#ifdef NACHIA #define _GLIBCXX_DEBUG #else #define NDEBUG #endif #include <iostream> #include <string> #include <vector> #include <algorithm> #include <utility> #include <cassert> namespace nachia{ // ax + by = gcd(a,b) // return ( x, - ) std::pair<long long, long long> ExtGcd(long long a, long long b){ long long x = 1, y = 0; while(b){ long long u = a / b; std::swap(a-=b*u, b); std::swap(x-=y*u, y); } return std::make_pair(x, a); } } // namespace nachia namespace nachia{ template<unsigned int MOD> struct StaticModint{ private: using u64 = unsigned long long; unsigned int x; public: using my_type = StaticModint; template< class Elem > static Elem safe_mod(Elem x){ if(x < 0){ if(0 <= x+MOD) return x + MOD; return MOD - ((-(x+MOD)-1) % MOD + 1); } return x % MOD; } StaticModint() : x(0){} StaticModint(const my_type& a) : x(a.x){} StaticModint& operator=(const my_type&) = default; template< class Elem > StaticModint(Elem v) : x(safe_mod(v)){} unsigned int operator*() const { return x; } my_type& operator+=(const my_type& r) { auto t = x + r.x; if(t >= MOD) t -= MOD; x = t; return *this; } my_type operator+(const my_type& r) const { my_type res = *this; return res += r; } my_type& operator-=(const my_type& r) { auto t = x + MOD - r.x; if(t >= MOD) t -= MOD; x = t; return *this; } my_type operator-(const my_type& r) const { my_type res = *this; return res -= r; } my_type operator-() const noexcept { my_type res = *this; res.x = ((res.x == 0) ? 0 : (MOD - res.x)); return res; } my_type& operator*=(const my_type& r){ x = (u64)x * r.x % MOD; return *this; } my_type operator*(const my_type& r) const { my_type res = *this; return res *= r; } bool operator==(const my_type& r) const { return x == r.x; } my_type pow(unsigned long long i) const { my_type a = *this, res = 1; while(i){ if(i & 1){ res *= a; } a *= a; i >>= 1; } return res; } my_type inv() const { return my_type(ExtGcd(x, MOD).first); } unsigned int val() const { return x; } static constexpr unsigned int mod() { return MOD; } static my_type raw(unsigned int val) { auto res = my_type(); res.x = val; return res; } my_type& operator/=(const my_type& r){ return operator*=(r.inv()); } my_type operator/(const my_type& r) const { return operator*(r.inv()); } }; } // namespace nachia namespace nachia{ struct WordsizeTree{ using Word = unsigned long long; static constexpr int W = 64; int N; std::vector<std::vector<Word>> A; static int highBit(Word x){ if(x == 0) return 0; return W-1 - __builtin_clzll(x); } static int lowBit(Word x){ if(x == 0) return W; return __builtin_ctzll(x); } WordsizeTree(int length){ N = length; int n = length; do { std::vector<Word> a(n/W+1,0); A.emplace_back(std::move(a)); n /= W; } while(n); } WordsizeTree(const std::string& binStr = ""){ N = binStr.size(); int n = N; { std::vector<Word> a(n/W+1); for(int i=0; i<n; i++) if(binStr[i] == '1'){ a[i/W] |= (Word)1 << (i%W); } A.emplace_back(std::move(a)); n /= W; } while(n){ std::vector<Word> a(n/W+1,0); for(int i=0; i<=n; i++){ if(A.back()[i]) a[i/W] |= (Word)1 << (i%W); } A.emplace_back(std::move(a)); n /= W; } } void insert(int x){ for(auto& a : A){ a[x/W] |= (Word)1 << (x % W); x /= W; } } void erase(int x){ for(auto& a : A){ a[x/W] &= ~((Word)1 << (x % W)); if(a[x/W]) return; x /= W; } } int count(int x) const { return (int)((A[0][x/W] >> (x%W)) & 1); } void flip(int x){ if(count(x)) erase(x); else insert(x); } int noLessThan(int x) const { if(x < 0) x = 0; if(N <= x) return N; int d = 0, i = x; while(true){ if(d >= (int)A.size()) return N; if(i/W >= (int)A[d].size()) return N; Word m = A[d][i/W] & ((~(Word)0) << (i%W)); if(!m){ d++; i /= W; i++; } else{ int to = lowBit(m); i = i/W*W + to; if(d == 0) break; i *= W; d--; } } return i; } int noGreaterThan(int x) const { if(x < 0) return -1; if(N <= x) x = N-1; int d = 0, i = x; while(true){ if(i < 0) return -1; if(d >= (int)A.size()) return -1; Word m = A[d][i/W] & ~((~(Word)1) << (i%W)); if(!m){ d++; i /= W; i--; } else{ int to = highBit(m); i = i/W*W + to; if(d == 0) break; i *= W; i += W-1; d--; } } return i; } }; } // namespace nachia #include <cstdint> namespace nachia{ int Popcount(unsigned long long c) noexcept { #ifdef __GNUC__ return __builtin_popcountll(c); #else c = (c & (~0ull/3)) + ((c >> 1) & (~0ull/3)); c = (c & (~0ull/5)) + ((c >> 2) & (~0ull/5)); c = (c & (~0ull/17)) + ((c >> 4) & (~0ull/17)); c = (c * (~0ull/257)) >> 56; return c; #endif } // please ensure x != 0 int MsbIndex(unsigned long long x) noexcept { #ifdef __GNUC__ return 63 - __builtin_clzll(x); #else using u64 = unsigned long long; int q = (x >> 32) ? 32 : 0; auto m = x >> q; constexpr u64 hi = 0x88888888; constexpr u64 mi = 0x11111111; m = (((m | ~(hi - (m & ~hi))) & hi) * mi) >> 35; m = (((m | ~(hi - (m & ~hi))) & hi) * mi) >> 31; q += (m & 0xf) << 2; q += 0x3333333322221100 >> (((x >> q) & 0xf) << 2) & 0xf; return q; #endif } // please ensure x != 0 int LsbIndex(unsigned long long x) noexcept { #ifdef __GNUC__ return __builtin_ctzll(x); #else return MsbIndex(x & -x); #endif } } namespace nachia{ template<class PosX, class PosY> struct TwoDRectangleQuery{ private: struct BitVectorRank { using u64 = std::uint64_t; using u32 = std::uint32_t; std::vector<std::pair<u64, u32>> a; BitVectorRank(const std::vector<bool>& b = {}){ int n = b.size(); a.assign(n/64 + 1, std::make_pair((u64)0, (u32)0)); auto p = b.begin(); u32 sum = 0; u64 tmp = 0; for(int i=0; i<=n; i+=64){ tmp = 0; int maxd = std::min<int>(n - i, 64); for(int d=0; d<maxd; d++){ tmp |= (u64)(*p ? 1 : 0) << d; ++p; } a[i/64] = std::make_pair(tmp, sum); sum += Popcount(tmp); } } std::uint32_t rank(std::uint32_t i) const { auto [b, s] = a[i >> 6]; return (u32)(Popcount(b & ~(~u64(0) << (i & 63)))) + s; } bool get(std::uint32_t i) const { return (a[i >> 6].first >> (i & 63)) & 1; } }; int n; int N; int logN; std::vector<PosX> Xsorted; std::vector<PosY> Ysorted; std::vector<int> rankX; std::vector<std::vector<int>> Idx; std::vector<int> Z; std::vector<BitVectorRank> L; public: TwoDRectangleQuery(){} TwoDRectangleQuery(const std::vector<std::pair<PosX, PosY>>& pos){ n = pos.size(); std::vector<int> sortIY(n); for(int i=0; i<n; i++) sortIY[i] = i; std::sort(sortIY.begin(),sortIY.end(),[&pos](int l,int r){ return pos[l].second<pos[r].second; }); Ysorted.resize(n); for(int i=0; i<n; i++) Ysorted[i] = pos[sortIY[i]].second; std::vector<int> sortIX(n); rankX.resize(n); for(int i=0; i<n; i++) sortIX[i] = i; std::sort(sortIX.begin(),sortIX.end(),[&pos](int l,int r){ return pos[l]<pos[r]; }); Xsorted.resize(n); for(int i=0; i<n; i++) Xsorted[i] = pos[sortIX[i]].first; for(int i=0; i<n; i++) rankX[sortIX[i]] = i; N = 1; logN = 0; while(N < n){ N *= 2; logN++; } Idx.assign(logN+1, std::vector<int>(n,-1)); L.resize(logN); Z.resize(logN); for(int i=0; i<n; i++) Idx.back()[i] = sortIY[i]; for(int i=logN-1; i>=0; i--){ std::vector<bool> Lbuf(n,0); auto& preList = Idx[i+1]; int z = ((n >> (i+1)) << i) + std::min(1<<i, (n % (2 << i))); Z[i] = z; int ai = 0, bi = z; for(int k=0; k<n; k++){ bool chooseb = rankX[preList[k]] & (1<<i); if(!chooseb) Idx[i][ai++] = preList[k]; else Idx[i][bi++] = preList[k]; Lbuf[k] = !chooseb; } L[i] = BitVectorRank(Lbuf); } for(int i=0; i<n; i++) rankX[sortIY[i]] = i; } int getSegmentCount() const { return Idx.size(); } int size() const { return n; } int toVtx(int d, int i) const { return Idx[d][i]; } struct UpdatePoint{ int d, i; }; std::vector<UpdatePoint> getUpdatePoints(int v) const { std::vector<UpdatePoint> res(logN+1); int p = rankX[v]; int d = logN; while(d > 0){ res[d] = { d,p }; d--; if(L[d].get(p)) p = L[d].rank(p); else p = Z[d] + p - L[d].rank(p); } res[d] = {d,p}; return res; } struct Query{ int d,l,r; }; std::vector<Query> getRangesFromIdx(int xl, int xr, int yl, int yr) const { if(xl >= xr || yl >= yr) return {}; std::vector<Query> res; struct Search{ int i, xa, xb, ys, yt; }; std::vector<Search> Q; res.reserve((logN+1)*2); Q.reserve((logN+1)*2); Q.push_back({ logN,0,n,yl,yr }); for(int i=0; i<(int)Q.size(); i++){ auto p = Q[i]; if(p.xa == p.xb) continue; if(xl <= p.xa && p.xb <= xr){ res.push_back({ p.i, p.ys, p.yt }); continue; } p.i--; int nxs = L[p.i].rank(p.ys), nxt = L[p.i].rank(p.yt); int xm = p.xa+(1<<p.i); if(xl < xm) Q.push_back({ p.i,p.xa,xm,nxs,nxt }); if(xm < xr) Q.push_back({ p.i,xm,p.xb,Z[p.i]+p.ys-nxs,Z[p.i]+p.yt-nxt }); } return res; } std::vector<Query> getRanges(PosX xl, PosX xr, PosY yl, PosY yr) const { return getRangesFromIdx( lower_bound(Xsorted.begin(),Xsorted.end(),xl) - Xsorted.begin(), lower_bound(Xsorted.begin(),Xsorted.end(),xr) - Xsorted.begin(), lower_bound(Ysorted.begin(),Ysorted.end(),yl) - Ysorted.begin(), lower_bound(Ysorted.begin(),Ysorted.end(),yr) - Ysorted.begin() ); } }; } // namespace nachia using i64 = long long; using u64 = unsigned long long; #define rep(i,n) for(i64 i=0; i<i64(n); i++) const i64 INF = 1001001001001001001; template<typename A> void chmin(A& l, const A& r){ if(r < l) l = r; } template<typename A> void chmax(A& l, const A& r){ if(l < r) l = r; } using namespace std; using mint = nachia::StaticModint<998244353>; int main(){ ios::sync_with_stdio(false); cin.tie(nullptr); int Z = 200000; vector<int> contribute(Z+1); vector<vector<int>> pf(Z+1); for(int p=2; p<=Z; p++) if(pf[p].empty()){ for(int pp=p; ; pp*=p){ contribute[pp] = p; for(int q=1; pp*q<=Z; q++){ pf[pp*q].push_back(pp); } if(i64(pp)*p > Z) break; } } const int th = 16; int N; cin >> N; vector<int> A(N); rep(i,N) cin >> A[i]; vector<nachia::WordsizeTree> fairy; vector<mint> cfairy; rep(i,Z+1) if(contribute[i] != 0 && contribute[i] < th){ int d = fairy.size(); fairy.push_back(nachia::WordsizeTree(N)); rep(p,N) if(A[p] % i == 0) fairy[d].insert(p); cfairy.push_back(contribute[i]); } vector<pair<int,int>> points; vector<mint> V; vector<int> P(Z+1, -1); for(auto& a : A) for(int p=2; p<th; p++) while(a%p == 0) a/=p; rep(i,N){ int a = A[i]; for(int pp : pf[a]) if(contribute[pp] >= th){ if(P[pp] != -1){ points.push_back({ P[pp], i }); V.push_back(contribute[pp]); } P[pp] = i; } } vector<mint> prod(N+1); prod[0] = 1; rep(i,N) prod[i+1] = prod[i] * A[i]; auto md = nachia::TwoDRectangleQuery<int,int>(points); vector<vector<mint>> F(md.getSegmentCount(), vector<mint>(points.size()+1)); rep(i,F.size()){ F[i][0] = 1; rep(j,points.size()) F[i][j+1] = F[i][j] * V[md.toVtx(i,j)]; } int Q; cin >> Q; mint ans = 1; //rep(i,points.size()) cout << points[i].first << " " << points[i].second << " " << V[i].val() << endl; //cout << endl; rep(qi,Q){ int a,b; cin >> a >> b; int l = (ans * mint(a)).val() % N; int r = (ans * mint(b)).val() % N; if(l > r) swap(l, r); r += 1; //cout << (l+1) << " " << r << endl; mint p = 1; mint q = 1; rep(i,fairy.size()) if(fairy[i].noLessThan(l) < r) p *= cfairy[i]; p *= prod[r]; q *= prod[l]; for(auto [d,ll,rr] : md.getRanges(l,r,l,r)){ q *= F[d][rr]; p *= F[d][ll]; } ans = p / q; cout << ans.val() << "\n"; } return 0; }