#line 1 "main.cpp" //#pragma GCC target("avx") //#pragma GCC optimize("O3") //#pragma GCC optimize("unroll-loops") #include #ifdef LOCAL #include #define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__) #else #define debug(...) (static_cast(0)) #endif using namespace std; using ll = long long; using ld = long double; using pll = pair; using pii = pair; using vi = vector; using vvi = vector; using vvvi = vector; using vl = vector; using vvl = vector; using vvvl = vector; using vpii = vector; using vpll = vector; using vs = vector; template using pq = priority_queue, greater>; #define overload4(_1, _2, _3, _4, name, ...) name #define overload3(a,b,c,name,...) name #define rep1(n) for (ll UNUSED_NUMBER = 0; UNUSED_NUMBER < (n); ++UNUSED_NUMBER) #define rep2(i, n) for (ll i = 0; i < (n); ++i) #define rep3(i, a, b) for (ll i = (a); i < (b); ++i) #define rep4(i, a, b, c) for (ll i = (a); i < (b); i += (c)) #define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__) #define rrep1(n) for(ll i = (n) - 1;i >= 0;i--) #define rrep2(i,n) for(ll i = (n) - 1;i >= 0;i--) #define rrep3(i,a,b) for(ll i = (b) - 1;i >= (a);i--) #define rrep4(i,a,b,c) for(ll i = (a) + ((b)-(a)-1) / (c) * (c);i >= (a);i -= c) #define rrep(...) overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)(__VA_ARGS__) #define all1(i) begin(i) , end(i) #define all2(i,a) begin(i) , begin(i) + a #define all3(i,a,b) begin(i) + a , begin(i) + b #define all(...) overload3(__VA_ARGS__, all3, all2, all1)(__VA_ARGS__) #define sum(...) accumulate(all(__VA_ARGS__),0LL) template bool chmin(T &a, const T &b){ if(a > b){ a = b; return 1; } else return 0; } template bool chmax(T &a, const T &b){ if(a < b){ a = b; return 1; } else return 0; } template auto min(const T& a){ return *min_element(all(a)); } template auto max(const T& a){ return *max_element(all(a)); } template void in(Ts&... t); #define INT(...) int __VA_ARGS__; in(__VA_ARGS__) #define LL(...) ll __VA_ARGS__; in(__VA_ARGS__) #define STR(...) string __VA_ARGS__; in(__VA_ARGS__) #define CHR(...) char __VA_ARGS__; in(__VA_ARGS__) #define DBL(...) double __VA_ARGS__; in(__VA_ARGS__) #define LD(...) ld __VA_ARGS__; in(__VA_ARGS__) #define VEC(type, name, size) vector name(size); in(name) #define VV(type, name, h, w) vector> name(h, vector(w)); in(name) ll intpow(ll a, ll b){ ll ans = 1; while(b){if(b & 1) ans *= a; a *= a; b /= 2;} return ans;} ll modpow(ll a, ll b, ll p){ ll ans = 1; a %= p;while(b){ if(b & 1) (ans *= a) %= p; (a *= a) %= p; b /= 2; } return ans; } ll GCD(ll a,ll b) { if(a == 0 || b == 0) return 0; if(a % b == 0) return b; else return GCD(b,a%b);} ll LCM(ll a,ll b) { if(a == 0) return b; if(b == 0) return a;return a / GCD(a,b) * b;} namespace IO{ #define VOID(a) decltype(void(a)) struct setting{ setting(){cin.tie(nullptr); ios::sync_with_stdio(false);fixed(cout); cout.precision(12);}} setting; template struct P : P{}; template<> struct P<0>{}; template void i(T& t){ i(t, P<3>{}); } void i(vector::reference t, P<3>){ int a; i(a); t = a; } template auto i(T& t, P<2>) -> VOID(cin >> t){ cin >> t; } template auto i(T& t, P<1>) -> VOID(begin(t)){ for(auto&& x : t) i(x); } template void ituple(T& t, index_sequence){ in(get(t)...);} template auto i(T& t, P<0>) -> VOID(tuple_size{}){ ituple(t, make_index_sequence::value>{});} #undef VOID } #define unpack(a) (void)initializer_list{(a, 0)...} template void in(Ts&... t){ unpack(IO :: i(t)); } #undef unpack static const double PI = 3.1415926535897932; template struct REC { F f; REC(F &&f_) : f(forward(f_)) {} template auto operator()(Args &&...args) const { return f(*this, forward(args)...); }}; //constexpr int mod = 1000000007; constexpr int mod = 998244353; #line 2 "library/modint/Modint.hpp" template struct Modint{ int x; Modint():x(0) {} Modint(long long y): x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {} Modint &operator += (const Modint &p) { if((x += p.x) >= mod) x -= mod; return *this;} Modint &operator -= (const Modint &p) { if ((x += mod - p.x) >= mod) x -= mod; return *this;} Modint &operator *= (const Modint &p) { x = (int)(1LL * x * p.x % mod); return *this;} Modint &operator /= (const Modint &p) { *this *= p.inverse(); return *this;} Modint operator -() const{return Modint(-x);} Modint operator +(const Modint &p) const {return Modint(*this) += p;} Modint operator -(const Modint &p) const {return Modint(*this) -= p;} Modint operator *(const Modint &p) const {return Modint(*this) *= p;} Modint operator /(const Modint &p) const {return Modint(*this) /= p;} Modint &operator ++() {if(x == mod - 1) x = 0; else x++; return *this;} Modint &operator --() {if(x == 0) x = mod - 1; else x--; return *this;} bool operator == (const Modint &p) const {return x == p.x;} bool operator != (const Modint &p) const {return x != p.x;} Modint inverse() const { int a = x, b = mod, u = 1, v = 0, t; while (b > 0) { t = a / b; swap(a -= t * b, b); swap(u -= t * v, v); } return Modint(u);} Modint pow(long long n) const { Modint ret(1), mul(x); while (n > 0) { if (n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret;} friend ostream &operator<<(ostream &os, const Modint &p) { return os << p.x; } friend istream &operator>>(istream &is, Modint &a) { long long t; is >> t; a = Modint(t); return (is); } static constexpr int get_mod() {return mod;} }; #line 87 "main.cpp" using mint = Modint; using vm = vector; using vvm = vector; using vvvm = vector; #line 2 "modulo/multipoint-binomial-sum.hpp" #line 2 "misc/mo.hpp" struct Mo { int width; vector left, right, order; Mo(int N, int Q) : order(Q) { width = max(1, 1.0 * N / max(1.0, sqrt(Q * 2.0 / 3.0))); iota(begin(order), end(order), 0); } void insert(int l, int r) { /* [l, r) */ left.emplace_back(l); right.emplace_back(r); } template void run(const AL &add_left, const AR &add_right, const DL &delete_left, const DR &delete_right, const REM &rem) { assert(left.size() == order.size()); sort(begin(order), end(order), [&](int a, int b) { int ablock = left[a] / width, bblock = left[b] / width; if (ablock != bblock) return ablock < bblock; if (ablock & 1) return right[a] < right[b]; return right[a] > right[b]; }); int nl = 0, nr = 0; for (auto idx : order) { while (nl > left[idx]) add_left(--nl); while (nr < right[idx]) add_right(nr++); while (nl < left[idx]) delete_left(nl++); while (nr > right[idx]) delete_right(--nr); rem(idx); } } }; /** * @brief Mo's algorithm * @docs docs/misc/mo.md */ #line 2 "modulo/binomial.hpp" template struct Binomial { vector f, g, h; Binomial(int MAX = 0) { assert(T::get_mod() != 0 && "Binomial()"); f.resize(1, T{1}); g.resize(1, T{1}); h.resize(1, T{1}); while (MAX >= (int)f.size()) extend(); } void extend() { int n = f.size(); int m = n * 2; f.resize(m); g.resize(m); h.resize(m); for (int i = n; i < m; i++) f[i] = f[i - 1] * T(i); g[m - 1] = f[m - 1].inverse(); h[m - 1] = g[m - 1] * f[m - 2]; for (int i = m - 2; i >= n; i--) { g[i] = g[i + 1] * T(i + 1); h[i] = g[i] * f[i - 1]; } } T fac(int i) { if (i < 0) return T(0); while (i >= (int)f.size()) extend(); return f[i]; } T finv(int i) { if (i < 0) return T(0); while (i >= (int)g.size()) extend(); return g[i]; } T inv(int i) { if (i < 0) return -inv(-i); while (i >= (int)h.size()) extend(); return h[i]; } T C(int n, int r) { if (n < 0 || n < r || r < 0) return T(0); return fac(n) * finv(n - r) * finv(r); } inline T operator()(int n, int r) { return C(n, r); } template T multinomial(const vector& r) { static_assert(is_integral::value == true); int n = 0; for (auto& x : r) { if (x < 0) return T(0); n += x; } T res = fac(n); for (auto& x : r) res *= finv(x); return res; } template T operator()(const vector& r) { return multinomial(r); } T C_naive(int n, int r) { if (n < 0 || n < r || r < 0) return T(0); T ret = T(1); r = min(r, n - r); for (int i = 1; i <= r; ++i) ret *= inv(i) * (n--); return ret; } T P(int n, int r) { if (n < 0 || n < r || r < 0) return T(0); return fac(n) * finv(n - r); } T H(int n, int r) { if (n < 0 || r < 0) return T(0); return r == 0 ? 1 : C(n + r - 1, r); } }; #line 5 "modulo/multipoint-binomial-sum.hpp" template vector multipoint_binomial_sum(const vector>& qs) { int N = 2; for (auto& p : qs) N = max(N, p.first); Binomial b(N + 1); int Q = qs.size(); Mo mo(N, Q); for (auto& p : qs) { assert(p.second <= p.first); assert(p.first <= N); mo.insert(p.second, p.first); } vector ans(Q); mint cur = 1; int n = 0, m = 0; auto al = [&](int) { cur -= b.C(n, m--); }; auto ar = [&](int) { cur += cur - b.C(n++, m); }; auto el = [&](int) { cur += b.C(n, ++m); }; auto er = [&](int) { cur = (cur + b.C(--n, m)) * b.inv(2); }; auto q = [&](int i) { ans[i] = cur; }; mo.run(al, ar, el, er, q); return ans; } /** * @brief 二項係数のprefix sumの多点評価 */ int main() { INT(TT); vpii q(TT); vm ans(TT); rep(i,TT) { cin >> q[i].first >> q[i].second; ans[i] = mint(2).pow(q[i].first) - 1; q[i].first--; q[i].second--; } auto ret = multipoint_binomial_sum(q); rep(i,TT) cout << ans[i] * ret[i] << '\n'; }