#include #include using namespace std; using ll = long long; using mint = atcoder::modint998244353; template struct csr { using itr = typename std::vector::iterator; struct Node { itr st, en; itr begin() { return st; } itr end() { return en; } int size() { return en - st; } T operator[](int p){ return st[p]; } }; const int N; std::vector start; std::vector E; std::vector> edge; csr(int n) : N(n), start(n + 1) {} void add_edge(int u, T v){ assert(0 <= u && u < N); start[u + 1]++; edge.emplace_back(u, v); } void build(){ E.resize(edge.size()); for(int i = 0; i < N; i++) start[i + 1] += start[i]; auto cnt = start; for(auto [u, v] : edge) E[cnt[u]++] = v; } Node operator[](int p) { return Node{E.begin() + start[p], E.begin() + start[p + 1]}; } }; int main(){ ios::sync_with_stdio(false); cin.tie(0); constexpr int r = 202500; vector fact(r + 1), inv(r + 1); fact[0] = 1; for(int i = 1; i <= r; i++) fact[i] = fact[i - 1] * mint::raw(i); inv[r] = fact[r].inv(); for(int i = r; i >= 1; i--) inv[i - 1] = inv[i] * mint::raw(i); auto binom = [&](int r, int c) -> mint { if(c < 0 || r < c) return 0; return fact[r] * inv[c] * inv[r - c]; }; csr divs(r + 1); for(int i = 1; i <= r; i++){ for(int j = i; j <= r; j += i){ divs.add_edge(j, i); } } divs.build(); int T; cin >> T; while(T--){ int n, a; cin >> n >> a; mint ans; n--; for(auto d : divs[a]){ int ad = a / d; int v = ad - n; if(v % 2 != 0 || v > 0) continue; v = -v / 2, ad++; ans += binom(n, v) - binom(n, v + ad); } cout << ans.val() << '\n'; } }