#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using Int = long long; template ostream &operator<<(ostream &os, const pair &a) { return os << "(" << a.first << ", " << a.second << ")"; }; template ostream &operator<<(ostream &os, const vector &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; } template void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; } template bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; } template bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; } #define COLOR(s) ("\x1b[" s "m") //////////////////////////////////////////////////////////////////////////////// // Barrett struct ModInt { static unsigned M; static unsigned long long NEG_INV_M; static void setM(unsigned m) { M = m; NEG_INV_M = -1ULL / M; } unsigned x; ModInt() : x(0U) {} ModInt(unsigned x_) : x(x_ % M) {} ModInt(unsigned long long x_) : x(x_ % M) {} ModInt(int x_) : x(((x_ %= static_cast(M)) < 0) ? (x_ + static_cast(M)) : x_) {} ModInt(long long x_) : x(((x_ %= static_cast(M)) < 0) ? (x_ + static_cast(M)) : x_) {} ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; } ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; } ModInt &operator*=(const ModInt &a) { const unsigned long long y = static_cast(x) * a.x; const unsigned long long q = static_cast((static_cast(NEG_INV_M) * y) >> 64); const unsigned long long r = y - M * q; x = r - M * (r >= M); return *this; } ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); } ModInt pow(long long e) const { if (e < 0) return inv().pow(-e); ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b; } ModInt inv() const { unsigned a = M, b = x; int y = 0, z = 1; for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast(q) * z; y = z; z = w; } assert(a == 1U); return ModInt(y); } ModInt operator+() const { return *this; } ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; } ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); } ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); } ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); } ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); } template friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); } template friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); } template friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); } template friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); } explicit operator bool() const { return x; } bool operator==(const ModInt &a) const { return (x == a.x); } bool operator!=(const ModInt &a) const { return (x != a.x); } friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; } }; unsigned ModInt::M; unsigned long long ModInt::NEG_INV_M; // !!!Use ModInt::setM!!! //////////////////////////////////////////////////////////////////////////////// using Mint = ModInt; constexpr int LIM_INV = 200'010; Mint inv[LIM_INV], fac[LIM_INV], invFac[LIM_INV]; void prepare() { inv[1] = 1; for (int i = 2; i < LIM_INV; ++i) { inv[i] = -((Mint::M / i) * inv[Mint::M % i]); } fac[0] = invFac[0] = 1; for (int i = 1; i < LIM_INV; ++i) { fac[i] = fac[i - 1] * i; invFac[i] = invFac[i - 1] * inv[i]; } } Mint binom(Int n, Int k) { if (n < 0) { if (k >= 0) { return ((k & 1) ? -1 : +1) * binom(-n + k - 1, k); } else if (n - k >= 0) { return (((n - k) & 1) ? -1 : +1) * binom(-k - 1, n - k); } else { return 0; } } else { if (0 <= k && k <= n) { assert(n < LIM_INV); return fac[n] * invFac[k] * invFac[n - k]; } else { return 0; } } } // https://oeis.org/A277663 int main() { int N, P; for (; ~scanf("%d%d", &N, &P); ) { Mint::setM(P); prepare(); vector as(N + 1, 0); for (int h = 0; h < 2; ++h) { const Mint k = (h == 0) ? (-7 * inv[2]) : (-4); const vector ps = (h == 0) ? vector{3, 19, -9, 2} : vector{-3, -15, 9, -5, 6}; // (x^2 - 6 x + 1)^k vector bs(N + 1); bs[0] = 1; for (int i = 1; i <= N; ++i) { Mint sum = 0; if (i >= 1) sum += ((k + 1) * 1 - i) * -6 * bs[i - 1]; if (i >= 2) sum += ((k + 1) * 2 - i) * 1 * bs[i - 2]; bs[i] = inv[i] * sum; } // *= -(2 x) ps for (int i = 0; i <= N; ++i) { for (int j = 0; j < (int)ps.size() && i + 1 + j <= N; ++j) { as[i + 1 + j] -= bs[i] * 2 * ps[j]; } } } // cerr<<"as = "<