#include #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; /* r: rotate 90deg s: transpose D_8 / | \ | / | \ 1 count perm. fixed by a subgroup N >= 2 ==> sr, sr^3 must change 2 2 +6 -2 4 4 4 ~~> -4 -4 -4 8 +8 */ void exper() { for (int N = 0; N <= 10; ++N) { vector ps(N); for (int x = 0; x < N; ++x) ps[x] = x; int cnt = 0; do { bool ok = true; for (int x = 0; x < N; ++x) { const int y = ps[x]; ok = ok && (ps[y] == x && ps[N - 1 - x] == N - 1 - y); // ok = ok && (ps[N - 1 - y] == x); } if (ok) ++cnt; } while (next_permutation(ps.begin(), ps.end())); cerr << N << ": " << cnt << endl; } } vector fac, two, match, invol, invol2; Mint calc_s_r2(int N) { return invol2[N/2]; } Mint calc_r(int N) { return (N/2 % 2 != 0) ? 0 : (match[N/2 / 2] * two[N/2 / 2]); } Mint calc_s(int N) { return invol[N]; } Mint calc_sr2(int N) { return invol[N]; } Mint calc_r2(int N) { return fac[N/2] * two[N/2]; } Mint calc_1(int N) { return fac[N]; } int T, M; vector Ns; int main() { // exper(); for (; ~scanf("%d%d", &T, &M); ) { Mint::setM(M); Ns.resize(T); for (int t = 0; t < T; ++t) { scanf("%d", &Ns[t]); } { const int N = *max_element(Ns.begin(), Ns.end()); fac.resize(N + 1); fac[0] = 1; for (int i = 1; i <= N; ++i) fac[i] = fac[i - 1] * i; two.resize(N/2 + 1); two[0] = 1; for (int i = 1; i <= N/2; ++i) two[i] = two[i - 1] * 2; match.resize(N/2 + 1); match[0] = 1; for (int i = 1; i <= N/2; ++i) match[i] = match[i - 1] * (2*i - 1); invol.resize(N + 1); invol[0] = invol[1] = 1; for (int i = 2; i <= N; ++i) invol[i] = invol[i - 1] + (i - 1) * invol[i - 2]; invol2.resize(max(N/2, 1) + 1); invol2[0] = 1; invol2[1] = 2; for (int i = 2; i <= N/2; ++i) invol2[i] = 2 * (invol2[i - 1] + (i - 1) * invol2[i - 2]); // cerr<<"invol = "<: ";for(int N=0;N<=20;++N)cerr<: " ;for(int N=0;N<=20;++N)cerr<