#include #include #include #include #include #include using namespace std; using ll = long long; using pli = pair; using mli = map; using vp = vector; constexpr int Z = 998244353; // copyed Pollard-rho part from cp-algorithms //ll mult(ll a, ll b, ll mod) { // return (__int128)a * b % mod; //} // //ll f(ll x, ll c, ll mod) { // return (mult(x, x, mod) + c) % mod; //} // //ll rho(ll n, ll x0=2, ll c=1) { // ll x = x0; // ll y = x0; // ll g = 1; // while (g == 1) { // x = f(x, c, n); // y = f(y, c, n); // y = f(y, c, n); // g = gcd(abs(x - y), n); // } // return g; //} // //ll bexp(ll a, ll n, ll m) { // if (n == 0) { // return 1; // } // if (n % 2 == 1) { // return mult(a, bexp(a, n - 1, m), m); // } // ll t = bexp(a, n / 2, m); // return mult(t, t, m); //} // //bool mr(ll p) { // if (p < 2) return 0; // if (p == 2) return 1; // if (p == 3) return 1; // ll d = p - 1, r = 0; // cerr << p << endl; // while (!(d & 1)) ++r, d >>= 1; // for (ll k = 0; k < 10; ++k) { // ll a = rand() % (p - 2) + 2; // ll x = bexp(a, d, p); // if (x == 1 || x == p - 1) continue; // for (int i = 0; i < r - 1; ++i) { // x = mult(x, x, p); // if (x == p - 1) break; // } // if (x != p - 1) return 0; // } // cerr << "YES" << endl; // return 1; //} // //void pr(ll a, mli &fmap, int exp=1) { // if (a == 1) { // return; // } // if (mr(a)) { // fmap[a] += exp; // return; // } // // ll f = -1; // for (int i = 1; i <= 10; i++) { // f = rho(a, 0, i); // if (f < a) { // break; // } // } // // if (f == -1) { // cerr << "NO" << endl; // } // // int e2 = 0; // while (a % f == 0) { // a /= f; // e2++; // } // // pr(a, fmap, exp); // pr(f, fmap, exp * e2); //} ll quick_pow(ll x, ll p, ll mod) { ll ans = 1; while (p) { if (p & 1) ans = (__int128)ans * x % mod; x = (__int128)x * x % mod; p >>= 1; } return ans; } bool Miller_Rabin(ll p) { if (p < 2) return 0; if (p == 2) return 1; if (p == 3) return 1; ll d = p - 1, r = 0; while (!(d & 1)) ++r, d >>= 1; for (ll k = 0; k < 10; ++k) { ll a = rand() % (p - 2) + 2; ll x = quick_pow(a, d, p); if (x == 1 || x == p - 1) continue; for (int i = 0; i < r - 1; ++i) { x = (__int128)x * x % p; if (x == p - 1) break; } if (x != p - 1) return 0; } return 1; } ll f(ll x, ll c, ll n) { return ((__int128)x * x + c) % n; } ll Pollard_Rho(ll x) { ll s = 0, t = 0; ll c = (ll)rand() % (x - 1) + 1; int step = 0, goal = 1; ll val = 1; for (goal = 1;; goal <<= 1, s = t, val = 1) { for (step = 1; step <= goal; ++step) { t = f(t, c, x); val = (__int128)val * abs(t - s) % x; if ((step % 127) == 0) { ll d = gcd(val, x); if (d > 1) return d; } } ll d = gcd(val, x); if (d > 1) return d; } } void fac(ll x, mli &fmap, int exp) { if (x < 2) return; if (Miller_Rabin(x)) { fmap[x] += exp; return; } ll p = x; while (p >= x) p = Pollard_Rho(x); int e = 0; while ((x % p) == 0) x /= p, e++; fac(x, fmap, exp), fac(p, fmap, exp * e); } int main() { int tc; ll m; cin >> tc >> m; // cerr << rho(4) << endl; bool mone = m == 1; mli facs_map; fac(m, facs_map, 1); vp facs(facs_map.begin(), facs_map.end()); // vp facs; // for (int i = 2; 1ll * i * i <= m; i++) { // if (m % i == 0) { // int p = 0; // while (m % i == 0) { // m /= i; // p++; // } // // facs.emplace_back(i, p); // } // } // if (m > 1) { // facs.emplace_back(m, 1); // } int fc = facs.size(); for (int i = 0; i < fc; i++) { cerr << facs[i].first << " " << facs[i].second << endl; } while (tc--) { int n, b, c, d; cin >> n >> b >> c >> d; int w[1<> a; int cur = 0; for (int j = 0; j < fc; j++) { auto [f, p] = facs[j]; int cp = 0; while (a % f == 0) { a /= f; cp++; } if (cp == p) { cur ^= 1 << j; } else if (cp > p) { cur = -1; break; } } if (cur >= 0 && a == 1) { w[cur] = 1ll * w[cur] * (cw + 1) % Z; } cw = (1ll * c * cw + d) % Z; } int dp[1<> j & 1) { dp[i] = 1ll * dp[i] * dp[i^(1<> j & 1; } ans = (0ll + ans + dp[i] * ((fc - pc) % 2 == 0 ? 1 : -1) + Z) % Z; } cout << (mone ? (ans + Z - 1) % Z : ans) << endl; } return 0; }