#pragma region Macros #include #define rep(i, n) for(int(i) = 0; (i) < (n); (i)++) #define rrep(i, n) for(int(i) = (n)-1; (i) >= 0; (i)--) #define FOR(i, m, n) for(int(i) = (m); (i) < (n); (i)++) #define ROF(i, m, n) for(int(i) = (n)-1; (i) >= (m); (i)--) #define ALL(v) (v).begin(), (v).end() #define LLA(v) (v).rbegin(), (v).rend() #define SZ(v) (int)(v).size() #define INT(...) \ int __VA_ARGS__; \ read(__VA_ARGS__) #define LL(...) \ ll __VA_ARGS__; \ read(__VA_ARGS__) #define DOUBLE(...) \ double __VA_ARGS__; \ read(__VA_ARGS__) #define CHAR(...) \ char __VA_ARGS__; \ read(__VA_ARGS__) #define STRING(...) \ string __VA_ARGS__; \ read(__VA_ARGS__) #define VEC(type, name, size) \ vector name(size); \ read(name) #define VEC2(type, name, height, width) \ vector> name(height, vector(width)); \ read(name) #define DVEC(type, name1, name2, size) \ vector name1(size), name2(size); \ read(name1, name2) #define TVEC(type, name1, name2, name3, size) \ vector name1(size), name2(size), name3(size); \ read(name1, name2, name3) using namespace std; using ll = long long; using pii = pair; using pll = pair; const int INF = 1 << 30; const ll LINF = 1LL << 60; const int MOD = 1e9 + 7; const char newl = '\n'; const int dx[] = {1, 0, -1, 0}; const int dy[] = {0, 1, 0, -1}; template inline bool between(T x, T l, T r) { return l <= x && x < r; } template inline vector make_vec(size_t a, T val) { return vector(a, val); } template inline auto make_vec(size_t a, Ts... ts) { return vector(a, make_vec(ts...)); } void read() {} template inline void read(T &a) { cin >> a; } template inline void read(pair &p) { read(p.first), read(p.second); } template inline void read(vector &v) { for(auto &&a : v) read(a); } template inline void read(vector &a, vector &b) { for(int i = 0; i < a.size(); i++) { read(a[i]); read(b[i]); } } template inline void read(vector &a, vector &b, vector &c) { for(int i = 0; i < a.size(); i++) { read(a[i]); read(b[i]); read(c[i]); } } template inline void read(Head &head, Tail &...tail) { read(head), read(tail...); } template void _write(const T &a) { cout << a; } template void _write(const std::pair &a) { cout << a.first << ' ' << a.second; } template void write(const T &a) { _write(a); cout << newl; } template void write(const vector &a) { for(int i = 0; i < a.size(); i++) { _write(a[i]); cout << (i + 1 == a.size() ? newl : ' '); } } template void write(const Head &head, const Tail &...tail) { _write(head); cout << ' '; write(tail...); } template void writel(const T &a) { cout << a << '\n'; } template void writel(const vector &a) { for(int i = 0; i < a.size(); i++) { _write(a[i]); cout << newl; } } template void writel(const Head &head, const Tail &...tail) { _write(head); cout << newl; write(tail...); } template void _debug(const T &a) { cerr << a; } template void _debug(const std::pair &a) { cerr << a.first << ' ' << a.second; } template void debug(const T &a) { _debug(a); cerr << newl; } template void debug(const vector &a) { for(int i = 0; i < a.size(); i++) { _debug(a[i]); cerr << (i + 1 == a.size() ? newl : ' '); } } template void debug(const Head &head, const Tail &...tail) { _debug(head); cerr << ' '; debug(tail...); } template void debugl(const T &a) { cerr << a << '\n'; } template void debugl(const vector &a) { for(int i = 0; i < a.size(); i++) { _debug(a[i]); cerr << newl; } } template void debugl(const Head &head, const Tail &...tail) { _debug(head); cerr << newl; debug(tail...); } template auto sum(const vector &a) { return accumulate(ALL(a), T(0)); } template auto min(const vector &a) { return *min_element(ALL(a)); } template auto max(const vector &a) { return *max_element(ALL(a)); } template void msort(vector &a, vector &b) { assert(a.size() == b.size()); vector> ab(a.size()); for(int i = 0; i < a.size(); i++) ab[i] = {a[i], b[i]}; sort(ALL(ab)); for(int i = 0; i < a.size(); i++) { a[i] = ab[i].first; b[i] = ab[i].second; } } template void msort(vector &a, vector &b, vector &c) { assert(a.size() == b.size() && b.size() == c.size()); vector> abc(a.size()); for(int i = 0; i < a.size(); i++) abc[i] = {a[i], b[i], c[i]}; sort(ALL(abc)); for(int i = 0; i < a.size(); i++) { a[i] = get<0>(abc[i]); b[i] = get<1>(abc[i]); c[i] = get<2>(abc[i]); } } template inline bool chmax(T &a, U b) { if(a < b) { a = b; return 1; } return 0; } template inline bool chmin(T &a, U b) { if(a > b) { a = b; return 1; } return 0; } int digit(ll a) { ll ret = 0; while(a && ++ret) a /= 10; return ret; } int digit_sum(ll a) { ll ret = 0; while(a) { ret += a % 10; a /= 10; } return ret; } ll llpow(ll a, ll n) { ll ret = 1; rep(i, n) ret *= a; return ret; } inline int bsf(int v) { return __builtin_ctz(v); } // 最下位の1が下から何番目か inline int bsf(ll v) { return __builtin_ctzll(v); } inline int bsr(int v) { return 31 - __builtin_clz(v); } // 最上位の1が下から何番目か inline int bsr(ll v) { return 63 - __builtin_clzll(v); } inline int lsb(int v) { return v & -v; } // 最下位の1だけ残す inline ll lsb(ll v) { return v & -v; } inline int msb(int v) { return 1 << bsr(v); } // 最上位の1だけ残す inline ll msb(ll v) { return 1LL << bsr(v); } struct IO { IO() { ios::sync_with_stdio(false); cin.tie(nullptr); cout << fixed << setprecision(10); } } io; #pragma endregion namespace math { std::set divisor(long long n) { std::set ret; for(long long i = 1; i * i <= n; i++) { if(n % i == 0) { ret.insert(i); if(i * i != n) ret.insert(n / i); } } return ret; } // 素数篩+素因数分解 // 初期化O(N),素因数分解O(logN) // たくさん素因数分解するときはこっち struct Sieve { int N; std::vector sieve; std::vector primes; Sieve(int n) : N(n), sieve(n + 1) { init(); } void init() { std::iota(sieve.begin(), sieve.end(), 0); for(int i = 2; i * i <= N; i++) { if(sieve[i] < i) continue; for(int j = i * i; j <= N; j += i) { if(sieve[j] == j) sieve[j] = i; } } for(int i = 2; i <= N; i++) { if(is_prime(i)) primes.push_back(i); } } bool is_prime(int x) { assert(x <= N); if(x == 1) return false; return sieve[x] == x; } std::map prime_factorize(int n) { assert(n <= N); std::map ret; while(n > 1) { ret[sieve[n]]++; n = n / sieve[n]; } return ret; } std::map prime_factorize_large(long long n) { std::map ret; for(auto p : primes) { while(n % p == 0) { ret[p]++; n /= p; } } if(n > 1) ret[n] = 1; return ret; } }; // 素因数分解 // O(sqrt(N)) std::map prime_factor(long long n) { std::map ret; for(long long i = 2; i * i <= n; i++) { while(n % i == 0) { ret[i]++; n /= i; } } if(n != 1) ret[n] = 1; return ret; } long long mod_pow(long long x, long long n, long long mod) { if(n == 0) return 1; long long res = mod_pow(x * x % mod, n / 2, mod); if(n & 1) res = res * x % mod; return res; } long long euler_phi(long long n) { long long ret = n; for(long long i = 2; i * i <= n; i++) { if(n % i == 0) { ret -= ret / i; while(n % i == 0) n /= i; } } if(n > 1) ret -= ret / n; return ret; } long long extgcd(long long a, long long b, long long &x, long long &y) { if(b == 0) { x = 1; y = 0; return a; } long long d = extgcd(b, a % b, y, x); y -= a / b * x; return d; } long long mod_inv(long long a, long long mod) { long long b = mod, u = 1, v = 0; while(b) { long long t = a / b; std::swap(a -= t * b, b); std::swap(u -= t * b, v); } u %= mod; if(u < 0) u += mod; return u; } std::pair crt2(const std::pair &rm1, const std::pair &rm2) { long long p, q; auto [r1, m1] = rm1; auto [r2, m2] = rm2; long long d = extgcd(r1, m2, p, q); if((r2 - r1) % d != 0) return {0, -1}; long long m = m1 * (m2 / d); long long tmp = (r2 - r1) / d * p % (m2 / d); long long c = (r1 + m1 * tmp); long long r = (c % m + m) % m; return {r, m}; } /** * @brief Garnerのアルゴリズム. x % m[i] == b[i] % m[i]を満たす最小のxを求める. * * @param rm {あまり,法}の配列. !!法はすべて互いに素!! * @return long long x % m[i] == b[i] % m[i]を満たす最小のx. */ long long garner(const std::vector> &rm) { int n = rm.size(); long long m_prod = 1; long long res = rm[0].first % rm[0].second; for(int i = 1; i < n; i++) { auto [r, m] = rm[i]; m_prod *= rm[i - 1].second; long long t = (((r - res) * mod_inv(m_prod, m)) % m + m) % m; res += t * m_prod; } return res; } /** * @brief Garnerのアルゴリズム. x % m[i] == b[i] % m[i]を満たす最小のxを求める. * * @param rm {あまり,法}の配列. !!法はすべて互いに素!! * @param mod 答えの法. * @return long long x % m[i] == b[i] % m[i]を満たす最小のx (mod M). */ long long garner_mod(std::vector> rm, long long mod) { rm.emplace_back(0, mod); int n = rm.size(); std::vector coffs(n, 1), constants(n, 0); for(int i = 0; i < n - 1; i++) { auto [r, m] = rm[i]; long long t = ((r - constants[i]) * mod_inv(coffs[i], m) % m + m) & m; for(int j = i + 1; j < n; j++) { (constants[j] += coffs[j] * t) %= rm[j].second; (coffs[j] *= m) %= rm[j].second; } } return constants.back(); } long long floor_div(long long a, long long b) { assert(b != 0); if(b < 0) a = -a, b = -b; return a >= 0 ? a / b : (a - (b - 1)) / b; } long long ceil_div(long long a, long long b) { assert(b != 0); if(b < 0) a = -a, b = -b; return a >= 0 ? (a + b - 1) / b : a / b; } int bit_length(long long x) { assert(x >= 0); int ret = 0; while(x > 0) { ret++; x /= 2; } return ret; } long long ll_sqrt(long long x) { long long ret = sqrt(x) - 1; while((ret + 1) * (ret + 1) <= x) ret++; return ret; } // multiple of d in [left,right],left>0 long long cmul(long long left, long long right, long long d) { if(left == 0) return right / d; return right / d - (left - 1) / d; } // multiple of d in [left,right] long long count_multiple(long long left, long long right, long long d) { if(right < 0) return cmul(-right, -left, d); if(left > 0) return cmul(left, right, d); return cmul(0, right, d) + cmul(0, -left, d) - 1; } }; // namespace math using namespace math; void solve() { INT(n, m, p, Q); rep(i, Q) { INT(x, f); int y = (f * mod_inv(x, p)) % p; auto fun = [&]() { ll ok = 0, ng = INF; while(ng - ok > 1) { ll mid = (ok + ng) / 2; if((y ? y : p) + p * (mid - 1) <= m) { ok = mid; } else { ng = mid; } } return ok; }; write(fun()); } } int main() { int t = 1; // cin >> t; while(t--) { solve(); } }