#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using lint = long long; using pint = pair; using plint = pair; struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_; #define ALL(x) (x).begin(), (x).end() #define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i=i##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; } template bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; } const std::vector> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}}; int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); } template T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); } template std::pair operator+(const std::pair &l, const std::pair &r) { return std::make_pair(l.first + r.first, l.second + r.second); } template std::pair operator-(const std::pair &l, const std::pair &r) { return std::make_pair(l.first - r.first, l.second - r.second); } template std::vector sort_unique(std::vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template int arglb(const std::vector &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); } template int argub(const std::vector &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); } template IStream &operator>>(IStream &is, std::vector &vec) { for (auto &v : vec) is >> v; return is; } template OStream &operator<<(OStream &os, const std::vector &vec); template OStream &operator<<(OStream &os, const std::array &arr); template OStream &operator<<(OStream &os, const std::unordered_set &vec); template OStream &operator<<(OStream &os, const pair &pa); template OStream &operator<<(OStream &os, const std::deque &vec); template OStream &operator<<(OStream &os, const std::set &vec); template OStream &operator<<(OStream &os, const std::multiset &vec); template OStream &operator<<(OStream &os, const std::unordered_multiset &vec); template OStream &operator<<(OStream &os, const std::pair &pa); template OStream &operator<<(OStream &os, const std::map &mp); template OStream &operator<<(OStream &os, const std::unordered_map &mp); template OStream &operator<<(OStream &os, const std::tuple &tpl); template OStream &operator<<(OStream &os, const std::vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } template OStream &operator<<(OStream &os, const std::array &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; } template std::istream &operator>>(std::istream &is, std::tuple &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template OStream &operator<<(OStream &os, const std::tuple &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; } template OStream &operator<<(OStream &os, const std::unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template OStream &operator<<(OStream &os, const std::set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::pair &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; } template OStream &operator<<(OStream &os, const std::map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::unordered_map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } #ifdef HITONANODE_LOCAL const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m"; #define dbg(x) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl #define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl : std::cerr) #else #define dbg(x) ((void)0) #define dbgif(cond, x) ((void)0) #endif struct ModIntRuntime { private: static int md; public: using lint = long long; static int mod() { return md; } int val_; static std::vector &facs() { static std::vector facs_; return facs_; } static int &get_primitive_root() { static int primitive_root_ = 0; if (!primitive_root_) { primitive_root_ = [&]() { std::set fac; int v = md - 1; for (lint i = 2; i * i <= v; i++) while (v % i == 0) fac.insert(i), v /= i; if (v > 1) fac.insert(v); for (int g = 1; g < md; g++) { bool ok = true; for (auto i : fac) if (ModIntRuntime(g).power((md - 1) / i) == 1) { ok = false; break; } if (ok) return g; } return -1; }(); } return primitive_root_; } static void set_mod(const int &m) { if (md != m) facs().clear(); md = m; get_primitive_root() = 0; } ModIntRuntime &_setval(lint v) { val_ = (v >= md ? v - md : v); return *this; } int val() const noexcept { return val_; } ModIntRuntime() : val_(0) {} ModIntRuntime(lint v) { _setval(v % md + md); } explicit operator bool() const { return val_ != 0; } ModIntRuntime operator+(const ModIntRuntime &x) const { return ModIntRuntime()._setval((lint)val_ + x.val_); } ModIntRuntime operator-(const ModIntRuntime &x) const { return ModIntRuntime()._setval((lint)val_ - x.val_ + md); } ModIntRuntime operator*(const ModIntRuntime &x) const { return ModIntRuntime()._setval((lint)val_ * x.val_ % md); } ModIntRuntime operator/(const ModIntRuntime &x) const { return ModIntRuntime()._setval((lint)val_ * x.inv().val() % md); } ModIntRuntime operator-() const { return ModIntRuntime()._setval(md - val_); } ModIntRuntime &operator+=(const ModIntRuntime &x) { return *this = *this + x; } ModIntRuntime &operator-=(const ModIntRuntime &x) { return *this = *this - x; } ModIntRuntime &operator*=(const ModIntRuntime &x) { return *this = *this * x; } ModIntRuntime &operator/=(const ModIntRuntime &x) { return *this = *this / x; } friend ModIntRuntime operator+(lint a, const ModIntRuntime &x) { return ModIntRuntime()._setval(a % md + x.val_); } friend ModIntRuntime operator-(lint a, const ModIntRuntime &x) { return ModIntRuntime()._setval(a % md - x.val_ + md); } friend ModIntRuntime operator*(lint a, const ModIntRuntime &x) { return ModIntRuntime()._setval(a % md * x.val_ % md); } friend ModIntRuntime operator/(lint a, const ModIntRuntime &x) { return ModIntRuntime()._setval(a % md * x.inv().val() % md); } bool operator==(const ModIntRuntime &x) const { return val_ == x.val_; } bool operator!=(const ModIntRuntime &x) const { return val_ != x.val_; } bool operator<(const ModIntRuntime &x) const { return val_ < x.val_; } // To use std::map friend std::istream &operator>>(std::istream &is, ModIntRuntime &x) { lint t; return is >> t, x = ModIntRuntime(t), is; } friend std::ostream &operator<<(std::ostream &os, const ModIntRuntime &x) { return os << x.val_; } lint power(lint n) const { lint ans = 1, tmp = this->val_; while (n) { if (n & 1) ans = ans * tmp % md; tmp = tmp * tmp % md; n /= 2; } return ans; } ModIntRuntime pow(lint n) const { return power(n); } ModIntRuntime inv() const { return this->pow(md - 2); } ModIntRuntime fac() const { int l0 = facs().size(); if (l0 > this->val_) return facs()[this->val_]; facs().resize(this->val_ + 1); for (int i = l0; i <= this->val_; i++) facs()[i] = (i == 0 ? ModIntRuntime(1) : facs()[i - 1] * ModIntRuntime(i)); return facs()[this->val_]; } ModIntRuntime doublefac() const { lint k = (this->val_ + 1) / 2; return (this->val_ & 1) ? ModIntRuntime(k * 2).fac() / (ModIntRuntime(2).pow(k) * ModIntRuntime(k).fac()) : ModIntRuntime(k).fac() * ModIntRuntime(2).pow(k); } ModIntRuntime nCr(int r) const { if (r < 0 or this->val_ < r) return ModIntRuntime(0); return this->fac() / ((*this - r).fac() * ModIntRuntime(r).fac()); } ModIntRuntime sqrt() const { if (val_ == 0) return 0; if (md == 2) return val_; if (power((md - 1) / 2) != 1) return 0; ModIntRuntime b = 1; while (b.power((md - 1) / 2) == 1) b += 1; int e = 0, m = md - 1; while (m % 2 == 0) m >>= 1, e++; ModIntRuntime x = power((m - 1) / 2), y = (*this) * x * x; x *= (*this); ModIntRuntime z = b.power(m); while (y != 1) { int j = 0; ModIntRuntime t = y; while (t != 1) j++, t *= t; z = z.power(1LL << (e - j - 1)); x *= z, z *= z, y *= z; e = j; } return ModIntRuntime(std::min(x.val_, md - x.val_)); } }; int ModIntRuntime::md = 1; using mint = ModIntRuntime; int main() { int M; cin >> M; mint::set_mod(M); constexpr int D = 28; vector G(D), H(D); cin >> G >> H; const mint hsum = accumulate(ALL(H), mint(0)); vector diff(D); REP(i, D) diff.at(i) = G.at(i) - H.at(i); const int L = 11, R = D - L; vector> dpl(L + 1), dpr(R + 1); auto recl = [&](auto &&self, int now, int nuse, mint sum) -> void { if (now == L) { dpl.at(nuse).push_back(sum.val()); return; } self(self, now + 1, nuse, sum); self(self, now + 1, nuse + 1, sum + diff.at(now)); }; auto recr = [&](auto &&self, int now, int nuse, mint sum) -> void { if (now == R) { dpr.at(nuse).push_back(sum.val()); return; } self(self, now + 1, nuse, sum); self(self, now + 1, nuse + 1, sum + diff.at(L + now)); }; recl(recl, 0, 0, 0); recr(recr, 0, 0, 0); for (auto &v : dpr) sort(v.begin(), v.end()); int Q; cin >> Q; while (Q--) { int k, x; cin >> k >> x; int ret = 0; FOR(luse, 0, k + 1) { const int ruse = k - luse; if (luse > L or ruse > R) continue; for (int v : dpl.at(luse)) { const int lo = (mint(x) - hsum - v).val(); const int hi = (mint(M - 1) - hsum - v).val() + 1; if (lo >= hi) { ret += (int)dpr.at(ruse).size() - (arglb(dpr.at(ruse), lo) - arglb(dpr.at(ruse), hi)); } else { ret += arglb(dpr.at(ruse), hi) - arglb(dpr.at(ruse), lo); } } } cout << ret << '\n'; } }