#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 #include #include #include #include #include using namespace std; using lint = long long; using pint = pair; using plint = pair; struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_; #define ALL(x) (x).begin(), (x).end() #define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i=i##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template void ndarray(vector& vec, const V& val, int len) { vec.assign(len, val); } template void ndarray(vector& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); } template bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; } template bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; } int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); } template pair operator+(const pair &l, const pair &r) { return make_pair(l.first + r.first, l.second + r.second); } template pair operator-(const pair &l, const pair &r) { return make_pair(l.first - r.first, l.second - r.second); } template vector sort_unique(vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template int arglb(const std::vector &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); } template int argub(const std::vector &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); } template istream &operator>>(istream &is, vector &vec) { for (auto &v : vec) is >> v; return is; } template ostream &operator<<(ostream &os, const vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const array &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; } #if __cplusplus >= 201703L template istream &operator>>(istream &is, tuple &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template ostream &operator<<(ostream &os, const tuple &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; } #endif template ostream &operator<<(ostream &os, const deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const pair &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; } template ostream &operator<<(ostream &os, const map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } #ifdef HITONANODE_LOCAL const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m"; #define dbg(x) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl #define dbgif(cond, x) ((cond) ? cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl : cerr) #else #define dbg(x) (x) #define dbgif(cond, x) 0 #endif #include using mint = atcoder::modint998244353; template struct acl_fac { std::vector facs, facinvs; acl_fac(int N) { assert(-1 <= N and N < modint::mod()); facs.resize(N + 1, 1); for (int i = 1; i <= N; i++) facs[i] = facs[i - 1] * i; facinvs.assign(N + 1, facs.back().inv()); for (int i = N; i > 0; i--) facinvs[i - 1] = facinvs[i] * i; } modint ncr(int n, int r) const { if (n < 0 or r < 0 or n < r) return 0; return facs[n] * facinvs[r] * facinvs[n - r]; } modint operator[](int i) const { return facs[i]; } modint finv(int i) const { return facinvs[i]; } }; constexpr int bias = 3010; acl_fac fac(bias + 10); int main() { lint N; int Q; cin >> N >> Q; map> mp; vector nplusiPj(bias * 2, vector(bias)); REP(i, nplusiPj.size()) { nplusiPj[i][0] = mint(N - bias) + i; FOR(j, 1, nplusiPj[i].size()) nplusiPj[i][j] = nplusiPj[i][j - 1] * (mint(N - bias) + i - j); } for (auto &w : nplusiPj) REP(j, w.size()) w[j] *= fac.facinvs[j + 1]; while (Q--) { lint K; int a, b, s, t; cin >> K >> a >> b >> s >> t; for (auto itr = mp[K].begin(); itr != mp[K].end(); itr++) { if (itr->second + 1 < a or itr->first - 1 > b) { } else { chmin(a, itr->first); chmax(b, itr->second); } } for (auto itr = mp[K].begin(); itr != mp[K].end(); itr++) { while (itr != mp[K].end() and itr->first >= a and itr->second <= b) { itr = mp[K].erase(itr); } if (itr == mp[K].end()) break; } mp[K].emplace(a, b); vector dp(1, vector(t + 1)); dp[0][0] = 1; for (auto [lval, ranges] : mp) { vector nxt(dp.size() + 1, vector(dp[0].size())); for (auto [l, r] : ranges) { REP(i, dp.size()) REP(j, int(dp[i].size()) - l) if (dp[i][j].val()) { nxt[i + 1][j + l] += dp[i][j]; if (j + r + 1 < int(nxt[i + 1].size())) nxt[i + 1][j + r + 1] -= dp[i][j]; } } for (auto &vec : nxt) { FOR(i, 1, vec.size()) vec[i] += vec[i - 1]; } REP(i, dp.size()) REP(j, dp[i].size()) nxt[i][j] += dp[i][j]; dp = nxt; } mint ret = 0; auto distribute = [&](lint a, lint M) -> mint { if (a < 0 or M < 0) return 0; if (a == 0) return 1; lint x = M + a - (N - bias); return nplusiPj[x][a - 1]; // *fac.facinvs[a]; }; REP(i, dp.size()) REP(sum, dp[i].size()) if (dp[i][sum].val()) { mint tmp = dp[i][sum] * (distribute(t - sum, N - i) - distribute(s - 1 - sum, N - i)); if (i % 2) ret -= tmp; else ret += tmp; } cout << ret.val() << '\n'; } }