#line 1 "..\\Main.cpp" #include #include #include #include #include #line 3 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\math\\combination.hpp" namespace nachia{ template class Comb{ private: static constexpr int MOD = Modint::mod(); std::vector F; std::vector iF; public: void extend(int newN){ int prevN = (int)F.size() - 1; if(newN >= MOD) newN = MOD - 1; if(prevN >= newN) return; F.resize(newN+1); iF.resize(newN+1); for(int i=prevN+1; i<=newN; i++) F[i] = F[i-1] * Modint::raw(i); iF[newN] = F[newN].inv(); for(int i=newN; i>prevN; i--) iF[i-1] = iF[i] * Modint::raw(i); } Comb(int n = 1){ F.assign(2, Modint(1)); iF.assign(2, Modint(1)); extend(n); } Modint factorial(int n) const { return F[n]; } Modint invFactorial(int n) const { return iF[n]; } Modint invOf(int n) const { return iF[n] * F[n-1]; } Modint comb(int n, int r) const { if(n < 0 || n < r || r < 0) return Modint(0); return F[n] * iF[r] * iF[n-r]; } Modint invComb(int n, int r) const { if(n < 0 || n < r || r < 0) return Modint(0); return iF[n] * F[r] * F[n-r]; } Modint perm(int n, int r) const { if(n < 0 || n < r || r < 0) return Modint(0); return F[n] * iF[n-r]; } Modint invPerm(int n, int r) const { if(n < 0 || n < r || r < 0) return Modint(0); return iF[n] * F[n-r]; } Modint operator()(int n, int r) const { return comb(n,r); } }; } // namespace nachia #line 7 "..\\Main.cpp" using Modint = atcoder::static_modint<998244353>; using namespace std; using i64 = long long; using u64 = unsigned long long; #define rep(i,n) for(int i=0; i<(int)(n); i++) const i64 INF = 1001001001001001001; void testcase(){ int T; cin >> T; auto comb = nachia::Comb(1000'000); int B = 500; int BB = 210000; vector> F(B+3); F[0] = {1}; rep(d,B+2){ F[d+1].resize(d+2); rep(i,d+1) F[d+1][i] += F[d][i]; rep(i,d+1) F[d+1][i+1] -= F[d][i]; } struct Query { int n, m, q; }; vector> NM(BB / B + 1); vector ans(T); rep(t,T){ int n,m; cin >> n >> m; if((m-1)*2 < n-1) continue; NM[(n-1) / B].push_back({ n-1, (m-1)*2-(n-1), t }); } rep(x,NM.size()){ int Z = BB * 2 + B * 2; vector buf(Z+1); int qn = (x+1) * B; buf[0] = comb(qn, qn); buf[1] = comb(qn+1, qn); for(int z=2; z<=Z; z++) buf[z] = buf[z-2] + comb(qn+z, qn); for(auto [n,m,i] : NM[x]){ int d = qn - n; Modint a = 0; rep(j,d+1) if(j<=m) a += buf[m-j] * F[d][j]; ans[i] = a; } } rep(t,T){ cout << ans[t].val() << '\n'; } } int main(){ ios::sync_with_stdio(false); cin.tie(nullptr); //int T; cin >> T; rep(t,T) testcase(); return 0; }