#pragma GCC optimize ("Ofast") #pragma GCC optimize ("unroll-loops") #pragma GCC target ("avx") #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 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; } //////////////////////////////////////////////////////////////////////////////// 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; // T: monoid representing information of an interval. // T() should return the identity. // T(S s) should represent a single element of the array. // T::push(T &l, T &r) should push the lazy update. // T::merge(const T &l, const T &r) should merge two intervals. template struct SegmentTreeRange { int logN, n; vector ts; SegmentTreeRange() {} explicit SegmentTreeRange(int n_) { for (logN = 0, n = 1; n < n_; ++logN, n <<= 1) {} ts.resize(n << 1); } template explicit SegmentTreeRange(const vector &ss) { const int n_ = ss.size(); for (logN = 0, n = 1; n < n_; ++logN, n <<= 1) {} ts.resize(n << 1); for (int i = 0; i < n_; ++i) at(i) = T(ss[i]); build(); } T &at(int i) { return ts[n + i]; } void build() { for (int u = n; --u; ) merge(u); } inline void push(int u) { ts[u].push(ts[u << 1], ts[u << 1 | 1]); } inline void merge(int u) { ts[u].merge(ts[u << 1], ts[u << 1 | 1]); } // Applies T::f(args...) to [a, b). template void ch(int a, int b, F f, Args &&... args) { assert(0 <= a); assert(a <= b); assert(b <= n); if (a == b) return; a += n; b += n; for (int h = logN; h; --h) { const int aa = a >> h, bb = b >> h; if (aa == bb) { if ((aa << h) != a || (bb << h) != b) push(aa); } else { if ((aa << h) != a) push(aa); if ((bb << h) != b) push(bb); } } for (int aa = a, bb = b; aa < bb; aa >>= 1, bb >>= 1) { if (aa & 1) (ts[aa++].*f)(args...); if (bb & 1) (ts[--bb].*f)(args...); } for (int h = 1; h <= logN; ++h) { const int aa = a >> h, bb = b >> h; if (aa == bb) { if ((aa << h) != a || (bb << h) != b) merge(aa); } else { if ((aa << h) != a) merge(aa); if ((bb << h) != b) merge(bb); } } } // Calculates T::f(args...) of a monoid type for [a, b). // op(-, -) should calculate the product. // e() should return the identity. template #if __cplusplus >= 201402L auto #else decltype((std::declval().*F())()) #endif get(int a, int b, Op op, E e, F f, Args &&... args) { assert(0 <= a); assert(a <= b); assert(b <= n); if (a == b) return e(); a += n; b += n; for (int h = logN; h; --h) { const int aa = a >> h, bb = b >> h; if (aa == bb) { if ((aa << h) != a || (bb << h) != b) push(aa); } else { if ((aa << h) != a) push(aa); if ((bb << h) != b) push(bb); } } auto prodL = e(), prodR = e(); for (int aa = a, bb = b; aa < bb; aa >>= 1, bb >>= 1) { if (aa & 1) prodL = op(prodL, (ts[aa++].*f)(args...)); if (bb & 1) prodR = op((ts[--bb].*f)(args...), prodR); } return op(prodL, prodR); } // Find min b s.t. T::f(args...) returns true, // when called for the partition of [a, b) from left to right. // Returns n + 1 if there is no such b. template int findRight(int a, F f, Args &&... args) { assert(0 <= a); assert(a <= n); if ((T().*f)(args...)) return a; if (a == n) return n + 1; a += n; for (int h = logN; h; --h) push(a >> h); for (; ; a >>= 1) { if (a & 1) { if ((ts[a].*f)(args...)) { for (; a < n; ) { push(a); a <<= 1; if (!(ts[a].*f)(args...)) ++a; } return a - n + 1; } ++a; if (!(a & (a - 1))) return n + 1; } } } // Find max a s.t. T::f(args...) returns true, // when called for the partition of [a, b) from right to left. // Returns -1 if there is no such a. template int findLeft(int b, F f, Args &&... args) { assert(0 <= b); assert(b <= n); if ((T().*f)(args...)) return b; if (b == 0) return -1; b += n; for (int h = logN; h; --h) push((b - 1) >> h); for (; ; b >>= 1) { if ((b & 1) || b == 2) { if ((ts[b - 1].*f)(args...)) { for (; b <= n; ) { push(b - 1); b <<= 1; if (!(ts[b - 1].*f)(args...)) --b; } return b - n - 1; } --b; if (!(b & (b - 1))) return -1; } } } }; //////////////////////////////////////////////////////////////////////////////// struct Node0 { int sz, sum; int lz; Node0() : sz(0), sum(0), lz(0) {} void push(Node0 &l, Node0 &r) { l.add(lz); r.add(lz); lz = 0; } void merge(const Node0 &l, const Node0 &r) { sz = l.sz + r.sz; sum = l.sum + r.sum; } void add(int val) { sum += sz * val; lz += val; } int getSum() const { return sum; } }; int getSum(SegmentTreeRange &seg, int a, int b) { return seg.get(a, b, [&](int l, int r) -> int { return l + r; }, [&]() -> int { return 0; }, &Node0::getSum); } struct Node { Mint x[2], y[3]; int lz; Node() : x{}, y{}, lz(0) {} void push(Node &l, Node &r) { l.add(lz); r.add(lz); lz = 0; } void merge(const Node &l, const Node &r) { x[0] = l.x[0] + r.x[0]; x[1] = l.x[1] + r.x[1]; y[0] = l.y[0] + r.y[0]; y[1] = l.y[1] + r.y[1]; y[2] = l.y[2] + r.y[2]; } void add(int val) { x[1] += val * x[0]; y[2] += val * (2 * y[1] + val * y[0]); y[1] += val * y[0]; lz += val; } Node getSum() const { return *this; } }; Node getSum(SegmentTreeRange &seg, int a, int b) { return seg.get(a, b, [&](const Node &l, const Node &r) -> Node { Node t; t.merge(l, r); return t; }, [&]() -> Node { return Node(); }, &Node::getSum); } int N, M; vector A; int main() { for (; ~scanf("%d%d", &N, &M); ) { A.resize(N + M); for (int i = 0; i < N; ++i) { A[i] = N - 1 - i; } for (int i = N; i < N + M; ++i) { scanf("%d", &A[i]); --A[i]; } // cerr<<"A = ";pv(A.begin(),A.end()); if (N == 1) { printf("%u\n", Mint(M).x); continue; } if (N == 2) { Mint ans2 = M; for (int i = N; i < N + M; ++i) { for (int a = 0; a < 2; ++a) for (int b = 0; b < 2; ++b) if (a != b) { Mint tmp = 1; tmp *= ((A[i - 1] == -2) ? Mint(2).inv() : (A[i - 1] == a) ? 1 : 0); tmp *= ((A[i] == -2) ? Mint(2).inv() : (A[i] == b) ? 1 : 0); ans2 += tmp; } } printf("%u\n", ans2.x); continue; } vector ls(N + M + 1, 0); for (int i = 0; i < N + M; ++i) { ls[i + 1] = ls[i] + ((A[i] == -2) ? 1 : 0); } // cerr<<"ls = ";pv(ls.begin(),ls.end()); Mint ans[2][2] = {}; vector pw0(N + M + 1), pw1(N + M + 1), pw2(N + M + 1), invPw1(N + M + 1), invPw2(N + M + 1); pw0[0] = pw1[0] = pw2[0] = invPw1[0] = invPw2[0] = 1; pw0[1] = Mint(N); pw1[1] = Mint(N - 1); pw2[1] = Mint(N - 2); invPw1[1] = Mint(N - 1).inv(); invPw2[1] = Mint(N - 2).inv(); for (int i = 2; i <= N + M; ++i) { pw0[i] = pw0[i - 1] * pw0[1]; pw1[i] = pw1[i - 1] * pw1[1]; pw2[i] = pw2[i - 1] * pw2[1]; invPw1[i] = invPw1[i - 1] * invPw1[1]; invPw2[i] = invPw2[i - 1] * invPw2[1]; } { vector app(N, 0); SegmentTreeRange seg0(N + M); SegmentTreeRange seg(N + M); for (int i = 0; i < N + M; ++i) { seg0.at(i).sz = 1; if (A[i] == -2) { seg.at(i).x[0] = pw0[ls[i]] * invPw1[ls[i + 1]]; seg.at(i).y[0] = pw0[ls[i]] * invPw2[ls[i + 1]]; } } seg0.build(); seg.build(); for (int i = 0; i < N + M; ++i) { // get if (i >= N) { if (A[i] != -2) { { const int m = getSum(seg0, app[A[i]], app[A[i]] + 1); Mint tmp = 0; tmp += pw1[ls[i] - ls[app[A[i]] + 1]] * Mint(1 + m); tmp += Mint(N - 1 - m) * (pw1[ls[i] - ls[app[A[i]] + 1]] - pw2[ls[i] - ls[app[A[i]] + 1]]); tmp *= pw0[ls[app[A[i]]] + (ls[N + M] - ls[i + 1])]; ans[0][0] += tmp; } { const Node res = getSum(seg, app[A[i]], i); Mint tmp = 0; tmp += pw1[ls[i]] * (res.x[0] + res.x[1]); tmp += pw1[ls[i]] * (Mint(N - 1) * res.x[0] - res.x[1]) - pw2[ls[i]] * (Mint(N - 1) * res.y[0] - res.y[1]); tmp *= pw0[ls[N + M] - ls[i + 1]]; ans[1][0] += tmp; } } else { { const Node res = getSum(seg, 0, i); Mint tmp = 0; tmp += pw1[ls[i]] * (Mint(N) * res.x[0] + Mint(N - 1) * res.x[1]); tmp += pw1[ls[i]] * (Mint(N) * Mint(N - 1) * res.x[0] - Mint(2 * N - 1) * res.x[1]) - pw2[ls[i]] * (Mint(N) * Mint(N - 1) * res.y[0] - Mint(2 * N - 1) * res.y[1] + res.y[2]); tmp *= pw0[ls[N + M] - ls[i + 1]]; ans[1][1] += tmp; } } } // add if (A[i] != -2) { seg0.ch(app[A[i]], i, &Node0::add, 1); seg.ch(app[A[i]], i, &Node::add, 1); app[A[i]] = i; } } } { reverse(A.begin(), A.end()); for (int i = 0; i < N + M; ++i) { ls[i + 1] = ls[i] + ((A[i] == -2) ? 1 : 0); } // cerr<<"A = ";pv(A.begin(),A.end()); // cerr<<"ls = ";pv(ls.begin(),ls.end()); vector app(N, 0); SegmentTreeRange seg(N + M); for (int i = 0; i < N + M; ++i) { if (A[i] == -2) { seg.at(i).x[0] = pw0[ls[i]] * invPw1[ls[i + 1]]; seg.at(i).y[0] = pw0[ls[i]] * invPw2[ls[i + 1]]; } } seg.build(); for (int i = 0; i < M + N; ++i) { // get { if (A[i] != -2) { {} { const Node res = getSum(seg, app[A[i]], i); Mint tmp = 0; tmp += pw1[ls[i]] * (res.x[0] + res.x[1]); tmp += pw1[ls[i]] * (Mint(N - 1) * res.x[0] - res.x[1]) - pw2[ls[i]] * (Mint(N - 1) * res.y[0] - res.y[1]); tmp *= pw0[ls[N + M] - ls[i + 1]]; ans[0][1] += tmp; } } else { {} } } // add if (A[i] != -2) { seg.ch(app[A[i]], i, &Node::add, 1); app[A[i]] = i; } } reverse(A.begin(), A.end()); for (int i = 0; i < N + M; ++i) { ls[i + 1] = ls[i] + ((A[i] == -2) ? 1 : 0); } } printf("%u\n", ((ans[0][0] + ans[0][1] + ans[1][0] + ans[1][1]) / Mint(N).pow(ls[N + M])).x); #ifdef LOCAL Mint brt[2][2] = {}; for (int i = 0; i < N + M; ++i) for (int j = N; j < N + M; ++j) { if (i < j) { set as(A.begin() + i + 1, A.begin() + j); as.erase(-2); const int m = as.size(); Mint tmp = 0; tmp += Mint(N - 1).pow(ls[j] - ls[i + 1]) * Mint(1 + m); tmp += Mint(N - 1 - m) * (Mint(N - 1).pow(ls[j] - ls[i + 1]) - Mint(N - 2).pow(ls[j] - ls[i + 1])); tmp *= Mint(N).pow(ls[i] + (ls[N + M] - ls[j + 1])); if (A[i] != -2) { if (A[j] != -2) { if (A[i] == A[j] && as.find(A[i]) == as.end()) { brt[0][0] += tmp; } } else { if (as.find(A[i]) == as.end()) { brt[0][1] += tmp; } } } else { if (A[j] != -2) { if (as.find(A[j]) == as.end()) { brt[1][0] += tmp; } } else { brt[1][1] += Mint(N - m) * tmp; } } } } cerr << "brt = " << ((brt[0][0] + brt[0][1] + brt[1][0] + brt[1][1]) / Mint(N).pow(ls[N + M])) << "; " << brt[0][0] << " " << brt[0][1] << " " << brt[1][0] << " " << brt[1][1] << endl; cerr << "ans = " << ((ans[0][0] + ans[0][1] + ans[1][0] + ans[1][1]) / Mint(N).pow(ls[N + M])) << "; " << ans[0][0] << " " << ans[0][1] << " " << ans[1][0] << " " << ans[1][1] << endl; #endif } return 0; }