#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") //////////////////////////////////////////////////////////////////////////////// template struct ModInt { static constexpr unsigned M = M_; unsigned x; constexpr ModInt() : x(0U) {} constexpr ModInt(unsigned x_) : x(x_ % M) {} constexpr ModInt(unsigned long long x_) : x(x_ % M) {} constexpr ModInt(int x_) : x(((x_ %= static_cast(M)) < 0) ? (x_ + static_cast(M)) : x_) {} constexpr 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) { x = (static_cast(x) * a.x) % 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; } }; //////////////////////////////////////////////////////////////////////////////// constexpr unsigned MO = 998244353; using Mint = ModInt; template void bAdd(vector &bit, int pos, const T &val) { const int bitN = bit.size(); for (int x = pos; x < bitN; x |= x + 1) bit[x] += val; } template T bSum(const vector &bit, int pos) { T ret = 0; for (int x = pos; x > 0; x &= x - 1) ret += bit[x - 1]; return ret; } template T bSum(const vector &bit, int pos0, int pos1) { return bSum(bit, pos1) - bSum(bit, pos0); } int N, M; vector A; Mint slow() { vector sums(M + 1, 0); for (int i = 0; i < M; ++i) sums[i + 1] = sums[i] + ((!~A[i]) ? 1 : 0); auto get = [&](int l, int r) -> int { chmax(l, 0); chmin(r, M); return (l <= r) ? (sums[r] - sums[l]) : 0; }; vector app(N); for (int a = 0; a < N; ++a) app[a] = ~a; const Mint prob = 1 - 2 / Mint(N); Mint ans = 0; for (int i = 0; i < M; ++i) { auto calc = [&](int a) -> Mint { Mint ret = 0; for (int b = 0; b < N; ++b) if (a != b) { // Pr[b above a] if (app[a] < app[b]) { ret += (1 + prob.pow(get(app[b], i))) / 2; } else { ret += (1 - prob.pow(get(app[a], i))) / 2; } } return ret; }; if (~A[i]) { ans += calc(A[i]); app[A[i]] = i; } else { Mint sum = 0; for (int a = 0; a < N; ++a) sum += calc(a); cerr<<"[slow] sum = "< sums(M + 1, 0); for (int i = 0; i < M; ++i) sums[i + 1] = sums[i] + ((!~A[i]) ? 1 : 0); vector app(N); for (int a = 0; a < N; ++a) app[a] = ~a; const Mint prob = 1 - 2 / Mint(N); const Mint invProb = prob.inv(); vector pw(M + 1), invPw(M + 1); pw[0] = 1; invPw[0] = 1; for (int i = 1; i <= M; ++i) { pw[i] = pw[i - 1] * prob; invPw[i] = invPw[i - 1] * invProb; } // \sum 1, \sum prob^(-sums[app[b]]) vector bit0(N + M, 0), bit1(N + M, 0); auto add = [&](int b, Mint val) -> void { bAdd(bit0, N + app[b], val); bAdd(bit1, N + app[b], val * invPw[sums[max(app[b], 0)]]); }; for (int b = 0; b < N; ++b) add(b, +1); Mint ans = 0; for (int i = 0; i < M; ++i) { auto calc = [&](int a) -> Mint { Mint ret = 0; /* app[a] < app[b] ret += (1 + prob.pow(get(app[b], i))) / 2; */ ret += bSum(bit0, N + app[a] + 1, N + M); ret += bSum(bit1, N + app[a] + 1, N + M) * pw[sums[i]]; /* app[a] > app[b] ret += (1 - prob.pow(get(app[a], i))) / 2; */ ret += bSum(bit0, N + app[a]) * (1 - pw[sums[i] - sums[max(app[a], 0)]]); return ret; }; if (~A[i]) { ans += calc(A[i]); add(A[i], -1); app[A[i]] = i; add(A[i], +1); } else { // 1/2 on average ans += Mint(N - 1); } } ans /= 2; ans += M; return ans; } int main() { for (; ~scanf("%d%d", &N, &M); ) { A.resize(M); for (int i = 0; i < M; ++i) { scanf("%d", &A[i]); if (~A[i]) --A[i]; } const Mint ans = fast(); printf("%u\n", ans.x); #ifdef LOCAL const Mint slw=slow(); cerr<<"slw = "<