; long long res = 1; for (int i = n; i >= n - m + 1; i--) res = res * i % mod; return res * inv[m] % mod; } bool ed; int main() { n = read(), d = read(), mod = read(); if (n <= 2) return puts("1"), 0; init(10); for (int i = 0; i <= n; i++) f[1][0][i] = 1; for (int i = 2; i <= n; i++) for (int j = 1; j <= min(i - 1, d); j++) for (int k = 1; k <= n; k++) { f[i][j][k] = f[i][j][k - 1]; for (int t = 1; t <= j && i - t * k > 0; t++) if (k ^ 1) Inc(f[i][j][k], mul(f[i - t * k][j - t][k - 1], C(f[k][d - 1][k - 1] + t - 1, t))); else Inc(f[i][j][k], mul(f[i - t * k][j - t][k - 1], C(f[k][0][k - 1] + t - 1, t))); } int ans = 0; if (n & 1) ans = f[n][d][n / 2]; else ans = del(f[n][d][n / 2], C(f[n / 2][d - 1][n / 2 - 1], 2)); printf("%d\n", ans); return 0; }
#include <bits/stdc++.h> using namespace std; int mod; long long powmod(long long a, long long b) { long long res = 1; a %= mod; assert(b >= 0); for (; b; b >>= 1) { if (b & 1) res = res * a % mod; a = a * a % mod; } return res; } const int N = 1010; long long dp[N][20], pd[N][20], f[N], t[20]; int n, d; int main() { scanf("%d%d%d", &n, &d, &mod); if (n <= 2) { puts("1"); return 0; } if ((n - 2) % (d - 1) != 0) { puts("0"); return 0; } dp[0][0] = 1; for (int i = 1; i < n / 2 + 1; i++) if ((i - 1) % (d - 1) == 0) { if (i == 1) f[i] = 1; else f[i] = dp[i - 1][d - 1]; t[0] = 1; for (int j = 1; j < d + 1; j++) { t[j] = t[j - 1] * (f[i] + j - 1) % mod * powmod(j, mod - 2) % mod; } for (int p = 0; p < n + 1; p++) for (int q = 0; q < d + 1; q++) pd[p][q] = 0; for (int r = 0; r < d + 1; r++) for (int q = 0; q < d + 1; q++) if (r + q <= d) for (int p = 0; p < n + 1; p++) if (p + q * i <= n) { pd[p + q * i][r + q] = (pd[p + q * i][r + q] + dp[p][r] * t[q]) % mod; } for (int p = 0; p < n + 1; p++) for (int q = 0; q < d + 1; q++) if (pd[p][q]) { dp[p][q] = pd[p][q]; } } int ret = dp[n - 1][d]; if (n % 2 == 0) { ret = (ret - dp[n / 2 - 1][d - 1] * (dp[n / 2 - 1][d - 1] - 1) / 2) % mod; if (ret < 0) ret += mod; } printf("%d\n", ret); }
#include <bits/stdc++.h> using namespace std; const int maxn = 1005, maxd = 15; int f[maxn][maxd], g[maxn][maxd], t[maxn]; int n, d, p, q; int fpm(int a, int b, int p) { int res = 1; while (b) { if (b & 1) res = 1ll * res * a % p; a = 1ll * a * a % p; b >>= 1; } return res; } int main() { scanf("%d%d%d", &n, &d, &p); if (n <= 2) { puts("1"); return 0; } if ((n - 2) % (d - 1)) { puts("0"); return 0; } f[0][0] = 1; for (int i = 1; i <= (n / 2); i++) if ((i - 1) % (d - 1) == 0) { q = (i == 1) ? 1 : f[i - 1][d - 1]; t[0] = 1; for (int j = 1; j <= d; j++) t[j] = 1ll * t[j - 1] * (q + j - 1) % p * fpm(j, p - 2, p) % p; for (int j = 0; j <= n; j++) for (int k = 0; k <= d; k++) g[j][k] = 0; for (int j = 0; j <= d; j++) for (int k = 0; j + k <= d; k++) for (int l = 0; l + k * i <= n; l++) g[l + k * i][j + k] = (1ll * f[l][j] * t[k] + g[l + k * i][j + k]) % p; for (int j = 0; j <= n; j++) for (int k = 0; k <= d; k++) f[j][k] = g[j][k]; } int res = f[n - 1][d]; if (n % 2 == 0) { q = f[n / 2 - 1][d - 1]; q = 1ll * q * (q - 1) % p * fpm(2, p - 2, p) % p; res = ((res - q) % p + p) % p; } printf("%d\n", res); return 0; }
#include <bits/stdc++.h> using namespace std; using ll = long long; const int mxn = 1006; const int mxd = 11; int n, d; ll MOD; ll f[mxn][mxd]; int inv[mxd]; int ifac[mxd]; int comb(int a, int b) { ll re = ifac[b]; for (int i = 0; i < b; ++i) (re *= a - i) %= MOD; return re; } int main() { cin >> n >> d >> MOD; if (n == 1 || n == 2) { cout << 1 % MOD << endl; return 0; } ifac[0] = inv[1] = ifac[1] = 1; for (int i = 2; i < mxd; ++i) { inv[i] = (ll)MOD / i * (MOD - inv[MOD % i]) % MOD; ifac[i] = (ll)ifac[i - 1] * inv[i] % MOD; } f[1][0] = 1; for (int i = 1; i * 2 < n; ++i) if ((i - 1) % (d - 1) == 0) { int w = (i == 1 ? 1 : f[i][d - 1]); for (int j = n; j >= i + 1; --j) for (int k = d; k >= 1; --k) for (int u = k - 1; u >= 0 && j - i * (k - u) >= 1; --u) (f[j][k] += f[j - i * (k - u)][u] * comb(w + k - u - 1, k - u)) %= MOD; } ll ans = f[n][d]; if (n % 2 == 0) ans += comb(f[n / 2][d - 1] + 1, 2); cout << (ans % MOD + MOD) % MOD << endl; return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 1010; int n, d, P, dp[N][11][N], ans; inline void upd(int &x, int y) { ((x += y) >= P) && (x -= P); } int ksm(int a, int b) { int ans = 1; for (; b; b >>= 1, a = 1ll * a * a % P) if (b & 1) ans = 1ll * ans * a % P; return ans; } inline int C(int n, int k) { if (n < k || k < 0) return 0; int ans = 1, inv = 1; for (int i = (1); i <= (k); ++i) ans = 1ll * ans * (n - i + 1) % P, inv = 1ll * inv * i % P; return 1ll * ans * ksm(inv, P - 2) % P; } int main() { scanf("%d%d%d", &n, &d, &P); if (n == 1) return puts("1"), 0; dp[1][0][0] = dp[1][d - 1][0] = 1; for (int i = (2); i <= (n); ++i) for (int j = (1); j <= (d); ++j) for (int k = (1); k <= (i - 1); ++k) { if (k) upd(dp[i][j][k], dp[i][j][k - 1]); for (int l = (1); l <= (j); ++l) { if (l * k + 1 > i) break; upd(dp[i][j][k], 1ll * dp[i - l * k][j - l][min(k - 1, i - l * k - 1)] * C(dp[k][d - 1][k - 1] + l - 1, l) % P); } } ans = dp[n][d][(n - 1) / 2]; if (!(n & 1)) upd(ans, C(dp[n / 2][d - 1][n / 2 - 1] + 1, 2)); printf("%d\n", ans); return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 1007, D = 11, C = 20; int M, dd, mod; int dp[N][N][D]; int rev[C]; long long power(int a, int b) { if (b == 0) return 1; long long res = power(a, b / 2); res *= res, res %= mod; if (b & 1) res *= a, res %= mod; return res; } int main() { ios_base::sync_with_stdio(0); cin.tie(0); cin >> M >> dd >> mod; if (M <= 2) return cout << 1 << endl, 0; if (dd == 2) return cout << 1 << endl, 0; if ((M - 2) % (dd - 1) != 0) return cout << 0 << endl, 0; int n = (M - 2) / (dd - 1); for (int i = 0; i < C; i++) rev[i] = power(i, mod - 2); for (int i = 0; i <= dd; i++) { dp[1][0][i] = 1; for (int j = 1; j < N; j++) dp[1][j][i] = 1; } for (int a = 2; a <= n; a++) for (int x = 1; x < N; x++) for (int d = 1; d < D; d++) { dp[a][x][d] = dp[a][x - 1][d]; long long comb = dp[x][x - 1][dd - 1], t = dp[x][x - 1][dd - 1]; for (int c = 1; c * x < a && d >= c; c++) { long long way = dp[a - c * x][x - 1][d - c]; way *= comb; way %= mod; dp[a][x][d] += way, dp[a][x][d] %= mod; comb *= (c + t) % mod, comb %= mod, comb *= rev[c + 1], comb %= mod; } } long long t1 = dp[n][(n - 1) / 2][dd]; if (n & 1) return cout << t1 << endl, 0; long long t2 = (1LL * dp[n / 2][n / 2 - 1][dd - 1] * (dp[n / 2][n / 2 - 1][dd - 1] + 1) % mod) * rev[2] % mod; t1 += t2, t1 %= mod; cout << t1 << endl; }
#include <bits/stdc++.h> using namespace std; const int nmax = 1000; const int gmax = 10; int mod; int t[nmax + 1]; int inv[gmax + 1]; int d[nmax + 1][gmax + 1][nmax + 1]; inline int C(int x, int y) { int ans = 1; for (int i = x - y + 1; i <= x; ++i) ans = 1LL * ans * i % mod; return 1LL * ans * inv[y] % mod; } int lgput(int b, int p) { int ans = 1; while (p > 0) { if (p & 1) ans = 1LL * ans * b % mod; b = 1LL * b * b % mod; p >>= 1; } return ans; } int main() { int n, g; fscanf(stdin, "%d%d%d", &n, &g, &mod); if (n == 1 || n == 2) { fprintf(stdout, "1\n"); return 0; } int fct = 1; inv[0] = 1; for (int i = 1; i <= n; ++i) { fct = 1LL * fct * i % mod; inv[i] = lgput(fct, mod - 2); } t[1] = 1; for (int i = 0; i <= n; ++i) d[0][0][i] = d[1][g - 1][i] = 1; for (int i = 2; i <= n; ++i) { for (int j = 1; j <= g; ++j) { for (int mx = 1; mx <= n; ++mx) { d[i][j][mx] = (d[i][j][mx] + d[i][j][mx - 1]) % mod; if (j * mx + 1 == i) { d[i][j][mx] = (d[i][j][mx] + C(t[mx] + j - 1, j)) % mod; } for (int x = 1; x < j && x * mx <= i; ++x) { d[i][j][mx] = (d[i][j][mx] + 1LL * d[i - x * mx][j - x][mx - 1] * C(t[mx] + x - 1, x)) % mod; } } } t[i] = d[i][g - 1][n]; } int ans = 0; if (n % 2 == 0) { ans += 1LL * (t[n / 2] + 1) * t[n / 2] % mod * inv[2] % mod; } ans = (ans + d[n][g][(n - 1) / 2]) % mod; fprintf(stdout, "%d\n", ans); return 0; }
#include <bits/stdc++.h> using namespace std; const long long N = 1005; long long n, d, mod; long long f[N][11][N / 2]; long long inv[11]; long long ksm(long long a, long long x) { long long ans = 1; while (x) { if (x % 2 == 1) ans = ans * a % mod; a = a * a % mod; x /= 2; } return ans % mod; } void pre() { long long tmp = 1; for (long long i = 1; i <= d; i++) { tmp = tmp * i; inv[i] = ksm(tmp, mod - 2); } } long long C(long long m, long long n) { long long ans = 1; for (long long i = m; i >= m - n + 1; i--) ans = (ans * i) % mod; ans = (ans * inv[n]) % mod; return ans; } int main() { cin >> n >> d >> mod; if (n <= 2) { cout << 1; return 0; } pre(); for (long long i = 0; i <= n / 2; i++) f[1][0][i] = 1; for (long long i = 2; i <= n; i++) { for (long long j = 1; j <= min(i - 1, d); j++) { for (long long k = 1; k <= n / 2; k++) { f[i][j][k] = f[i][j][k - 1]; for (long long t = 1; t <= min((i - 1) / k, j); t++) { long long tmp = (k == 1) ? 0 : d - 1; f[i][j][k] = (f[i][j][k] + f[i - t * k][j - t][k - 1] * C(f[k][tmp][k - 1] + t - 1, t) % mod) % mod; } } } } long long ans = f[n][d][n / 2]; if (n % 2 == 0) ans = (ans + mod - C(f[n / 2][d - 1][n / 2], 2)) % mod; cout << ans; }
#include <bits/stdc++.h> using namespace std; int p, f[1005][11][505], iv[15], inv[15]; int c(int n, int m) { int res = 1; for (int i = n; i > n - m; i--) res = 1ll * res * i % p; return 1ll * res * inv[m] % p; } int main() { int n, d; scanf("%d%d%d", &n, &d, &p); if (n == 1) { puts("1"); return 0; } inv[0] = inv[1] = iv[1] = 1; for (int i = 2; i <= d; i++) iv[i] = p - 1ll * (p / i) * iv[p % i] % p, inv[i] = 1ll * inv[i - 1] * iv[i] % p; for (int i = 0; i <= n / 2; i++) f[1][0][i] = f[1][d - 1][i] = 1; for (int i = 2; i <= n; i++) for (int j = 1; j <= d; j++) for (int k = 1; k <= n / 2; k++) { f[i][j][k] = f[i][j][k - 1]; for (int t = 1; t <= j; t++) if (i > t * k) f[i][j][k] = (f[i][j][k] + 1ll * f[i - t * k][j - t][k - 1] * c(f[k][d - 1][k - 1] + t - 1, t)) % p; } int res = f[n][d][n / 2]; if (!(n & 1)) res = (res - c(f[n / 2][d - 1][n / 2 - 1], 2) + p) % p; printf("%d", res); return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 1009; int f[N][12][N / 2], n, d, mod; int inv[N], fac[N]; inline void Plus(int &x, int y) { x = (x + y >= mod ? x + y - mod : x + y); } inline int mins(int &x, int y) { return (x - y < 0 ? x - y + mod : x - y); } void Init() { inv[0] = inv[1] = fac[1] = 1; for (int i = 2; i < N; i++) fac[i] = 1ll * fac[i - 1] * i % mod; for (int i = 2; i < N; i++) inv[i] = 1ll * (mod - mod / i) * inv[mod % i] % mod; for (int i = 2; i < N; i++) inv[i] = 1ll * inv[i - 1] * inv[i] % mod; } inline int C(int n, int m) { if (m > n) return 0; int res = 1; for (int i = n - m + 1; i <= n; i++) res = 1ll * res * i % mod; return 1ll * res * inv[m] % mod; } int main() { scanf("%d%d%d", &n, &d, &mod); if (n <= 2) return puts("1"), 0; Init(); for (int i = 0; i <= n / 2; i++) f[1][0][i] = 1; f[1][d - 1][0] = 1; for (int i = 2; i <= n; i++) for (int j = 1; j <= min(d, i - 1); j++) for (int k = 1; k <= n / 2; k++) { f[i][j][k] = f[i][j][k - 1]; for (int t = 1; t * k <= i && t <= j; t++) Plus(f[i][j][k], 1ll * f[i - t * k][j - t][k - 1] * C(f[k][d - 1][k - 1] + t - 1, t) % mod); } if (n & 1) printf("%d", f[n][d][n / 2]); else printf("%d", mins(f[n][d][n / 2], C(f[n / 2][d - 1][n / 2 - 1], 2))); return 0; }
#include <bits/stdc++.h> using namespace std; const int MaxN = 1005; const int MaxD = 11; int n, d, mod; int inv[MaxN]; int f[MaxN][MaxD][MaxN]; int main() { cin >> n >> d >> mod; if (n <= 2) { puts("1"); return 0; } inv[1] = 1; for (int i = 2; i <= n; ++i) inv[i] = (long long)(mod - mod / i) * inv[mod % i] % mod; f[1][0 + 0][0] = 1; f[1][d - 1][0] = 1; for (int i = 2; i <= n; ++i) for (int j = 1; j <= d; ++j) for (int k = 1; k < i; ++k) { f[i][j][k] = f[i][j][k - 1]; int coe = 1; int now = f[k][d - 1][k - 1] - 1; for (int t = 1; t * k < i && t <= j; ++t) { coe = (long long)coe * ++now % mod * inv[t] % mod; f[i][j][k] += (long long)coe * f[i - t * k][j - t][min(k - 1, i - t * k - 1)] % mod; if (f[i][j][k] >= mod) f[i][j][k] -= mod; } } int res = f[n][d][(n + 1) / 2 - 1]; if (~n & 1) { int l = f[n / 2][d - 1][n / 2 - 1]; res = (res + (long long)l * (l + 1) / 2) % mod; } cout << res << endl; return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 1000 + 10, D = 15; int n, d, mod; int dp[D][N][N]; int ifac[N]; void Add(int &x, int y) { if ((x += y) >= mod && (x -= mod)) ; } int binom(int n, int m) { n %= mod; if (n < m) return 0; int pro = 1; for (int i = n; i >= n - m + 1; i--) pro = 1ll * pro * i % mod; pro = 1ll * pro * ifac[m] % mod; return pro; } int DP(int g, int n, int k) { if (dp[g][n][k] != -1) return dp[g][n][k]; int &res = dp[g][n][k]; if (n == 1) return res = (g % (d - 1) == 0); if (g == 0) return res = (n == 1); if (k == 0) return 0; res = 0; Add(res, DP(g, n, k - 1)); if ((k - 1) % (d - 1)) return res; int f = DP(d - 1, k, k - 1); for (int i = 1; i <= g; i++) { if (i * k >= n) break; Add(res, 1ll * DP(g - i, n - k * i, k - 1) * binom(f + i - 1, i) % mod); } return res; } void quit(int x) { printf("%d\n", x), exit(0); } void initmath(int n) { ifac[0] = ifac[1] = 1; for (int i = 2; i <= n; i++) ifac[i] = 1ll * (mod - mod / i) * ifac[mod % i] % mod; for (int i = 1; i <= n; i++) ifac[i] = 1ll * ifac[i - 1] * ifac[i] % mod; return; } int calc(int g, int n, int k) { if (n == 1 || n == 2) return 1; if (n < g + 1) return 0; if ((n - g - 1) % (d - 1) != 0) return 0; return DP(g, n, k); } int main() { memset(dp, -1, sizeof(dp)); scanf("%d%d%d", &n, &d, &mod); if (n == 1 || n == 2) quit(1); if (n < d + 1) quit(0); if ((n - d - 1) % (d - 1) != 0) quit(0); initmath(d); if (n & 1) quit(DP(d, n, n / 2)); int ans = DP(d, n, n / 2); ans = (ans - binom(DP(d - 1, n / 2, n / 2), 2) + mod) % mod; quit(ans); return 0; }
#include <bits/stdc++.h> using namespace std; const int MAXN = 1e3 + 10; const int MAXD = 15; int n, d, MOD; int phi; void add(int& x, int y) { ((x += y) >= MOD) && (x -= MOD); } int mul(int x, int y) { return x * 1ll * y % MOD; } bool read() { if (scanf("%d%d%d", &n, &d, &MOD) < 3) { return false; } return true; } int dp[MAXD][MAXN][MAXN]; int mpow(int a, int p) { int res = 1; for (; p > 0; a = mul(a, a), p >>= 1) { if (p & 1) { res = mul(res, a); } } return res; } int inv[MAXD]; void precalc() { for (int i = 1; i < MAXD; ++i) { inv[i] = mpow(i, MOD - 2); assert(mul(i, inv[i]) == 1); } } int solve() { if (n <= 2) { return 1; } int ans = 0; memset(dp, 0, sizeof dp); for (int last = 0; last < (int)n + 1; ++last) { dp[0][0][last] = 1; } for (int sum = 0; sum <= n; ++sum) { for (int sons = 1; sons <= d; ++sons) { for (int cur = 1; cur <= n; ++cur) { add(dp[sons][sum][cur], dp[sons][sum][cur - 1]); if (cur * 2 > n) { continue; } int A = cur == 1 ? 1 : dp[d - 1][cur - 1][n]; int B = 1; int C = A / B; for (int cnt_cur = 1; sum - cnt_cur * cur >= 0 && sons - cnt_cur >= 0; ++cnt_cur) { int aux = mul(dp[sons - cnt_cur][sum - cnt_cur * cur][cur - 1], C); add(dp[sons][sum][cur], aux); if (sons == d && sum == n - 1) { if ((n - cur) * 2 > n) { add(ans, aux); } } add(A, 1); add(B, 1); C = mul(C, A); C = mul(C, inv[B]); } } } } for (int left_________________ = d - 1; left_________________ <= n - 2; ++left_________________) { int right_______________ = n - 2 - left_________________; if (right_______________ < d - 1 || left_________________ > right_______________) { continue; } if ((left_________________ + 1) * 2 > n || (right_______________ + 1) * 2 > n) { continue; } int cur_ans = mul(dp[d - 1][left_________________][n], dp[d - 1][right_______________][n]); if (left_________________ == right_______________) { cur_ans = mul(dp[d - 1][left_________________][n], dp[d - 1][left_________________][n] + 1); cur_ans = mul(cur_ans, inv[2]); } add(ans, cur_ans); } return ans; } int main() { while (read()) { precalc(); printf("%d\n", solve()); } return 0; }
#include <bits/stdc++.h> #pragma GCC optimize(2) #pragma GCC optimize(3) #pragma GCC optimize("Ofast") using namespace std; namespace ywy { int p; unsigned char bv[1001][1001][11]; long long f[1001][1001][11]; int d; inline long long mi(int a, int b) { long long ans = 1, tmp = a; while (b) { if (b & 1) ans = (ans * tmp) % p; tmp = (tmp * tmp) % p; b >>= 1; } return (ans); } long long ny[1001]; long long dp(int sz, int mx, int dk) { if (bv[sz][mx][dk]) return (f[sz][mx][dk]); bv[sz][mx][dk] = 1; if (sz == 1) { return (f[sz][mx][dk] = (dk == 0)); } if (!dk || !mx || dk >= sz) return (f[sz][mx][dk] = 0); if (mx == 1) { return (f[sz][mx][dk] = (sz == dk + 1)); } long long ans = dp(sz, mx - 1, dk); long long h = dp(mx, mx, d - 1); if (!h) return (f[sz][mx][dk] = ans); long long ji = 1; for (register int i = 1; i <= dk && i * mx < sz; i++) { ji *= ny[i]; ji %= p; ji *= (h + i - 1); ji %= p; ans = (ans + dp(sz - i * mx, mx - 1, dk - i) * ji) % p; } return (f[sz][mx][dk] = ans); } void ywymain() { int n; cin >> n >> d >> p; for (register int i = 1; i <= d; i++) ny[i] = mi(i, p - 2); if (n <= 2) { cout << 1 << endl; return; } if (n & 1) { cout << dp(n, n / 2, d) << endl; return; } long long cjr = dp(n / 2, n / 2 - 1, d - 1); cjr = ((cjr + 1) * cjr) / 2; cjr %= p; cjr %= p; cjr += dp(n, n / 2 - 1, d); cjr %= p; cout << cjr << endl; } } // namespace ywy signed main() { ywy::ywymain(); return (0); }
#include <bits/stdc++.h> using namespace std; template <class T> bool cmax(T &x, T y) { return y > x ? x = y, 1 : 0; } template <class T> bool cmin(T &x, T y) { return y < x ? x = y, 1 : 0; } const int N = 1005, M = 15; int n, m, mod, f[N][M][N], ifac[M], fac[M]; int kpow(int a, int k) { int res = 1; for (; k; k >>= 1, a = 1ll * a * a % mod) if (k & 1) res = 1ll * res * a % mod; return res; } int C(int n, int m) { int res = 1; for (int i = 0; i < m; ++i) res = 1ll * res * (n - i) % mod; return 1ll * res * ifac[m] % mod; } int F(int n, int d, int mx) { if (!d || !mx || n == 1) return n == 1 && !d; if (~f[n][d][mx]) return f[n][d][mx]; f[n][d][mx] = F(n, d, mx - 1); for (int i = 1; i <= min(n - 1, d) && i * mx < n; ++i) (f[n][d][mx] += 1ll * F(n - i * mx, d - i, mx - 1) * C((mx == 1 ? 1 : F(mx, m - 1, mx)) + i - 1, i) % mod) %= mod; return f[n][d][mx]; } int main() { ios::sync_with_stdio(false); cin >> n >> m >> mod; if (n <= 2) { cout << 1 << endl; return 0; } fac[0] = 1; for (int i = 1; i <= m; ++i) fac[i] = 1ll * i * fac[i - 1] % mod; ifac[m] = kpow(fac[m], mod - 2); for (int i = m - 1; i >= 0; --i) ifac[i] = 1ll * ifac[i + 1] * (i + 1) % mod; memset(f, -1, sizeof f); if (n & 1) cout << F(n, m, n / 2) << endl; else { cout << (F(n, m, n / 2) + mod - C(F(n / 2, m - 1, n / 2 - 1), 2)) % mod << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 1009; int f[N][12][N / 2], n, d, mod; int inv[N], fac[N]; inline void Plus(int &x, int y) { x = (x + y >= mod ? x + y - mod : x + y); } inline int mins(int &x, int y) { return (x - y < 0 ? x - y + mod : x - y); } void Init() { inv[1] = 1; for (int i = 2; i < N; i++) inv[i] = 1ll * (mod - mod / i) * inv[mod % i] % mod; for (int i = 2; i < N; i++) inv[i] = 1ll * inv[i - 1] * inv[i] % mod; } inline int C(int n, int m) { if (m > n) return 0; int res = 1; for (int i = n - m + 1; i <= n; i++) res = 1ll * res * i % mod; return 1ll * res * inv[m] % mod; } int main() { scanf("%d%d%d", &n, &d, &mod); if (n <= 2) return puts("1"), 0; Init(); for (int i = 0; i <= n / 2; i++) f[1][0][i] = 1; f[1][d - 1][0] = 1; for (int i = 2; i <= n; i++) for (int j = 1; j <= min(d, i - 1); j++) for (int k = 1; k <= n / 2; k++) { f[i][j][k] = f[i][j][k - 1]; for (int t = 1; t * k <= i && t <= j; t++) Plus(f[i][j][k], 1ll * f[i - t * k][j - t][k - 1] * C(f[k][d - 1][k - 1] + t - 1, t) % mod); } if (n & 1) printf("%d", f[n][d][n / 2]); else printf("%d", mins(f[n][d][n / 2], C(f[n / 2][d - 1][n / 2 - 1], 2))); return 0; }
#include <bits/stdc++.h> using namespace std; const int maxn = 1e3 + 10; const int maxD = 12; int mod; inline int ad(int x, int y) { return x >= mod - y ? x - mod + y : x + y; } inline int re(int x, int y) { return x < y ? x - y + mod : x - y; } inline int mu(int x, int y) { return (long long)x * y % mod; } inline int qp(int x, long long y) { int r = 1; while (y) { if (y & 1) r = mu(r, x); x = mu(x, x); y >>= 1; } return r; } inline int iv(int x) { return qp(x, mod - 2); } inline int dv(int x, int y) { return mu(x, qp(y, mod - 2)); } int f[maxn][maxD][maxn]; int inv[maxD]; int C(int x, int l) { int ret = 1; for (int i = 1; i <= l; i++) ret = mu(ret, mu(inv[i], x)), x = re(x, 1); return ret; } int main() { int n, D; scanf("%d%d%d", &n, &D, &mod); if (n <= 2) { puts("1"); return 0; } for (int i = 0; i <= n; i++) f[1][0][i] = 1; for (int i = 1; i <= D; i++) inv[i] = iv(i), f[i + 1][i][1] = 1; for (int k = 2; k < n; k++) for (int i = 1; i <= n; i++) for (int j = 1; j <= D; j++) { f[i][j][k] = ad(f[i][j][k], f[i][j][k - 1]); for (int l = 1; l <= j && i > l * k; l++) f[i][j][k] = ad(f[i][j][k], mu(f[i - l * k][j - l][k - 1], C(f[k][D - 1][k - 1] + l - 1, l))); } printf("%d\n", re(f[n][D][n / 2], ((n & 1) ? 0 : C(f[n / 2][D - 1][n / 2], 2)))); return 0; }
#include <bits/stdc++.h> using namespace std; const int MAXN = 1E3 + 10, MAXD = 10 + 2; int MOD; long long inv[20]; long long dp[2][MAXN][MAXD]; long long Com(long long n, long long m) { n %= MOD; if (m < 0 || n < m) return 0; long long ret = n; for (int i = 1; i < m; ++i) ret = ret * (n - i) % MOD * inv[i + 1] % MOD; return ret; } int main() { int n, d; scanf("%d%d%d", &n, &d, &MOD); if (n <= 2) { puts("1"); return 0; } inv[0] = 0, inv[1] = 1; for (int i = 2; i <= d; ++i) inv[i] = inv[MOD % i] * (MOD - MOD / i) % MOD; int n0 = n - 1 >> 1; for (int i = 0; i <= d; ++i) dp[1][i + 1][i] = 1; for (int k = 2; k <= n0; ++k) { long long(&f)[MAXN][MAXD] = dp[k - 1 & 1], (&g)[MAXN][MAXD] = dp[k & 1]; for (int i = 0; i <= n; ++i) for (int j = 0; j <= d; ++j) { g[i][j] = f[i][j]; for (int t = 1; t <= j && k * t < i; ++t) g[i][j] = (g[i][j] + f[i - k * t][j - t] * Com(f[k][d - 1] + t - 1, t) % MOD) % MOD; } } long long ans = dp[n0 & 1][n][d]; if (n + 1 & 1) ans = (ans + Com(dp[n0 & 1][n >> 1][d - 1] + 1, 2)) % MOD; printf("%d\n", (int)ans); return 0; }
#include <bits/stdc++.h> using namespace std; struct sam { int son[1057 << 1][26], pre[1057 << 1], dis[1057 << 1]; int Right[1057 << 1]; int p, np, q, nq, lst, cnt; int lth; char read_s[1057]; void insert(int x) { dis[np = ++cnt] = dis[p = lst] + 1; Right[np] = 1, lst = np; for (; p && !son[p][x]; p = pre[p]) son[p][x] = np; if (!p) return pre[np] = 1, void(); q = son[p][x]; if (dis[q] == dis[p] + 1) return pre[np] = q, void(); else { dis[nq = ++cnt] = dis[p] + 1; memcpy(son[nq], son[q], sizeof son[q]); pre[nq] = pre[q]; pre[q] = pre[np] = nq; for (; p && son[p][x] == q; p = pre[p]) son[p][x] = nq; } } void build() { lst = cnt = 1; scanf("%s", read_s); lth = strlen(read_s); for (int i = 0; i < lth; ++i) insert(read_s[i] - 'a'); } void build_() { lst = cnt = 1; scanf("%s", read_s); lth = strlen(read_s); for (int i = lth - 1; ~i; --i) insert(read_s[i] - 'a'); } int s[1057 << 1], v[1057 << 1]; void sort() { for (int i = 1; i <= cnt; ++i) ++v[dis[i]]; for (int i = 1; i <= lth; ++i) v[i] += v[i - 1]; for (int i = 1; i <= cnt; ++i) s[v[dis[i]]--] = i; } long long ans; void DP() { for (int i = cnt; i; --i) { int now = s[i], fth = pre[now]; Right[fth] += Right[now]; ans += 1ll * (dis[now] - dis[fth]) * Right[now] * (lth - Right[now]); } } } SAM; int n, d, MOD; const int MAXD = 15; int dp[1057][1057][MAXD]; int Inv[1057]; inline void update(int &a, int b) { a += b; if (a >= MOD) a -= MOD; } int qpow(int a, int b) { int tmp = a, ret = 1; for (; b; b >>= 1, tmp = 1LL * tmp * tmp % MOD) { if (b & 1) ret = 1LL * ret * tmp % MOD; } return ret; } void Init() { for (int i = 1; i <= 1000; i++) { Inv[i] = qpow(i, MOD - 2); } } int f[1057]; void Dodp() { f[1] = 1; dp[0][0][0] = 1; for (int j = 0; j <= d; j++) { dp[1][j][j] = 1; } for (int i = 2; i + i <= n; i++) { f[i] = dp[i - 1][i - 1][d - 1]; for (int k = 0; k <= d; k++) { for (int j = 0; j <= n; j++) { if (dp[i - 1][j][k]) { int tmp = dp[i - 1][j][k]; for (int use = 0; j + use * i <= n && use + k <= d && tmp; use++) { update(dp[i][j + use * i][use + k], tmp); tmp = 1LL * tmp * (f[i] + use) % MOD * Inv[use + 1] % MOD; } } } } } } void Solve() { if (n <= 2) { puts("1"); return; } if (n & 1) { printf("%d\n", dp[n >> 1][n - 1][d]); } else { int ans = dp[(n >> 1) - 1][n - 1][d], tmp = f[n >> 1]; tmp = 1LL * (tmp + 1) * tmp % MOD * Inv[2] % MOD; ans = (ans + tmp) % MOD; printf("%d\n", ans); } } int main() { scanf("%d%d%d", &n, &d, &MOD); Init(); Dodp(); Solve(); }
#include <bits/stdc++.h> using namespace std; inline int read() { register int data = 0, w = 1; char ch = 0; while (ch != '-' && (ch < '0' || ch > '9')) ch = getchar(); if (ch == '-') w = -1, ch = getchar(); while (ch >= '0' && ch <= '9') data = (data << 1) + (data << 3) + (ch ^ 48), ch = getchar(); return data * w; } int n, d, mod, f[1005][11][1005], g[1000005], inv[1000005]; int main() { n = read(), d = read(), mod = read(); if (n == 1 || n == 2) { puts("1"); return 0; } f[1][0][0] = g[1] = 1; inv[0] = inv[1] = 1; for (int i = 2; i <= n; i++) inv[i] = 1ll * inv[mod % i] * (mod - mod / i) % mod; for (int i = 2; i <= n; i++) inv[i] = 1ll * inv[i - 1] * inv[i] % mod; for (int i = 2; i <= n; i++) { for (int j = 1; j <= d; j++) for (int k = 1; k <= i; k++) { f[i][j][k] = f[i][j][k - 1]; for (int t = 1, x = g[k]; t <= j && t * k + 1 <= i; ++t, x = 1ll * x * (g[k] + t - 1) % mod) { f[i][j][k] = (f[i][j][k] + 1ll * f[i - t * k][j - t][min(k - 1, i - t * k - 1)] * x % mod * inv[t] % mod) % mod; } } g[i] = f[i][d - 1][i - 1]; } int ans = f[n][d][n / 2]; if (n % 2 == 0) ans = (ans - 1ll * g[n / 2] * (g[n / 2] - 1) / 2 % mod + mod) % mod; cout << ans << '\n'; return 0; }
#include <bits/stdc++.h> using namespace std; void Read(int &x) { char c; while (c = getchar(), c != EOF) if (c >= '0' && c <= '9') { x = c - '0'; while (c = getchar(), c >= '0' && c <= '9') x = x * 10 + c - '0'; ungetc(c, stdin); return; } } int n, d, MOD, f[1000 + 10][11], g[1000 + 10], inv[1000 + 10], ans; int main() { Read(n), Read(d), Read(MOD); if (n <= 2) { puts("1"); return 0; } if ((n - 2) % (d - 1)) { puts("0"); return 0; } int i, j, p, q, w; inv[0] = inv[1] = 1; for (i = 2; i <= n; i++) inv[i] = 1ll * (MOD - MOD / i) * inv[MOD % i] % MOD; for (i = 2; i <= n; i++) inv[i] = 1ll * inv[i] * inv[i - 1] % MOD; g[1] = f[1][0] = 1; for (i = 1; i <= (n >> 1); i++) { for (j = n - i + 1; j >= 1; j--) for (p = 0; p < d; p++) if (f[j][p]) { w = 1; for (q = 1; p + q <= d && j + q * i <= n; q++) { w = 1ll * w * (g[i] + q - 1) % MOD; f[j + q * i][p + q] = (f[j + q * i][p + q] + 1ll * w * inv[q] % MOD * f[j][p]) % MOD; } } g[i + 1] = f[i + 1][d - 1]; } ans = f[n][d]; if (!(n & 1)) ans = (ans + MOD - (1ll * g[n >> 1] * (g[n >> 1] - 1) / 2) % MOD) % MOD; printf("%d\n", ans); }
#include <bits/stdc++.h> using namespace std; inline void rd(int &x) { char ch; x = 0; bool fl = false; while (!isdigit(ch = getchar())) (ch == '-') && (fl = true); for (x = (ch ^ '0'); isdigit(ch = getchar()); x = x * 10 + (ch ^ '0')) ; (fl == true) && (x = -x); } namespace Miracle { const int N = 1005; int mod, n, d; int f[N][11][N]; int jie[11], inv[11]; int qm(int x, int y) { int ret = 1; while (y) { if (y & 1) ret = (long long)ret * x % mod; x = (long long)x * x % mod; y >>= 1; } return ret; } int dp(int i, int j, int k) { if (f[i][j][k] != -1) return f[i][j][k]; if (i == 1) { if (j == d - 1 || !j) return f[i][j][k] = 1; return f[i][j][k] = 0; } if (i == 0) { if (k == 0 && j == 0) return f[i][j][k] = 1; else return f[i][j][k] = 0; } if (j > i - 1) return f[i][j][k] = 0; if (i > 1 && k == 0) return f[i][j][k] = 0; int C = 1; int ret = 0; int tmp = dp(k, d - 1, k - 1); for (register int m = 0; m <= j && m * k <= i - 1; ++m) { ret = (ret + (long long)dp(i - m * k, j - m, k - 1) * C % mod * inv[m] % mod) % mod; C = (long long)C * (tmp - 1 + m + 1) % mod; } return f[i][j][k] = ret; } int main() { rd(n); rd(d); rd(mod); if (n <= 2) { puts("1"); return 0; } memset(f, -1, sizeof f); jie[0] = 1; for (register int i = 1; i <= 10; ++i) jie[i] = (long long)jie[i - 1] * i % mod; inv[10] = qm(jie[10], mod - 2); for (register int i = 9; i >= 0; --i) inv[i] = (long long)inv[i + 1] * (i + 1) % mod; long long ans = 0; ans = (ans + dp(n, d, (n - 1) / 2)); if (n % 2 == 0) { long long tmp = 0; tmp = dp(n / 2, d - 1, n / 2 - 1); ans = (ans + (tmp * (tmp + 1) / 2 % mod)) % mod; } printf("%I64d", ans); return 0; } } // namespace Miracle signed main() { Miracle::main(); return 0; }
#include <bits/stdc++.h> using namespace std; int IN() { int x = 0, f = 0, ch; for (; (ch = getchar()) < '0' || ch > '9';) f = (ch == '-'); for (; ch >= '0' && ch <= '9'; (ch = getchar())) x = x * 10 + ch - '0'; return f ? -x : x; } int N, M, P, A[1005], B[1005][15], C[15]; int Pow(int a, int b) { int ret = 1; for (; b; b >>= 1, a = 1ll * a * a % P) if (b & 1) ret = 1ll * ret * a % P; return ret; } int main(int argc, char* argv[]) { N = IN(); M = IN(); P = IN(); if (N <= 2) return puts("1"), 0; B[0][0] = 1; for (int i = 1, lim = N / 2; i <= lim; i++) { if (i == 1) A[i] = 1; else A[i] = B[i - 1][M - 1]; C[0] = 1; for (int j = 1, lim = M; j <= lim; j++) C[j] = 1ll * C[j - 1] * (A[i] + j - 1) % P * Pow(j, P - 2) % P; for (int j = N, lim = 0; j >= lim; j--) for (int k = M, lim = 0; k >= lim; k--) if (B[j][k]) for (int t = 1, lim = M - k; t <= lim; t++) { int x = j + t * i; if (x <= N) B[x][k + t] = (B[x][k + t] + 1ll * B[j][k] * C[t]) % P; } } int Ans = B[N - 1][M]; if (N % 2 == 0) { int t = B[N / 2 - 1][M - 1]; Ans = (Ans - 1ll * t * (t - 1) / 2) % P; } cout << (Ans + P) % P << endl; return 0; }
#include <bits/stdc++.h> using namespace std; int n, d, mo, inv[20], dp[1005][11][1005]; void ntr(int &x) { x = x >= mo ? x - mo : (x < 0 ? x + mo : x); } void inc(int &x, int y) { x += y, ntr(x); } long long qry(int x, int y) { if (y == 0) return 1; if (x == 0) return 0; x = x + y - 1; long long r = 1; for (int i = 1; i <= y; i++) r = r * (x - i + 1) % mo; return r * inv[y] % mo; } int ask(int n, int deg, int sz) { if (n == 1) return deg == 0 || deg == d - 1; if (sz == 0) return 0; int &ans = dp[n][deg][sz]; if (ans != -1) return ans; else ans = 0; int tmp = ask(sz, d - 1, sz - 1); for (int p = 0, f = 1; p <= deg && sz * p <= n - 1; ++p) { inc(ans, ask(n - p * sz, deg - p, sz - 1) * qry(tmp, p) % mo); } return ans; } int main() { scanf("%d%d%d", &n, &d, &mo); if (n < 2) return puts("1"), 0; inv[1] = 1; for (int i = 2; i <= 15; i++) inv[i] = 1ll * (mo - mo / i) * inv[mo % i] % mo; inv[0] = 1; for (int i = 1; i <= 15; i++) inv[i] = 1ll * inv[i] * inv[i - 1] % mo; memset(dp, -1, sizeof(dp)); int ans; if (n & 1) ans = ask(n, d, n / 2); else { ans = ask(n, d, n / 2 - 1); int tmp = ask(n / 2, d - 1, n / 2 - 1); inc(ans, qry(tmp, 2)); } printf("%d\n", ans); return 0; }
#include <bits/stdc++.h> using namespace std; int n, d, mo, ans; int f[1005][12], inv[12], tmp[12]; int power(int x, int y) { int s = 1; for (; y; y /= 2, x = 1ll * x * x % mo) if (y & 1) s = 1ll * s * x % mo; return s; } int main() { scanf("%d%d%d", &n, &d, &mo); inv[0] = 1; for (int i = 1; i <= d; i++) inv[i] = power(i, mo - 2); f[1][0] = f[1][d - 1] = 1; for (int k = 1; k <= n / 2; k++) if (f[k][d - 1]) { int m = f[k][d - 1]; tmp[0] = 1; for (int l = 1; l <= d; l++) tmp[l] = 1ll * tmp[l - 1] * (l + m - 1) % mo * inv[l] % mo; for (int i = n - k; i; i--) for (int j = 0; j < d; j++) if (f[i][j]) for (int l = 1; i + l * k <= n && j + l <= d; l++) f[i + l * k][j + l] = (f[i + l * k][j + l] + 1ll * f[i][j] * tmp[l]) % mo; } ans = (f[n][d] + f[n][0]) % mo; if (!(n & 1)) { int tmp = f[n / 2][d - 1]; ans = (ans + mo - 1ll * tmp * (tmp - 1) / 2 % mo) % mo; } printf("%d\n", ans); }
#include <bits/stdc++.h> using namespace std; int d; int num_leaf(int sz) { if (sz == 1) { return 1; } if (sz == 2) { return 1; } sz--; int cnt = d; sz -= d; if (sz < 0) { return -1; } while (sz) { if (sz < d - 1) { return -1; } sz -= (d - 1); cnt += (d - 1); cnt--; } return cnt; } int lf[1002]; long long int dp[1002]; bool us[1002]; long long int tmp[1002][1002][11]; long long int tmp2[1002][1002][11]; long long int MOD; bool us2[1002]; long long int dp2[1002]; long long int ppow(long long int i, long long int j) { long long int res = 1; while (j) { if (j & 1LL) { res *= i; if (res >= MOD) res %= MOD; } j >>= 1LL; i *= i; if (i >= MOD) i %= MOD; } return res; } long long int sel(long long int val, int ch) { val += ch - 1; long long int up = 1; long long int dw = 1; for (int j = 0; j < ch; j++) { up *= (val - j); if (up >= MOD) up %= MOD; dw *= (j + 1); if (dw >= MOD) dw %= MOD; } up *= ppow(dw, MOD - 2); if (up >= MOD) up %= MOD; return up; } long long int ww[1002][11]; inline long long int dfs2(int sz) { if (sz == 1) { return 1; } if (us2[sz]) return dp2[sz]; us2[sz] = true; dp2[sz] = 0; tmp2[sz][0][0] = 1; int deg = d - 1; for (int add = 1; add <= sz - 1; add++) { if ((add - 1) % deg) { continue; } long long int way = dfs2(add); for (int z = 0; z <= deg; z++) { ww[sz][z] = sel(way, z); } for (int j = sz - 1 - add; j >= 0; j--) { for (int k = deg - 1; k >= 0; k--) { long long int bs = tmp2[sz][j][k]; for (int z = k + 1; z <= deg; z++) { if ((z - k) * add + j > sz - 1) break; tmp2[sz][(z - k) * add + j][z] += bs * ww[sz][z - k]; if (tmp2[sz][(z - k) * add + j][z] > MOD) { tmp2[sz][(z - k) * add + j][z] %= MOD; } } } } } dp2[sz] = tmp2[sz][sz - 1][deg]; return dp2[sz]; } inline long long int dfs(int sz) { if (sz <= 1) { return 1; } if (us[sz]) return dp[sz]; us[sz] = true; int maxi = (sz - 1) / 2; tmp[sz][0][0] = 1; for (int add = 1; add <= maxi; add++) { if (add > 2 && ((add - 1) % (d - 1))) continue; for (int j = sz - 1 - add; j >= 0; j--) { for (int k = d - 1; k >= 0; k--) { long long int bs = tmp[sz][j][k]; long long int way = dfs2(add); for (int z = k + 1; z <= d; z++) { if ((z - k) * add + j > sz - 1) break; tmp[sz][(z - k) * add + j][z] += bs * sel(way, z - k); if (tmp[sz][(z - k) * add + j][z] > MOD) { tmp[sz][(z - k) * add + j][z] %= MOD; } } } } } dp[sz] = tmp[sz][sz - 1][d]; return dp[sz]; } int main() { int n; cin >> n >> d >> MOD; for (int i = 0; i < 1002; i++) { lf[i] = num_leaf(i); } long long int ans = dfs(n); if (n % 2 == 0) { long long int ans2 = dfs2(n / 2); ans += sel(ans2, 2); if (ans >= MOD) ans %= MOD; } printf("%lld\n", ans); return 0; }
#include <bits/stdc++.h> using namespace std; int n, d, mod, inv[15], f[1005], comp[1005][15], dp[1005][15][1005], g[1005][15]; inline void ch(int &x, int y) { x += y; if (x >= mod) x -= mod; } inline int sel(int k, int u) { if (~comp[k][u]) return comp[k][u]; int &ans = comp[k][u]; ans = 1; k = f[k]; for (int i = 1; i <= u; i++) ans = (long long)ans * inv[i] % mod; for (int i = k + u - 1; i >= k; i--) ans = (long long)ans * i % mod; return ans; } inline int exp(int x, int y) { int ans = 1; while (y) { if (y & 1) ans = (long long)ans * x % mod; x = (long long)x * x % mod; y >>= 1; } return ans; } void solve(int n) { memset(comp, -1, sizeof(comp)); f[1] = 1; dp[1][0][0] = 1; for (int k = 1; k <= n; k += d) { int typ = (k - 1) / d + 1; dp[1][0][typ] = 1; } for (int i = 2; i <= n; i++) { for (int j = 1; j <= d + 1; j++) for (int k = 1; k <= n; k += d) { int typ = (k - 1) / d + 1; for (int u = 0; u <= j && u * k < i; u++) ch(dp[i][j][typ], (long long)dp[i - u * k][j - u][typ - 1] * sel(k, u) % mod); } if ((i - 1) % d == 0) f[i] = dp[i][d][(n - 1) / d]; } } int main() { scanf("%d%d%d", &n, &d, &mod); if (n == 1) { puts("1"); return 0; } for (int i = 1; i <= d; i++) inv[i] = exp(i, mod - 2); d--; solve(n / 2); int ans = 0; if (n % 2 == 0) ch(ans, sel(n / 2, 2)); g[1][0] = 1; for (int i = 1; i <= (n - 1) / 2; i++) { if ((i - 1) % d != 0) continue; for (int j = n; j > 1; j--) for (int k = d + 1; ~k; k--) for (int u = 1; u <= k && u * i <= j; u++) ch(g[j][k], (long long)g[j - u * i][k - u] * sel(i, u) % mod); } ch(ans, g[n][d + 1]); printf("%d\n", ans); return 0; }
#include <bits/stdc++.h> #pragma GCC optimize("O2,Ofast,inline,unroll-all-loops,-ffast-math") #pragma GCC target("avx,sse2,sse3,sse4,popcnt") using namespace std; int n, d; long long f[1010][15][1010], g[1010][15], ifac[15], mod; template <class T> void read(T &x) { char ch = x = 0; bool fl = false; while (!isdigit(ch)) fl |= ch == '-', ch = getchar(); while (isdigit(ch)) x = x * 10 + ch - '0', ch = getchar(); x = fl ? -x : x; } long long pw(long long a, long long b) { long long ret = 1; while (b) { if (b & 1) ret = ret * a % mod; a = a * a % mod, b >>= 1; } return ret; } long long C(long long a, int b) { long long ret = ifac[b]; for (int i = 1; i <= b; i++) ret = ret * (a - i + 1) % mod; return ret; } int main() { read(n), read(d), read(mod); if (n <= 2) return puts("1"), 0; ifac[0] = 1; for (int i = 1; i <= d; i++) ifac[i] = ifac[i - 1] * pw(i, mod - 2) % mod; for (int i = 0; i <= n; i++) f[1][0][i] = 1; for (int i = 1; i <= d; i++) g[1][i] = 1; for (int i = 2; i <= n; i++) { for (int j = 1; j <= d; j++) { for (int k = 1; k <= n; k++) { f[i][j][k] = f[i][j][k - 1]; for (int l = 1; l <= min(j, i / k); l++) f[i][j][k] = (f[i][j][k] + f[i - l * k][j - l][k - 1] * g[k][l]) % mod; } } for (int j = 1; j <= d; j++) g[i][j] = C(f[i][d - 1][n] + j - 1, j); } long long ans = f[n][d][n / 2]; if (~n & 1) ans = (ans - f[n / 2][d - 1][n / 2] * (f[n / 2][d - 1][n / 2] - 1) / 2 % mod + mod) % mod; printf("%lld\n", ans); return 0; }
#include <bits/stdc++.h> using namespace std; inline void R(int &x) { x = 0; int f = 1; char ch = getchar(); while (ch < '0' || ch > '9') { if (ch == '-') f = -1; ch = getchar(); } while (ch >= '0' && ch <= '9') { x = x * 10 + ch - '0'; ch = getchar(); } x *= f; } void Redirect() { freopen(".in", "r", stdin); freopen(".out", "w", stdout); } int anc[5]; struct splay_node { int num, maxx, ls, rs, fath; bool lazy; } p[5]; struct lct { inline void _pushdown(int i) { p[i].lazy ^= 1; p[p[i].ls].lazy ^= 1; p[p[i].rs].lazy ^= 1; int t = p[i].ls; p[i].ls = p[i].rs; p[i].rs = t; } inline void _pushup(int i) { p[i].maxx = max(max(p[p[i].ls].maxx, p[p[i].rs].maxx), p[i].num); } inline void _zig(int i) { int j = p[i].fath, k; k = p[j].fath; if (k != 0 && j == p[k].ls) p[k].ls = i; else if (k != 0) p[k].rs = i; p[i].fath = k; p[j].fath = i; p[p[i].rs].fath = j; p[j].ls = p[i].rs; p[i].rs = j; anc[i] = anc[j]; p[i].maxx = p[j].maxx; _pushup(j); } inline void _zag(int i) { int j = p[i].fath, k; k = p[j].fath; if (k != 0 && j == p[k].ls) p[k].ls = i; else if (k != 0) p[k].rs = i; p[i].fath = k; p[j].fath = i; p[p[i].ls].fath = j; p[j].rs = p[i].ls; p[i].ls = j; anc[i] = anc[j]; p[i].maxx = p[j].maxx; _pushup(j); } void _splay(int i) { int j; while (p[i].fath != 0) { j = p[i].fath; if (p[p[j].fath].lazy == true) _pushdown(p[j].fath); if (p[j].lazy == true) _pushdown(j); if (p[i].lazy == true) _pushdown(i); if (p[j].fath == 0) { if (i == p[j].ls) _zig(i); else _zag(i); } else if (j == p[p[j].fath].ls) { if (i == p[j].ls) _zig(j), _zig(i); else _zag(i), _zig(i); } else { if (i == p[j].rs) _zag(j), _zag(i); else _zig(i), _zag(i); } } } int _find_max(int i) { while (i != 0) { if (p[i].lazy == true) _pushdown(i); if (p[i].ls != 0 && p[i].maxx == p[p[i].ls].maxx) i = p[i].ls; else if (p[i].maxx == p[i].num) return i; else i = p[i].rs; } return i; } void _access(int i) { int j = 0; while (i != 0) { _splay(i); if (p[i].lazy == true) _pushdown(i); if (p[i].rs != 0) { p[p[i].rs].fath = 0; anc[p[i].rs] = i; } p[i].rs = j; p[j].fath = i; _pushup(i); j = i; i = anc[i]; } } void _setroot(int i) { _access(i); _splay(i); p[i].lazy ^= 1; } } T; int n, d, MOD; const int MAXN = 1010; const int MAXD = 11; int dp[MAXN][MAXN][MAXD]; int Inv[MAXN]; inline void update(int &a, int b) { a += b; if (a >= MOD) a -= MOD; } int qpow(int a, int b) { int tmp = a, ret = 1; for (; b; b >>= 1, tmp = 1LL * tmp * tmp % MOD) { if (b & 1) ret = 1LL * ret * tmp % MOD; } return ret; } void Init() { for (int i = 1; i <= 1000; i++) { Inv[i] = qpow(i, MOD - 2); } } int f[MAXN]; void DP() { f[1] = 1; dp[0][0][0] = 1; for (int j = 0; j <= d; j += 1) { dp[1][j][j] = 1; } for (int i = 2; 2 * i <= n; ++i) { f[i] = dp[i - 1][i - 1][d - 1]; for (int k = 0; k <= d; k += 1) { for (int j = 0; j <= n; j += 1) { if (dp[i - 1][j][k]) { long long temp = dp[i - 1][j][k]; for (int mt = 0; j + i * mt <= n && mt + k <= d && temp; ++mt) { update(dp[i][j + i * mt][mt + k], temp); temp = temp * (f[i] + mt) % MOD * Inv[mt + 1] % MOD; } } } } } } void Solve() { if (n < 3) { cout << "1\n"; exit(0); } else if (n % 2 == 1) { cout << dp[n / 2][n - 1][d] << endl; } else { long long ans = dp[n / 2 - 1][n - 1][d]; long long naive = f[n / 2]; naive = (naive + 1) * naive % MOD * Inv[2] % MOD; ans += naive; ans %= MOD; cout << ans << endl; } } int main() { R(n); R(d); R(MOD); Init(); DP(); Solve(); }
#include <bits/stdc++.h> using namespace std; template <class T> inline void read(T &x) { x = 0; char c = getchar(); int f = 1; while (!isdigit(c)) { if (c == '-') f = -1; c = getchar(); } while (isdigit(c)) { x = x * 10 + c - '0'; c = getchar(); } x *= f; } template <class T> inline void umin(T &x, T y) { x = x < y ? x : y; } template <class T> inline void umax(T &x, T y) { x = x > y ? x : y; } inline unsigned int R() { static unsigned int seed = 416; return seed ^= seed >> 5, seed ^= seed << 17, seed ^= seed >> 13; } const int N = 1234; int n, d, mo, dp[N], f[N][N][11], inv[N]; int power(int a, int n) { int res = 1; while (n) { if (n & 1) res = 1LL * res * a % mo; a = 1LL * a * a % mo; n >>= 1; } return res; } inline int calc(int tot, int c, int now) { return tot == 0 ? (c == 0) : now; } inline void add(int &x, int y) { x = x + y < mo ? x + y : x + y - mo; } int main() { read(n); read(d); read(mo); int mx = N - 1; if (n == 1) { puts("1"); return 0; } inv[1] = 1; for (register int i = (2); i <= (N - 1); i++) inv[i] = 1LL * (mo - mo / i) * inv[mo % i] % mo; f[0][0][0] = 1; for (register int i = (1); i <= (n); i++) { dp[i] = f[i - 1][i - 1][d - 1]; if (i == 1) dp[i] = 1; for (register int j = (0); j <= (n); j++) for (register int k = (0); k <= (d); k++) if (f[i - 1][j][k]) for (int c = 0, now = 1; k + c <= d && j + i * c <= n; c++) { add(f[i][j + i * c][k + c], 1LL * f[i - 1][j][k] * calc(dp[i], c, now) % mo); now = 1LL * now * (dp[i] + c) % mo * inv[c + 1] % mo; } } printf("%d", ((n % 2 == 0 ? 1LL * (dp[n / 2] + 1) * dp[n / 2] / 2 % mo : 0) + f[(n - 1) / 2][n - 1][d]) % mo); return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 1005; const int M = 12; long long MOD; long long dp[N][M][N]; long long curCom[M]; long long inv2[M]; long long inv1[M]; inline long long mypow(long long a, long long b) { int res = 1; while (b) { if (b & 1) { res = ((long long)res * a) % MOD; } a = ((long long)a * a) % MOD; b >>= 1; } return res; } inline long long cmb(long long a, long long b) { long long d1, d2; if (a < b) { return 0; } d1 = 1; d2 = inv2[b]; while (b) { d1 = (long long)d1 * a % MOD; b--; a--; } return (long long)d1 * d2 % MOD; } void calCurCom(long long n, int m) { memset(curCom, 0, sizeof(curCom)); if (n = 0) { return; } int i, j; long long d1, d2; long long tmp = n + m - 1; for (i = m; i >= 1; i--, tmp--) { inv1[i] = mypow(tmp, MOD - 2); } d1 = d2 = 1; } int main() { int n, d, i, j, k, l; scanf("%d%d%lld", &n, &d, &MOD); if (n <= 2) { printf("1\n"); return 0; } long long tmp = 1; inv1[0] = 1; inv2[1] = 1; for (i = 2; i <= d; i++) { tmp = tmp * i; inv2[i] = mypow(tmp, MOD - 2); } for (k = 0; k <= n; k++) { dp[1][0][k] = 1; } for (i = 2; i <= d + 1; i++) { for (k = 1; k <= n; k++) { dp[i][i - 1][k] = 1; } } for (i = 3; i <= n; i++) { for (j = 1; j <= d && j < i - 1; j++) { for (k = 2; k <= n - 1; k++) { dp[i][j][k] = dp[i][j][k - 1]; for (l = 1; l <= j && l * k < i; l++) { tmp = (long long)dp[i - k * l][j - l][k - 1] * cmb(dp[k][d - 1][k - 1] + l - 1, l) % MOD; dp[i][j][k] = ((long long)dp[i][j][k] + tmp) % MOD; } } } } long long ans = 0; ans = dp[n][d][(n + 1) / 2 - 1]; if ((n & 1) == 0) { ans = ((long long)ans + cmb(dp[n / 2][d - 1][n / 2 - 1] + 1, 2)) % MOD; } printf("%lld\n", ans); return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 1005, M = 12; int n, d, P, f[N][M][N / 2], ifc[N]; int C(int n, int m) { if (n < m) return 0; int res = 1; for (int i = n; i > n - m; --i) res = 1LL * res * i % P; return 1LL * res * ifc[m] % P; } int main() { scanf("%d%d%d", &n, &d, &P), ifc[1] = 1; if (n <= 2) return puts("1"), 0; for (int i = 2; i <= n; ++i) ifc[i] = 1LL * (P - P / i) * ifc[P % i] % P; for (int i = 2; i <= n; ++i) ifc[i] = 1LL * ifc[i] * ifc[i - 1] % P; for (int i = 0; i <= n / 2; ++i) f[1][0][i] = 1; f[1][d - 1][0] = 1; for (int i = 2; i <= n; ++i) for (int j = 1; j <= min(d, i - 1); ++j) for (int k = 1; k <= n / 2; ++k) { f[i][j][k] = f[i][j][k - 1]; for (int t = 1; t * k <= i && t <= j; ++t) (f[i][j][k] += 1LL * f[i - t * k][j - t][k - 1] * C(f[k][d - 1][k - 1] + t - 1, t) % P) %= P; } if (n & 1) printf("%d", f[n][d][n / 2]); else printf("%d", (f[n][d][n / 2] + P - C(f[n / 2][d - 1][n / 2 - 1], 2)) % P); return 0; }
#include <bits/stdc++.h> using namespace std; int n, m; long long P; long long ine[1010]; int f[1010][11][1010]; long long DP(int n, int d, int k) { k = min(k, n - 1); if (f[n][d][k] != -1) return f[n][d][k]; if ((n == 1 && d == m - 1) || (n == 1 && !d)) return 1; if (n == 1 || !k) return 0; int j; long long ret = DP(n, d, k - 1), t = DP(k, m - 1, k), tmp = 1; for (j = 1; j * k < n && j <= d; j++) { tmp = tmp * (t + j - 1) % P * ine[j] % P; ret = (ret + tmp * DP(n - k * j, d - j, k - 1)) % P; } return f[n][d][k] = ret; } int main() { scanf("%d%d%lld", &n, &m, &P); if (n == 1 || n == 2) { puts("1"); return 0; } if ((n - 2) % (m - 1) != 0) { puts("0"); return 0; } int i; ine[0] = ine[1] = 1; for (i = 2; i <= n; i++) ine[i] = P - (P / i) * ine[P % i] % P; memset(f, -1, sizeof(f)); long long ans = DP(n, m, (n - 1) / 2); if (!(n & 1)) { long long t = DP(n / 2, m - 1, n / 2 - 1); ans = (ans + t * (t + 1) / 2) % P; } printf("%lld", ans); return 0; }
#include <bits/stdc++.h> const int N = 1e3 + 100; const int D = 12; int n; int d; int mod; void init() { std::cin >> n; std::cin >> d; std::cin >> mod; } int inverse(int x, int mod) { if (x == 1) { return 1; } else { return (long long)(mod - mod / x) * inverse(mod % x, mod) % mod; } } int comb(int r, int k) { static int inv[D]; int result = 1; for (int i = 1; i <= k; i++) { result = (long long)result * (r - i + 1) % mod; if (inv[i] == 0) { inv[i] = inverse(i, mod); } result = (long long)result * inv[i] % mod; } return result; } void update(int &x, int y) { x = (x + y) % mod; } void work() { if (n <= 2) { std::cout << 1 % mod << std::endl; return; } static int f[N][D][N]; std::memset(f, 0, sizeof(f)); f[1][0][0] = 1; for (int i = 1; i <= n; i++) { for (int j = 0; j <= d; j++) { for (int k = 0; k <= n / 2; k++) { if (k > 0) { update(f[i][j][k], f[i][j][k - 1]); for (int t = 1; t * k < i && t <= j; t++) { if (k == 1) { update(f[i][j][k], f[i - t * k][j - t][k - 1]); } else if (f[i - t * k][j - t][k - 1] != 0) { update(f[i][j][k], (long long)f[i - t * k][j - t][k - 1] * comb(f[k][d - 1][k - 1] + t - 1, t) % mod); } } } } } } int answer = f[n][d][(n - 1) / 2]; if (n % 2 == 0) { answer += comb(f[n / 2][d - 1][n / 2 - 1] + 1, 2); answer %= mod; } std::cout << answer << std::endl; } int main() { init(); work(); return 0; }
#include <bits/stdc++.h> using namespace std; inline char gc() { static char buf[100000], *p1 = buf, *p2 = buf; return p1 == p2 && (p2 = (p1 = buf) + fread(buf, 1, 100000, stdin), p1 == p2) ? EOF : *p1++; } inline long long read() { char c = getchar(); long long tot = 1; while ((c < '0' || c > '9') && c != '-') c = getchar(); if (c == '-') { tot = -1; c = getchar(); } long long sum = 0; while (c >= '0' && c <= '9') { sum = sum * 10 + c - '0'; c = getchar(); } return sum * tot; } inline void wr(long long x) { if (x < 0) { putchar('-'); wr(-x); return; } if (x >= 10) wr(x / 10); putchar(x % 10 + '0'); } inline void wrn(long long x) { wr(x); putchar('\n'); } inline void wri(long long x) { wr(x); putchar(' '); } inline void wrn(long long x, long long y) { wri(x); wrn(y); } inline void wrn(long long a, long long b, long long c) { wri(a); wrn(b, c); } long long n, m, d, inv[500055], mod, ans; long long f[1005][11][505]; inline void add(long long &x, long long k) { x += k; x -= (x >= mod) ? mod : 0; x += (x < 0) ? mod : 0; } void init(long long x) { inv[0] = inv[1] = 1; for (long long i = (2); i <= (n); i++) inv[i] = mod - 1LL * (mod / i) * inv[mod % i] % mod; } inline long long dp(long long n, long long d, long long k) { k = min(k, n - 1); if (f[n][d][k] != -1) return f[n][d][k]; if ((n == 1 && d == m - 1) || (n == 1 && !d)) return f[n][d][k] = 1; if (n == 1 || !k) return f[n][d][k] = 0; long long t = dp(k, m - 1, k); f[n][d][k] = dp(n, d, k - 1); long long num = 1; for (long long i = (1); i <= (min((n - 1) / k, d)); i++) { num = 1LL * num * (t + i - 1) % mod * inv[i] % mod; add(f[n][d][k], dp(n - k * i, d - i, k - 1) * num % mod); } return f[n][d][k]; } signed main() { n = read(); m = read(); mod = read(); init(n); if (n == 1 || n == 2) { return puts("1"), 0; } if ((n - 2) % (m - 1) != 0) return puts("0"), 0; ; memset(f, -1, sizeof(f)); ans = dp(n, m, (n - 1) / 2); if (n % 2 == 0) { long long t = dp(n / 2, m - 1, n / 2 - 1); add(ans, 1LL * t * (t + 1) / 2 % mod); } wrn(ans); return 0; }
#include <bits/stdc++.h> #pragma GCC optimize("Ofast") using namespace std; const long double eps = 1e-7; const int inf = 1000000010; const long long INF = 10000000000000010LL; const int MAXN = 1110, LOG = 20; long long n, m, k, d, x, y, t, a, b, mod; long long dp[MAXN][MAXN][11]; long long F[MAXN]; long long I[MAXN]; long long inv[MAXN]; long long powmod(long long a, long long b) { if (!b) return 1; if (b & 1) return a * powmod(a * a % mod, b >> 1) % mod; return powmod(a * a % mod, b >> 1); } long long C(long long n, long long r) { if (r > n || r < 0) return 0; if (n < MAXN) return (F[n] * I[r] % mod) * I[n - r] % mod; long long res = 1; r = min(r, n - r); for (int i = 1; i <= r; i++) res = res * ((n - i + 1) * inv[i] % mod) % mod; return res; } int main() { ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); cin >> n >> d >> mod; if (n <= 2 || d == 2) return cout << 1 << '\n', 0; F[0] = inv[0] = 1; for (int i = 1; i < MAXN; i++) F[i] = F[i - 1] * i % mod; I[MAXN - 1] = powmod(F[MAXN - 1], mod - 2); for (int i = MAXN - 1; i; i--) I[i - 1] = I[i] * i % mod; for (int i = 1; i < MAXN - 1; i++) inv[i] = I[i] * F[i - 1] % mod; for (int i = 0; i <= n; i++) dp[0][i][0] = dp[1][i][0] = dp[1][i][d - 1] = 1; for (int i = 2; i <= n; i++) for (int j = 1; j <= n; j++) for (int k = 1; k <= d; k++) { dp[i][j][k] = dp[i][j - 1][k]; for (int t = 1; t <= k; t++) if (i - t * j > 0) dp[i][j][k] += dp[i - t * j][j - 1][k - t] * C(dp[j][n / 2][d - 1] + t - 1, t) % mod; dp[i][j][k] %= mod; } long long ans = dp[n][n / 2 - 1][d]; if (n % 2 == 0) ans = (ans + C(dp[n / 2][n / 2][d - 1] + 1, 2)) % mod; cout << ans << '\n'; return 0; }
#include <bits/stdc++.h> using namespace std; const int MAXN = 1005; long long n, d, Mod, ans, f[MAXN][12], g[MAXN], inv[MAXN]; int main() { scanf("%lld%lld%lld", &n, &d, &Mod); if (n <= 2) { puts("1"); return 0; } if ((n - 2) % (d - 1)) { puts("0"); return 0; } inv[0] = inv[1] = 1; for (register int i = 2; i <= n; ++i) inv[i] = 1LL * (Mod - Mod / i) * inv[Mod % i] % Mod; for (register int i = 2; i <= n; ++i) inv[i] = 1LL * inv[i] * inv[i - 1] % Mod; g[1] = f[0][0] = 1; for (register int i = 1; i <= (n >> 1); ++i) { for (register int j = n - i; j >= 0; --j) for (register int p = 0; p < d; ++p) if (f[j][p]) { register long long w = 1; for (register int q = 1; p + q <= d && j + q * i <= n; ++q) { (w *= g[i] + q - 1) %= Mod; f[j + q * i][p + q] = (f[j + q * i][p + q] + 1LL * w * inv[q] % Mod * f[j][p] % Mod) % Mod; } } g[i + 1] = f[i][d - 1]; } ans = f[n - 1][d]; if (n & 1 ^ 1) (ans += Mod - (g[n >> 1] * (g[n >> 1] - 1) >> 1) % Mod) %= Mod; printf("%lld\n", ans); return 0; }
#include <bits/stdc++.h> using namespace std; int n, m; int mod; int read() { char ch = getchar(); int x = 0, f = 1; for (; ch < '0' || ch > '9'; ch = getchar()) if (ch == '-') f = -1; for (; ch >= '0' && ch <= '9'; ch = getchar()) x = 10 * x + (ch - 48); return x; } int ksm(int x, int k) { int res = 1; for (; k; k >>= 1) { if (k & 1) res = 1ll * res * x % mod; x = 1ll * x * x % mod; } return res; } int kss[100100]; int ks(int x) { if (kss[x]) return kss[x]; return kss[x] = ksm(x, mod - 2); } int C(int n, int m) { if (n < m) return 0; int res = 1; for (int i = 1; i <= m; i++) res = 1ll * res * (n - i + 1) % mod * ks(i) % mod; return res; } int f[1010][12][510]; int main() { n = read(); m = read(); mod = read(); if (n <= 2) { printf("1"); return 0; } for (int i = 0; i <= n / 2; i++) f[1][0][i] = 1; f[1][m - 1][0] = 1; for (int i = 2; i <= n; i++) for (int j = 1; j <= m; j++) for (int k = 1; k <= n / 2; k++) { f[i][j][k] = f[i][j][k - 1]; for (int t = 1; t * k < i && t <= j; t++) f[i][j][k] = (f[i][j][k] + 1ll * f[i - t * k][j - t][k - 1] * C(f[k][m - 1][k - 1] + t - 1, t) % mod) % mod; } if (n & 1) printf("%d", f[n][m][n / 2]); else printf("%d", (f[n][m][n / 2] - C(f[n / 2][m - 1][n / 2 - 1], 2) + mod) % mod); return 0; }
#include <bits/stdc++.h> using namespace std; const int maxn = 1005, maxd = 15; int f[maxn], g[maxn][maxd][maxn], rfac[maxn], n, d, mo; int pow(int a, int b) { int tmp = 1; for (; b; b >>= 1, a = a * 1ll * a % mo) if (b & 1) tmp = tmp * 1ll * a % mo; return tmp; } int main() { cin >> n >> d >> mo; if (n == 1) { cout << 1 << endl; return 0; } rfac[0] = 1; for (int i = 1; i <= 1000; i++) rfac[i] = rfac[i - 1] * 1ll * pow(i, mo - 2) % mo; for (int i = 0; i <= n; i++) g[0][0][i] = 1; for (int i = 1; i <= n; i++) { if (i != 1) f[i] = g[i - 1][d - 1][n]; else f[i] = 1; for (int dd = 1; dd <= d; dd++) { for (int x = 1; x <= n / 2; x++) { int v = f[x]; for (int k = 1, cv = 1; k <= dd && x * k <= i; k++) { cv = cv * 1ll * (v + k - 1) % mo; g[i][dd][x] = (g[i][dd][x] + g[i - x * k][dd - k][x - 1] * 1ll * cv % mo * rfac[k] % mo) % mo; } } for (int x = 1; x <= n; x++) g[i][dd][x] = (g[i][dd][x] + g[i][dd][x - 1]) % mo; } } int ans = g[n - 1][d][(n - 1) / 2]; if (!(n & 1)) { int v = f[n / 2]; ans = (ans + v * 1ll * (v + 1) % mo * rfac[2] % mo) % mo; } cout << ans << endl; }
#include <bits/stdc++.h> using namespace std; long long n, d, ans = 0, mod, f[1010][20][1010], c[1010][20], inv[20]; long long qpow(long long a, long long b) { long long ans = 1, k = a; while (b) { if (b & 1) ans = ans * k % mod; k = k * k % mod; b >>= 1; } return ans; } int main() { scanf("%lld%lld%lld", &n, &d, &mod); inv[0] = 1; for (int i = 1; i <= n; i++) inv[i] = qpow(i, mod - 2); for (int i = 0; i <= n; i++) f[1][0][i] = 1; for (int i = 1; i <= d; i++) c[1][i] = 1; for (int i = 2; i <= n; i++) { for (int j = 1; j <= d; j++) { for (int k = 1; k < i; k++) for (int l = 1; l <= j && l * k <= i; l++) f[i][j][k] = (f[i][j][k] + f[i - l * k][j - l][k - 1] * c[k][l]) % mod; for (int k = 1; k <= n; k++) f[i][j][k] = (f[i][j][k] + f[i][j][k - 1]) % mod; } c[i][1] = f[i][d - 1][n]; for (int j = 2; j <= d; j++) c[i][j] = c[i][j - 1] * (f[i][d - 1][n] + j - 1) % mod * inv[j] % mod; } if (n <= 2) ans = 1; else ans = f[n][d][n / 2]; if (n > 2 && !(n & 1)) ans = (ans - (f[n / 2][d - 1][n / 2] - 1) * f[n / 2][d - 1][n / 2] % mod * inv[2] % mod + mod) % mod; printf("%lld\n", ans); }
#include <bits/stdc++.h> using namespace std; int n, d, p, dp[1003][13][1003], jc[13], iv[13]; bool ok[1003][13][1003]; inline int qpow(int x, int y) { int z = 1; for (; y; y >>= 1, x = (long long)x * x % p) if (y & 1) z = (long long)z * x % p; return z; } inline int cbn(int x, int y) { int z = 1; for (register int i = x - y + 1; i <= x; ++i) z = (long long)z * i % p; return z = (long long)z * iv[y] % p; } int dfs(int a, int b, int c) { if (a == 1) return b == d - 1 || b == 0; if (b == 0) return 0; if (c == 0) return 0; if (ok[a][b][c]) return dp[a][b][c]; int res = 0; ok[a][b][c] = 1; res = dfs(a, b, c - 1); for (register int i = 1; i <= b && i * c < a; ++i) res = (res + (long long)dfs(a - i * c, b - i, c - 1) * cbn(dfs(c, d - 1, c - 1) + i - 1, i)) % p; return dp[a][b][c] = res; } int main() { scanf("%d%d%d", &n, &d, &p); if (n <= 2) { puts("1"); return 0; } jc[0] = 1; for (register int i = 1; i <= d; ++i) jc[i] = (long long)jc[i - 1] * i % p; iv[d] = qpow(jc[d], p - 2); for (register int i = d - 1; i >= 0; --i) iv[i] = (long long)iv[i + 1] * (i + 1) % p; int ans = dfs(n, d, n - 1 >> 1); if (!(n & 1)) (ans += cbn(dfs(n >> 1, d - 1, (n >> 1) - 1) + 1, 2)) %= p; if (ans < 0) ans += p; printf("%d", ans); return 0; }
#include <bits/stdc++.h> using namespace std; int mod; void sadd(int &a, int b) { a += b; if (a >= mod) a -= mod; } int add(int a, int b) { sadd(a, b); return a; } int mul(int a, int b) { return (a * 1LL * b) % mod; } void smul(int &a, int b) { a = mul(a, b); } int fpow(int x, int n) { if (n == 0) return 1; int a = fpow(x, n >> 1); smul(a, a); if (n & 1) smul(a, x); return a; } int rev(int x) { return fpow(x, mod - 2); } int _div(int a, int b) { return mul(a, rev(b)); } void sdiv(int &a, int b) { smul(a, rev(b)); } const int N = 1005; const int D = 11; int n, d; int dpTree[N][D]; int dpForestEq[D][N]; int dpForest[N][D][N]; int getTree(int v, int rd); int getForest(int vs, int rs, int md); int getForestEq(int cnt, int vone); int C(int a, int b) { int ans = 1; for (int i = 0; i < b; i++) { smul(ans, (a - i + mod) % mod); sdiv(ans, i + 1); } 42; return ans; } int place(int cnt, int diff) { return C(cnt - 1, diff - 1); } int getSplit(int k, int cnt) { if (cnt == 0) return 1; int ans = 0; for (int diff = 1; diff <= min(cnt, k); diff++) sadd(ans, mul(C(k, diff), place(cnt, diff))); 42; return ans; } int getForestEq(int cnt, int vone) { 42; int &ans = dpForestEq[cnt][vone]; if (ans != -1) return ans; if (vone <= 0) return ans = 0; int k = ((cnt == 0) ? 1 : getTree(vone, d - 1)); ans = getSplit(k, cnt); 42; return ans; } int getForest(int vs, int rs, int md) { 42; int &ans = dpForest[vs][rs][md]; if (ans != -1) return ans; if (vs == 0 && rs == 0) return 1; if (md == 0) return 0; if (rs > vs) return 0; if (rs * md < vs) return 0; int curans = 0; for (int cnt = 0; cnt * md <= vs && cnt <= rs; cnt++) { sadd(curans, mul(getForest(vs - cnt * md, rs - cnt, md - 1), getForestEq(cnt, md))); } 42; return ans = curans; } int getTree(int vs, int rd) { 42; int &ans = dpTree[vs][rd]; if (ans != -1) return ans; if (vs == 0) return 0; ans = getForest(vs - 1, rd, (n - 1) / 2); 42; return ans; } int main(int, char **) { memset(dpForest, -1, sizeof dpForest); memset(dpForestEq, -1, sizeof dpForestEq); memset(dpTree, -1, sizeof dpTree); scanf("%d%d%d", &n, &d, &mod); dpTree[1][d] = 1; dpTree[1][d - 1] = 1; int ans = 0; sadd(ans, getTree(n, d)); if (n % 2 == 0) sadd(ans, getForestEq(2, n / 2)); printf("%d\n", ans); return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 1000 + 10, D = 15; int n, d, mod; int dp[D][N][N]; int ifac[N]; void Add(int &x, int y) { if ((x += y) >= mod && (x -= mod)) ; } int binom(int n, int m) { n %= mod; if (n < m) return 0; int pro = 1; for (int i = n; i >= n - m + 1; i--) pro = 1ll * pro * i % mod; pro = 1ll * pro * ifac[m] % mod; return pro; } int DP(int g, int n, int k) { if (dp[g][n][k] != -1) return dp[g][n][k]; int &res = dp[g][n][k]; if (n == 1) return res = 1; if (k == 0 || g == 0) return res = (n == 1 && g == 0); res = 0; Add(res, DP(g, n, k - 1)); if ((k - 1) % (d - 1)) return res; int f = DP(d - 1, k, k - 1); for (int i = 1; i <= g; i++) { if (i * k >= n) break; Add(res, 1ll * DP(g - i, n - k * i, k - 1) * binom(f + i - 1, i) % mod); } return res; } void quit(int x) { printf("%d\n", x), exit(0); } void initmath(int n) { ifac[0] = ifac[1] = 1; for (int i = 2; i <= n; i++) ifac[i] = 1ll * (mod - mod / i) * ifac[mod % i] % mod; for (int i = 1; i <= n; i++) ifac[i] = 1ll * ifac[i - 1] * ifac[i] % mod; return; } int calc(int g, int n, int k) { if (n == 1 || n == 2) return 1; if (n < g + 1) return 0; if ((n - g - 1) % (d - 1) != 0) return 0; return DP(g, n, k); } int main() { memset(dp, -1, sizeof(dp)); scanf("%d%d%d", &n, &d, &mod); if (n == 1 || n == 2) quit(1); if (n < d + 1) quit(0); if ((n - d - 1) % (d - 1) != 0) quit(0); initmath(d); if (n & 1) quit(calc(d, n, n / 2)); int ans = calc(d, n, n / 2); ans = (ans - binom(calc(d - 1, n / 2, n / 2 - 1), 2) + mod) % mod; quit(ans); return 0; }
#include <bits/stdc++.h> using namespace std; int N, d, mod, inv[12], dp[1009][1009][12]; int pow(int a, int b) { int p = 1; for (int i = 0; (1 << i) <= b; i++) { if (b & (1 << i)) p = (1LL * p * a) % mod; a = (1LL * a * a) % mod; } return p; } int main() { scanf("%d %d %d", &N, &d, &mod); if (N <= 2) { printf("1\n"); return 0; } for (int i = 0; i <= N; i++) dp[1][i][0] = dp[1][i][d - 1] = 1; for (int i = 1; i <= 10; i++) inv[i] = pow(i, mod - 2); for (int i = 1; i <= N; i++) for (int k = 1; k <= d; k++) { if ((i - k - 1) % (d - 1) != 0) continue; for (int j = 1; j <= N; j++) { dp[i][j][k] = dp[i][j - 1][k]; if (j > i) continue; int val = dp[j][j][d - 1], curr = 1; for (int p = 1; p <= k && j * p <= i; p++) { curr = (1LL * curr * (val + p - 1)) % mod; curr = (1LL * curr * inv[p]) % mod; dp[i][j][k] = ((long long)dp[i][j][k] + 1LL * curr * dp[i - j * p][j - 1][k - p]) % mod; } } } int ans = dp[N][N / 2][d]; if (N % 2 == 0) { ans = dp[N][N / 2 - 1][d]; int val = dp[N / 2][N / 2][d - 1]; val = (1LL * val * (val + 1)) % mod; val = (1LL * val * inv[2]) % mod; ans += val; if (ans >= mod) ans -= mod; } printf("%d\n", ans); return 0; }
#include <bits/stdc++.h> long long f[1001][11][1001], p, v[20]; int n, d; long long q(long long a, int t) { long long x = 1; while (t) { if (t & 1) x = x * a % p; a = a * a % p; t >>= 1; } return x; } long long c(long long a, long long b) { long long x = 1; for (int i = a - b + 1; i <= a; i++) x = x * i % p; for (int i = 1; i <= b; i++) x = x * v[i] % p; return x; } long long ff(int i, int j, int k) { if (k == 0) f[i][j][k] = 0; if (i == 1 && j == 0 && k == 0) f[i][j][k] = 1; if (i == j + 1 && k == 1) f[i][j][k] = 1; if (f[i][j][k] != -1) return f[i][j][k]; else f[i][j][k] = 0; for (int t = 0; t <= j && t * k <= i; t++) { f[i][j][k] += ff(i - t * k, j - t, k - 1) * c(ff(k, d - 1, k - 1) + t - 1, t); f[i][j][k] %= p; } return f[i][j][k]; } int main() { int i, j, k, t; long long s, r; scanf("%d%d%I64d", &n, &d, &p); if (n <= 2) { printf("1"); return 0; } if ((n - 2) % (d - 1)) { printf("0"); return 0; } for (i = 1; i <= d; i++) v[i] = q(i, p - 2); memset(f, 0xFF, sizeof(f)); s = ff(n, d, (n - 1) / 2); r = ff(n / 2, d - 1, n / 2 - 1); if (n % 2 == 0) s += r * (r + 1) / 2, s %= p; printf("%I64d", s); return 0; }
#include <bits/stdc++.h> using namespace std; inline long long read() { register long long x = 0, f = 1; char ch = getchar(); while (!isdigit(ch)) { if (ch == '-') f = -1; ch = getchar(); } while (isdigit(ch)) { x = (x << 3) + (x << 1) + ch - '0'; ch = getchar(); } return (f == 1) ? x : -x; } inline void file() { freopen(".in", "r", stdin); freopen(".out", "w", stdout); } long long ljc, n, D, f[1010][11][1010], _inv[1010], inv[1010], fac[1010]; inline long long getC(long long n, long long m) { if (n < m) return 0; long long _ = 1; for (long long i = 0; i < m; i++) _ = _ * (n - i) % ljc; _ = _ * _inv[m] % ljc; return _; } inline void add(long long &a, const long long &b) { a += b; a %= ljc; } signed main() { n = read(), D = read(), ljc = read(); if (n <= 2) { puts("1"); return 0; } fac[0] = inv[0] = inv[1] = _inv[0] = 1; for (long long i = 1; i <= 100; i++) fac[i] = fac[i - 1] * i % ljc; for (long long i = 2; i <= 100; i++) inv[i] = (ljc - inv[ljc % i] * (ljc / i) % ljc) % ljc; for (long long i = 1; i <= 100; i++) _inv[i] = _inv[i - 1] * inv[i] % ljc; for (int i = 0; i <= n; i++) f[1][0][i] = 1; for (int i = 2; i <= n; i++) { for (int j = 0; j <= D; j++) { for (int k = 1; k <= n; k++) { f[i][j][k] = f[i][j][k - 1]; for (int l = 1; l <= j; l++) { if (i < l * k) break; if (k > 1) add(f[i][j][k], f[i - l * k][j - l][k - 1] * getC(f[k][D - 1][k - 1] + l - 1, l) % ljc); else add(f[i][j][k], f[i - l * k][j - l][k - 1] * getC(f[k][0][k - 1] + l - 1, l) % ljc); } } } } if (n & 1) { cout << f[n][D][n / 2]; } else { cout << (f[n][D][n / 2] - getC(f[n / 2][D - 1][n / 2 - 1], 2) + ljc) % ljc; } return 0; }
#include <bits/stdc++.h> using namespace std; const long long N = 1010, D = 15; long long n, d, mod; long long dp[N][D][N]; long long fac[N]; long long qpow(long long a, long long b) { long long ans = 1; while (b) { if (b & 1) ans = ans * a % mod; a = a * a % mod; b >>= 1; } return ans; } void sovle_fac() { fac[0] = 1; for (long long i = 1; i <= d + 3; i++) fac[i] = (fac[i - 1] * i) % mod; for (long long i = 0; i <= d + 3; i++) fac[i] = qpow(fac[i], mod - 2) % mod; } long long C(long long a, long long b) { if (b > a) return 0; long long ret = 1; for (int i = 1; i <= b; i++) ret = ret * (a - i + 1) % mod; return ret * fac[b] % mod; } int main() { scanf("%lld %lld %lld", &n, &d, &mod); if (n <= 2) { cout << 1; return 0; } sovle_fac(); for (long long i = 0; i <= n; i++) dp[1][0][i] = 1; for (long long i = 2; i <= n; i++) { for (long long j = 1; j < i && j <= d; j++) { for (long long k = 1; k <= n; k++) { dp[i][j][k] = dp[i][j][k - 1]; for (long long t = 1; t <= j && t * k < i; t++) { dp[i][j][k] += (dp[i - t * k][j - t][k - 1] * C(dp[k][(k <= 1) ? (0) : (d - 1)][k - 1] + t - 1, t) % mod) % mod; dp[i][j][k] %= mod; } } } } long long ans = dp[n][d][n / 2]; if (n % 2 == 0) { ans = (ans - C(dp[n / 2][d - 1][(n / 2) + 1], 2) + mod) % mod; } cout << ans << endl; }
#include <bits/stdc++.h> const int N = 1005; int f[N][15][N], n, d, i, j, mo, k, l, inv[N]; inline int C(int x, int y) { if (x < y) return 0; register int ans = 1, i = 1; for (; i <= y; ++i) ans = 1ll * ans * inv[i] % mo * (x - i + 1) % mo; return ans; } int main() { scanf("%d%d%d", &n, &d, &mo); if (n <= 2) return puts("1"), 0; for (i = 2, inv[1] = 1; i <= d; ++i) inv[i] = 1ll * (mo - mo / i) * inv[mo % i] % mo; for (i = 0; i <= n; ++i) f[1][0][i] = 1; for (i = 2; i <= n; ++i) for (j = 1; j < i && j <= d; ++j) for (k = 1; k <= n; ++k) { f[i][j][k] = f[i][j][k - 1]; for (l = 1; l * k < i && l <= j; ++l) f[i][j][k] = (f[i][j][k] + 1ll * f[i - k * l][j - l][k - 1] * C(f[k][k > 1 ? d - 1 : 0][k - 1] + l - 1, l)) % mo; } j = f[n][d][n >> 1]; if (!(n & 1)) j = (j + mo - C(f[n >> 1][d - 1][n >> 1], 2)) % mo; return printf("%d\n", j), 0; }
#include <bits/stdc++.h> using namespace std; int n, d, mod; int sum(int a, int b) { int s = a + b; if (s >= mod) s -= mod; return s; } int sub(int a, int b) { int s = a - b; if (s < 0) s += mod; return s; } int mult(int a, int b) { return (1LL * a * b) % mod; } int pw(int a, int b) { if (b == 0) return 1; if (b & 1) return mult(a, pw(a, b - 1)); int res = pw(a, b / 2); return mult(res, res); } const int maxN = 1005; const int maxD = 12; int c[maxN][maxD]; int val[maxN]; int invfact[maxN]; int ways[maxN]; void init() { for (int i = 0; i <= n; i++) { val[i] = (d - 1) * i + 1; } for (int i = 0; i <= d; i++) { invfact[i] = 1; if (i > 0) { invfact[i] = mult(invfact[i - 1], pw(i, mod - 2)); } } } void calcC(int k) { int mlt = 1; c[k][0] = 1; for (int i = 1; i <= d; i++) { mlt = mult(mlt, ways[k] + i - 1); c[k][i] = mult(mlt, invfact[i]); } } int dp[maxN][maxN][maxD]; int main() { ios_base::sync_with_stdio(false); cin >> n >> d >> mod; if (n <= 2) { cout << 1; return 0; } if ((n - 2) % (d - 1) != 0) { cout << 0; return 0; } int need = (n - 2) / (d - 1); init(); ways[0] = 1; for (int i = 0; i <= d; i++) { dp[0][0][i] = 1; } for (int i = 1; i < need; i++) { ways[i] = dp[i - 1][i - 1][d - 1]; calcC(i); for (int have = 0; have < need; have++) { for (int cnt = 0; cnt <= d; cnt++) { for (int take = 0; take <= cnt && take * i <= have; take++) { dp[i][have][cnt] = sum(dp[i][have][cnt], mult(dp[i - 1][have - take * i][cnt - take], c[i][take])); } } } } int at_most = 0; for (at_most = 0;; at_most++) { if (1 + at_most * (d - 1) > n / 2) { at_most--; break; } } int ans = dp[at_most][need - 1][d]; if (n % 2 == 0) { for (int p = 0;; p++) { if (1 + p * (d - 1) == n / 2) { int all = ways[p]; ans = sub(ans, mult((mod + 1) / 2, mult(all, sub(all, 1)))); } if (1 + p * (d - 1) > n / 2) break; } } cout << ans; return 0; }
#include <bits/stdc++.h> using namespace std; int n, d; long long int modulo; int n2; long long int eleva(long long int b, long long int e) { if (e == 0) return 1; if (e % 2 == 0) return eleva(b * b % modulo, e / 2); return b * eleva(b * b % modulo, e / 2) % modulo; } long long int inverso(long long int x) { return eleva(x, modulo - 2); } void anyade(long long int &a, long long int b) { a = (a + b) % modulo; } bool puede(int n) { if (n == 0) return false; return (n - 1) % (d - 1) == 0; } long long int elecciones(int n, int ndown, int a); long long int memmaner[1001]; int calcul[1001]; long long int maner(int n) { if (n == 1) return 1; long long int &mem = memmaner[n]; if (calcul[n]) return mem; calcul[n] = 1; mem = elecciones(n - 1, n - 1, d - 1); return mem; } long long int memcombi[1001][11]; long long int calccombi[1001][11]; long long int combi(int n, int a) { long long int &mem = memcombi[n][a]; if (calccombi[n][a]) return mem; calccombi[n][a] = 1; if (a == 0) { mem = 1; return mem; } if (not puede(n)) return mem; long long int man = maner(n) - 1 + a; long long int num = 1; long long int div = 1; for (int i = 1; i <= a; i++) { num = num * (man - i + 1) % modulo; div = div * i % modulo; } mem = num * inverso(div) % modulo; return mem; } long long int memelecciones[1001][1001][11]; int calcelec[1001][1001][11]; long long int elecciones(int n, int ndown, int a) { if (a == 0) return n == 0; if (n == 0 or ndown == 0) return 0; long long int &mem = memelecciones[n][ndown][a]; if (calcelec[n][ndown][a]) return mem; calcelec[n][ndown][a] = 1; for (int aa = 0, suma = 0; aa <= a and suma <= n; aa++, suma += ndown) anyade(mem, combi(ndown, aa) * elecciones(n - suma, min(n - suma, ndown - 1), a - aa)); return mem; } int main() { cin >> n >> d >> modulo; long long int sol = 0; if (n % 2 == 0) anyade(sol, combi(n / 2, 2)); n2 = n / 2; if (2 * n2 == n) n2--; if (n == 1) anyade(sol, 1); else anyade(sol, elecciones(n - 1, n2, d)); sol = ((sol % modulo) + modulo) % modulo; cout << sol << endl; }
#include <bits/stdc++.h> using namespace std; const int MAXN = 2005; int n, d, mod, inv[MAXN], f[MAXN][15][MAXN]; inline int read() { int x = 0; char ch = getchar(); while (!isdigit(ch)) ch = getchar(); while (isdigit(ch)) { x = x * 10 + ch - '0'; ch = getchar(); } return x; } inline void Add(int &x, int y) { x += y, x >= mod && (x -= mod); } inline void prepare() { inv[1] = 1; for (int i = 2; i < MAXN; i++) inv[i] = mod - 1ll * mod / i * inv[mod % i] % mod; for (int i = 2; i < MAXN; i++) inv[i] = 1ll * inv[i - 1] * inv[i] % mod; } inline int C(int n, int m) { if (n < 0 || m < 0 || m > n) return 0; int ans = 1; for (int i = n - m + 1; i <= n; i++) ans = 1ll * ans * i % mod; return 1ll * ans * inv[m] % mod; } inline void solve() { if (n <= 2) { puts("1"); return; } f[1][0][0] = 1; for (int i = 1; i <= n; i++) for (int j = 0; j <= d && j < i; j++) { f[i][j][1] = (j == i - 1); for (int k = 2; k <= i; k++) { f[i][j][k] = f[i][j][k - 1]; for (int t = 1; t * k <= i && t <= j; t++) Add(f[i][j][k], 1ll * f[i - t * k][j - t][min(k - 1, i - t * k)] * C(f[k][d - 1][k - 1] + t - 1, t) % mod); } } int ans = f[n][d][n >> 1]; if ((n & 1) == 0) ans = (ans - C(f[n >> 1][d - 1][n >> 1], 2) + mod) % mod; printf("%d\n", ans); } int main() { n = read(), d = read(), mod = read(); prepare(), solve(); return 0; }
#include <bits/stdc++.h> using namespace std; const long long N = 1e3 + 5, M = 20; long long n, d, mod, dp[N][M][N], f[M], g[M], ans; long long mul(long long x, long long n, long long mod) { long long ans = mod != 1; for (x %= mod; n; n >>= 1, x = x * x % mod) if (n & 1) ans = ans * x % mod; return ans; } void init() { long long n = 10; f[0] = g[0] = 1; for (long long i = 1; i <= n; i++) f[i] = f[i - 1] * i % mod; g[n] = mul(f[n], mod - 2, mod); for (long long i = n - 1; i; i--) g[i] = g[i + 1] * (i + 1) % mod; } long long C(long long n, long long m) { if (n < m) return 0; long long ans = 1; for (long long i = 1; i <= m; i++) ans = ans * (n - i + 1) % mod; return ans * g[m] % mod; } signed main() { scanf("%lld%lld%lld", &n, &d, &mod), init(); if (n <= 2) puts("1"), exit(0); for (long long i = 0; i <= n; i++) dp[1][0][i] = 1; for (long long i = 2; i <= n; i++) for (long long j = 1; j <= min(i - 1, d); j++) for (long long k = 1; k <= n; k++) { dp[i][j][k] = dp[i][j][k - 1]; for (long long t = 1; i - t * k > 0 && j - t >= 0; t++) { if (k != 1) dp[i][j][k] = (dp[i][j][k] + dp[i - t * k][j - t][k - 1] * C(dp[k][d - 1][k - 1] + t - 1, t) % mod) % mod; else dp[i][j][k] = (dp[i][j][k] + dp[i - t * k][j - t][k - 1] * C(dp[k][0][k - 1] + t - 1, t) % mod) % mod; } } if (n & 1) ans = dp[n][d][n / 2]; else ans = (dp[n][d][n / 2] - C(dp[n / 2][d - 1][n / 2], 2) + mod) % mod; printf("%lld\n", ans); return 0; }
#include <bits/stdc++.h> using namespace std; const long long Maxn = 1010; long long f[Maxn][11][Maxn], g[Maxn][Maxn]; long long n, K, Mod; long long inv[Maxn]; void up(long long &x, long long y) { x = (x + y) % Mod; } long long _min(long long x, long long y) { return x < y ? x : y; } int main() { long long i, j, k; scanf("%I64d%I64d%I64d", &n, &K, &Mod); if (n <= 2) { printf("1\n"); return 0; } f[1][K - 1][0] = f[1][0][0] = 1; inv[0] = inv[1] = 1; for (i = 2; i <= n; i++) inv[i] = inv[Mod % i] * (Mod - Mod / i) % Mod; for (i = 1; i <= n; i++) { for (j = 1; j <= K; j++) { for (k = 1; k < i; k++) { up(f[i][j][k], f[i][j][k - 1]); for (long long x = 1; x <= j && x * k < i; x++) up(f[i][j][k], f[i - x * k][j - x][_min(k - 1, i - x * k - 1)] * g[k][x]); } } g[i][0] = 1; for (j = 1; i * j <= n; j++) { g[i][j] = g[i][j - 1] * (f[i][K - 1][i - 1] + j - 1) % Mod * inv[j] % Mod; } } long long ans = f[n][K][(n - 1) / 2]; if (!(n & 1)) up(ans, f[n / 2][K - 1][n / 2 - 1] * (f[n / 2][K - 1][n / 2 - 1] + 1) % Mod * inv[2]); printf("%I64d\n", ans); return 0; }
#include <bits/stdc++.h> using namespace ::std; const long long maxn = 1050; const long long maxd = 11; long long mod; const long long inf = 1e9 + 500; long long dp[maxn][maxd][maxn]; long long rev[15]; long long poww(long long a, long long b) { if (b == 0) { return 1; } long long v = poww(a, b / 2); v = (v * v) % mod; if (b & 1) { return (v * a) % mod; } return v; } long long ent(long long n, long long k) { if (n < k || k < 0) { return 0; } long long ans = 1; for (long long i = n; i > n - k; i--) { ans *= i; ans %= mod; } for (long long i = 2; i <= k; i++) { ans *= rev[i]; ans %= mod; } return ans; } int main() { long long n, d; cin >> n >> d >> mod; for (long long i = 1; i < 15; i++) { rev[i] = poww(i, mod - 2); } if (n == 1) { cout << 1; return 0; } if (n == 2) { cout << 1; return 0; } dp[1][0][0] = 1; dp[2][1][1] = 1; for (long long x = 3; x <= n; x++) { dp[x][1][x - 1] = dp[x - 1][d - 1][x - 2]; for (long long y = 2; y <= d; y++) { if ((x - y - 1) % (d - 1) != 0) { continue; } if (x - 1 == y) { dp[x][y][1] = 1; } for (long long z = 2; z <= x - 1; z++) { dp[x][y][z] += dp[x][y][z - 1]; for (long long i = 1; i <= y && x > z * i; i++) { dp[x][y][z] += (dp[x - z * i][y - i][min(z - 1, x - z * i - 1)] * ent(dp[z][d - 1][z - 1] + i - 1, i)) % mod; dp[x][y][z] %= mod; } } } } for (long long i = 0; i <= n; i++) { for (long long j = 0; j <= d; j++) { for (long long k = 0; k <= n; k++) { if (dp[i][j][k] > 0) { } } } } long long ans = 0; if (n % 2 == 0) { ans += dp[n][d][n / 2 - 1]; long long res = dp[n / 2][d - 1][n / 2 - 1]; res += ((res * (res - 1) / 2) % mod); res %= mod; ans += res; ans %= mod; cout << ans << endl; } else { cout << dp[n][d][n / 2]; } }