#include #ifndef LOCAL_TEST #pragma GCC target ("avx") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native") #endif // LOCAL_TEST using namespace std; using ll = long long; using pii = pair; using pll = pair; using vi = vector; using vvi = vector; using vvvi = vector; using vl = vector; using vvl = vector; using vvvl = vector; using vb = vector; using vvb = vector; using vvvb = vector; using vc = vector; using vvc = vector; using vvvc = vector; using vd = vector; using vvd = vector; using vvvd = vector; using vs = vector; using vvs = vector>; using vvvs = vector>>; template using priority_queue_min = priority_queue, greater>; const double PI = acos(-1.0); int INF = 100100111; ll INFL = 3300300300300300491LL; double EPS = 1e-8; double EPSL = 1e-16; constexpr int MODINT998244353 = 998244353; constexpr int MODINT1000000007 = 1000000007; struct fast_io { fast_io() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(18); } } fastIOtmp; #define all(a) (a).begin(), (a).end() #define sz(x) ((int)(x).size()) #define lbpos(a, x) (int)distance((a).begin(), std::lower_bound(all(a), x)) #define ubpos(a, x) (int)distance((a).begin(), std::upper_bound(all(a), x)) #define rep(i, n) for(ll i = 0, i##_len = ll(n); i < i##_len; ++i) // 0 から n-1 まで昇順 #define repi(i, s, t) for(ll i = ll(s), i##_end = ll(t); i < i##_end; ++i) // s から t まで昇順 #define repis(i, s, t, step) for(ll i = ll(s), i##_end = ll(t); i < i##_end; i+=step) // s から t まで stepずつ #define repir(i, s, t, step) for(ll i = ll(s), i##_end = ll(t); i > i##_end; i+=step) // s から t まで stepずつ #define repe(a, v) for(auto& a : (v)) // v の全要素(変更可能) #define repea(a, v) for(const auto& a : (v)) // v の全要素(変更不可能) #define smod(n, m) ((((n) % (m)) + (m)) % (m)) // 非負mod #define sdiv(n, m) (((n) - smod(n, m)) / (m)) // 非負div #define uniq(a) {sort(all(a)); (a).erase(unique(all(a)), (a).end());} // 重複除去 #define EXIT(a) {cout << (a) << endl; exit(0);} // 強制終了 void Yes(bool b) { cout << (b ? "Yes\n" : "No\n"); return; } ll powm(ll a, ll n, ll mod=INFL) { ll res = 1; while (n > 0) { if (n & 1) res = (res * a) % mod; a = (a * a) % mod; n >>= 1; } return res; } template inline bool chmax(T& M, const T& x) { if (M < x) { M = x; return true; } return false; } // 最大値を更新(更新されたら true を返す) template inline bool chmin(T& m, const T& x) { if (m > x) { m = x; return true; } return false; } // 最小値を更新(更新されたら true を返す) int digit(ll x, int d=10) { int rev=0; while (x > 0) { rev++; x /= d;}; return rev; } // xのd進数桁数 #include #include #include #include #ifdef _MSC_VER #include #endif #include #ifdef _MSC_VER #include #endif namespace atcoder { namespace internal { constexpr long long safe_mod(long long x, long long m) { x %= m; if (x < 0) x += m; return x; } struct barrett { unsigned int _m; unsigned long long im; explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {} unsigned int umod() const { return _m; } unsigned int mul(unsigned int a, unsigned int b) const { unsigned long long z = a; z *= b; #ifdef _MSC_VER unsigned long long x; _umul128(z, im, &x); #else unsigned long long x = (unsigned long long)(((unsigned __int128)(z)*im) >> 64); #endif unsigned int v = (unsigned int)(z - x * _m); if (_m <= v) v += _m; return v; } }; constexpr long long pow_mod_constexpr(long long x, long long n, int m) { if (m == 1) return 0; unsigned int _m = (unsigned int)(m); unsigned long long r = 1; unsigned long long y = safe_mod(x, m); while (n) { if (n & 1) r = (r * y) % _m; y = (y * y) % _m; n >>= 1; } return r; } constexpr bool is_prime_constexpr(int n) { if (n <= 1) return false; if (n == 2 || n == 7 || n == 61) return true; if (n % 2 == 0) return false; long long d = n - 1; while (d % 2 == 0) d /= 2; constexpr long long bases[3] = {2, 7, 61}; for (long long a : bases) { long long t = d; long long y = pow_mod_constexpr(a, t, n); while (t != n - 1 && y != 1 && y != n - 1) { y = y * y % n; t <<= 1; } if (y != n - 1 && t % 2 == 0) { return false; } } return true; } template constexpr bool is_prime = is_prime_constexpr(n); constexpr std::pair inv_gcd(long long a, long long b) { a = safe_mod(a, b); if (a == 0) return {b, 0}; long long s = b, t = a; long long m0 = 0, m1 = 1; while (t) { long long u = s / t; s -= t * u; m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b auto tmp = s; s = t; t = tmp; tmp = m0; m0 = m1; m1 = tmp; } if (m0 < 0) m0 += b / s; return {s, m0}; } constexpr int primitive_root_constexpr(int m) { if (m == 2) return 1; if (m == 167772161) return 3; if (m == 469762049) return 3; if (m == 754974721) return 11; if (m == 998244353) return 3; int divs[20] = {}; divs[0] = 2; int cnt = 1; int x = (m - 1) / 2; while (x % 2 == 0) x /= 2; for (int i = 3; (long long)(i)*i <= x; i += 2) { if (x % i == 0) { divs[cnt++] = i; while (x % i == 0) { x /= i; } } } if (x > 1) { divs[cnt++] = x; } for (int g = 2;; g++) { bool ok = true; for (int i = 0; i < cnt; i++) { if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) { ok = false; break; } } if (ok) return g; } } template constexpr int primitive_root = primitive_root_constexpr(m); unsigned long long floor_sum_unsigned(unsigned long long n, unsigned long long m, unsigned long long a, unsigned long long b) { unsigned long long ans = 0; while (true) { if (a >= m) { ans += n * (n - 1) / 2 * (a / m); a %= m; } if (b >= m) { ans += n * (b / m); b %= m; } unsigned long long y_max = a * n + b; if (y_max < m) break; n = (unsigned long long)(y_max / m); b = (unsigned long long)(y_max % m); std::swap(m, a); } return ans; } } // namespace internal } // namespace atcoder #include #include #include namespace atcoder { namespace internal { #ifndef _MSC_VER template using is_signed_int128 = typename std::conditional::value || std::is_same::value, std::true_type, std::false_type>::type; template using is_unsigned_int128 = typename std::conditional::value || std::is_same::value, std::true_type, std::false_type>::type; template using make_unsigned_int128 = typename std::conditional::value, __uint128_t, unsigned __int128>; template using is_integral = typename std::conditional::value || is_signed_int128::value || is_unsigned_int128::value, std::true_type, std::false_type>::type; template using is_signed_int = typename std::conditional<(is_integral::value && std::is_signed::value) || is_signed_int128::value, std::true_type, std::false_type>::type; template using is_unsigned_int = typename std::conditional<(is_integral::value && std::is_unsigned::value) || is_unsigned_int128::value, std::true_type, std::false_type>::type; template using to_unsigned = typename std::conditional< is_signed_int128::value, make_unsigned_int128, typename std::conditional::value, std::make_unsigned, std::common_type>::type>::type; #else template using is_integral = typename std::is_integral; template using is_signed_int = typename std::conditional::value && std::is_signed::value, std::true_type, std::false_type>::type; template using is_unsigned_int = typename std::conditional::value && std::is_unsigned::value, std::true_type, std::false_type>::type; template using to_unsigned = typename std::conditional::value, std::make_unsigned, std::common_type>::type; #endif template using is_signed_int_t = std::enable_if_t::value>; template using is_unsigned_int_t = std::enable_if_t::value>; template using to_unsigned_t = typename to_unsigned::type; } // namespace internal } // namespace atcoder namespace atcoder { namespace internal { struct modint_base {}; struct static_modint_base : modint_base {}; template using is_modint = std::is_base_of; template using is_modint_t = std::enable_if_t::value>; } // namespace internal template * = nullptr> struct static_modint : internal::static_modint_base { using mint = static_modint; public: static constexpr int mod() { return m; } static mint raw(int v) { mint x; x._v = v; return x; } static_modint() : _v(0) {} template * = nullptr> static_modint(T v) { long long x = (long long)(v % (long long)(umod())); if (x < 0) x += umod(); _v = (unsigned int)(x); } template * = nullptr> static_modint(T v) { _v = (unsigned int)(v % umod()); } unsigned int val() const { return _v; } mint& operator++() { _v++; if (_v == umod()) _v = 0; return *this; } mint& operator--() { if (_v == 0) _v = umod(); _v--; return *this; } mint operator++(int) { mint result = *this; ++*this; return result; } mint operator--(int) { mint result = *this; --*this; return result; } mint& operator+=(const mint& rhs) { _v += rhs._v; if (_v >= umod()) _v -= umod(); return *this; } mint& operator-=(const mint& rhs) { _v -= rhs._v; if (_v >= umod()) _v += umod(); return *this; } mint& operator*=(const mint& rhs) { unsigned long long z = _v; z *= rhs._v; _v = (unsigned int)(z % umod()); return *this; } mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); } mint operator+() const { return *this; } mint operator-() const { return mint() - *this; } mint pow(long long n) const { assert(0 <= n); mint x = *this, r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; } mint inv() const { if (prime) { assert(_v); return pow(umod() - 2); } else { auto eg = internal::inv_gcd(_v, m); assert(eg.first == 1); return eg.second; } } friend mint operator+(const mint& lhs, const mint& rhs) { return mint(lhs) += rhs; } friend mint operator-(const mint& lhs, const mint& rhs) { return mint(lhs) -= rhs; } friend mint operator*(const mint& lhs, const mint& rhs) { return mint(lhs) *= rhs; } friend mint operator/(const mint& lhs, const mint& rhs) { return mint(lhs) /= rhs; } friend bool operator==(const mint& lhs, const mint& rhs) { return lhs._v == rhs._v; } friend bool operator!=(const mint& lhs, const mint& rhs) { return lhs._v != rhs._v; } private: unsigned int _v; static constexpr unsigned int umod() { return m; } static constexpr bool prime = internal::is_prime; }; template struct dynamic_modint : internal::modint_base { using mint = dynamic_modint; public: static int mod() { return (int)(bt.umod()); } static void set_mod(int m) { assert(1 <= m); bt = internal::barrett(m); } static mint raw(int v) { mint x; x._v = v; return x; } dynamic_modint() : _v(0) {} template * = nullptr> dynamic_modint(T v) { long long x = (long long)(v % (long long)(mod())); if (x < 0) x += mod(); _v = (unsigned int)(x); } template * = nullptr> dynamic_modint(T v) { _v = (unsigned int)(v % mod()); } unsigned int val() const { return _v; } mint& operator++() { _v++; if (_v == umod()) _v = 0; return *this; } mint& operator--() { if (_v == 0) _v = umod(); _v--; return *this; } mint operator++(int) { mint result = *this; ++*this; return result; } mint operator--(int) { mint result = *this; --*this; return result; } mint& operator+=(const mint& rhs) { _v += rhs._v; if (_v >= umod()) _v -= umod(); return *this; } mint& operator-=(const mint& rhs) { _v += mod() - rhs._v; if (_v >= umod()) _v -= umod(); return *this; } mint& operator*=(const mint& rhs) { _v = bt.mul(_v, rhs._v); return *this; } mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); } mint operator+() const { return *this; } mint operator-() const { return mint() - *this; } mint pow(long long n) const { assert(0 <= n); mint x = *this, r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; } mint inv() const { auto eg = internal::inv_gcd(_v, mod()); assert(eg.first == 1); return eg.second; } friend mint operator+(const mint& lhs, const mint& rhs) { return mint(lhs) += rhs; } friend mint operator-(const mint& lhs, const mint& rhs) { return mint(lhs) -= rhs; } friend mint operator*(const mint& lhs, const mint& rhs) { return mint(lhs) *= rhs; } friend mint operator/(const mint& lhs, const mint& rhs) { return mint(lhs) /= rhs; } friend bool operator==(const mint& lhs, const mint& rhs) { return lhs._v == rhs._v; } friend bool operator!=(const mint& lhs, const mint& rhs) { return lhs._v != rhs._v; } private: unsigned int _v; static internal::barrett bt; static unsigned int umod() { return bt.umod(); } }; template internal::barrett dynamic_modint::bt(998244353); using modint998244353 = static_modint<998244353>; using modint1000000007 = static_modint<1000000007>; using modint = dynamic_modint<-1>; namespace internal { template using is_static_modint = std::is_base_of; template using is_static_modint_t = std::enable_if_t::value>; template struct is_dynamic_modint : public std::false_type {}; template struct is_dynamic_modint> : public std::true_type {}; template using is_dynamic_modint_t = std::enable_if_t::value>; } // namespace internal } // namespace atcoder inline std::ostream& operator<<(std::ostream& os, const atcoder::modint x); inline std::ostream& operator<<(std::ostream& os, const atcoder::modint998244353 x); inline std::ostream& operator<<(std::ostream& os, const atcoder::modint1000000007 x); inline std::ostream& operator<<(std::ostream& os, const atcoder::modint x) { os << x.val(); return os; } inline std::ostream& operator<<(std::ostream& os, const atcoder::modint998244353 x) { os << x.val(); return os; } inline std::ostream& operator<<(std::ostream& os, const atcoder::modint1000000007 x) { os << x.val(); return os; } #include using namespace std; template inline istream& operator>>(istream& is, pair& p); template inline istream& operator>>(istream& is, vector& v); template inline ostream& operator<<(ostream& os, const pair& p); template inline ostream& operator<<(ostream& os, const vector& v); template ostream &operator<<(ostream &os, const map &mp); template ostream &operator<<(ostream &os, const set &st); template ostream &operator<<(ostream &os, const multiset &st); template ostream &operator<<(ostream &os, queue q); template ostream &operator<<(ostream &os, deque q); template ostream &operator<<(ostream &os, stack st); template ostream &operator<<(ostream &os, priority_queue pq); template inline istream& operator>>(istream& is, pair& p) { is >> p.first >> p.second; return is; } template inline istream& operator>>(istream& is, vector& v) { repe(x, v) is >> x; return is; } template inline ostream& operator<<(ostream& os, const pair& p) { os << p.first << " " << p.second; return os; } template inline ostream& operator<<(ostream& os, const vector& v) { rep(i, sz(v)) { os << v.at(i); if (i != sz(v) - 1) os << " "; } return os; } template ostream &operator<<(ostream &os, const map &mp) { for (auto &[key, val] : mp) { os << key << ":" << val << " "; } return os; } template ostream &operator<<(ostream &os, const set &st) { auto itr = st.begin(); for (int i = 0; i < (int)st.size(); i++) { os << *itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; } template ostream &operator<<(ostream &os, const multiset &st) { auto itr = st.begin(); for (int i = 0; i < (int)st.size(); i++) { os << *itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; } template ostream &operator<<(ostream &os, queue q) { while (q.size()) { os << q.front() << " "; q.pop(); } return os; } template ostream &operator<<(ostream &os, deque q) { while (q.size()) { os << q.front() << " "; q.pop_front(); } return os; } template ostream &operator<<(ostream &os, stack st) { while (st.size()) { os << st.top() << " "; st.pop(); } return os; } template ostream &operator<<(ostream &os, priority_queue pq) { while (pq.size()) { os << pq.top() << " "; pq.pop(); } return os; } template inline vector& operator--(vector& v) { repe(x, v) --x; return v; } template inline vector& operator++(vector& v) { repe(x, v) ++x; return v; } #define debug(...) debug_func(0, #__VA_ARGS__, __VA_ARGS__) // debug print #ifdef LOCAL_TEST template void debug_func(int i, T name) { (void)i; (void)name; cerr << endl; } template void debug_func(int i, const T1 &name, const T2 &a, const T3 &...b) { for ( ; name[i] != ',' && name[i] != '\0'; i++ ) cerr << name[i]; cerr << ":" << a << " "; debug_func(i + 1, name, b...); } #endif #ifndef LOCAL_TEST template void debug_func(const T &...) {} #endif using mint = atcoder::modint998244353; int main() { int n; ll k; cin >> n >> k; mint ansi = 1; int maxa = 2 * powm(10, 5) + 10; vl imos(maxa, 0); vl imos2(maxa, 0); vl l(n), r(n); rep(i, n) cin >> l[i] >> r[i]; rep(i, n) { imos[l[i]]++; imos[r[i]]--; imos2[l[i]+1]++; imos2[r[i]]--; } rep(i, 10) debug(imos[i], imos2[i]); debug(k); rep(i, maxa-1) imos[i+1] += imos[i]; rep(i, maxa-1) imos2[i+1] += imos2[i]; rep(i, 10) debug(imos[i], imos2[i]); mint ans = 1; mint powk = 1; rep(i, n) powk *= k; rep(i, maxa) { if (imos[i] == imos2[i]) continue; if (imos[i] > k) { ans = 0; break; } ll maxk = k - imos2[i]; debug(i, maxk); rep(j, imos[i] - imos2[i]) { debug(j); ans *= maxk - j; } } debug(ans); cout << powk - ans << endl; }