#include <iostream> #include <unordered_map> #include <utility> int n, m; int p = 1000000007; long long m_pow[3005]; long long dp[3005]; void input() { std::cin >> n >> m; } void prepare_m_pow() { m_pow[0] = 1; for (int i = 1; i < n; i++) { m_pow[i] = (m_pow[i - 1] * m) % p; } } long long pow_mod(int a, int b) { if (b == 0) { return 1; } if (b == 1) { return a % p; } if (b % 2 == 1) { return (pow_mod(a, b - 1) * a) % p; } return pow_mod((((long long)a) * a) % p, b / 2); } long long solve() { long long m_inv = pow_mod(m, p - 2); dp[1] = 0; dp[2] = m; for (int k = 3; k <= n; k++) { long long result = m_pow[k - 1]; for (int i = 2; i <= k - 2; i++) { long long r = (dp[i] * dp[k - i]) % p; r = (r * (m - 1)) % p; r = (r * m_inv) % p; result = (result + r) % p; } dp[k] = result; } return dp[n]; } int main() { std::ios_base::sync_with_stdio(false); std::cin.tie(NULL); input(); prepare_m_pow(); std::cout << solve() << "\n"; return 0; }
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 | #include <iostream> #include <unordered_map> #include <utility> int n, m; int p = 1000000007; long long m_pow[3005]; long long dp[3005]; void input() { std::cin >> n >> m; } void prepare_m_pow() { m_pow[0] = 1; for (int i = 1; i < n; i++) { m_pow[i] = (m_pow[i - 1] * m) % p; } } long long pow_mod(int a, int b) { if (b == 0) { return 1; } if (b == 1) { return a % p; } if (b % 2 == 1) { return (pow_mod(a, b - 1) * a) % p; } return pow_mod((((long long)a) * a) % p, b / 2); } long long solve() { long long m_inv = pow_mod(m, p - 2); dp[1] = 0; dp[2] = m; for (int k = 3; k <= n; k++) { long long result = m_pow[k - 1]; for (int i = 2; i <= k - 2; i++) { long long r = (dp[i] * dp[k - i]) % p; r = (r * (m - 1)) % p; r = (r * m_inv) % p; result = (result + r) % p; } dp[k] = result; } return dp[n]; } int main() { std::ios_base::sync_with_stdio(false); std::cin.tie(NULL); input(); prepare_m_pow(); std::cout << solve() << "\n"; return 0; } |