#ifdef NACHIA #define _GLIBCXX_DEBUG #else #define NDEBUG #endif #include #include #include #include #include #include #include #include #include using namespace std; using i64 = long long; using u64 = unsigned long long; #define rep(i,n) for(i64 i=0; i<(i64)(n); i++) #define repr(i,n) for(i64 i=(i64)(n)-1; i>=0; i--) const i64 INF = 1001001001001001001; const char* yn(bool x){ return x ? "Yes" : "No"; } template void chmin(A& l, const A& r){ if(r < l) l = r; } template void chmax(A& l, const A& r){ if(l < r) l = r; } template using nega_queue = priority_queue,greater>; using Modint = atcoder::static_modint<998244353>; //#include "nachia/vec.hpp" 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 = (n >> 32) ? 32 : 0; auto m = n >> q; constexpr u64 hi = 0x8888'8888; constexpr u64 mi = 0x1111'1111; m = (((m | ~(hi - (m & ~hi))) & hi) * mi) >> 35; m = (((m | ~(hi - (n & ~hi))) & hi) * mi) >> 31; q += (m & 0xf) << 2; q += 0x3333'3333'2222'1100 >> (((n >> 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 Int BinaryGcd(Int a, Int b){ if(a < 0) a = -a; if(b < 0) b = -b; if(!a || !b) return a|b; int q = LsbIndex(a|b); b >>= LsbIndex(b); a >>= LsbIndex(a); while(a!=b){ if(a>=LsbIndex(b); } else{ a-=b; a>>=LsbIndex(a); } } return a< namespace nachia{ bool IsPrime(unsigned long long x) noexcept { if(x <= 1) return false; if(x % 2 == 0) return x == 2; using u64 = unsigned long long; using u128 = __uint128_t; u64 d = x-1; int s = 0; int q = 63; while(!(d&1)){ d >>= 1; s++; } while(!(d >> q)) q--; u64 r = x; for(int t=0; t<6; t++) r*=2-r*x; u128 n2 = -(u128)x % x; auto red = [=](u128 t) noexcept -> u64 { t = (t + (u128)((u64)t*-r)*x) >> 64; return (t >= x) ? t-x : t; }; u64 one = red(n2); for(u64 base : { 2, 325, 9375, 28178, 450775, 9780504, 1795265022 }){ if(base%x==0) continue; u64 a = base = red(base%x*n2); for(int e=q-1; e>=0; e--){ a = red((u128)a*a); if((d>>e)&1) a = red((u128)a*base); } if(a == one) continue; for(int t=1; t> Factorize(unsigned long long x){ if(x == 1) return {}; if(IsPrime(x)) return {{x,1}}; using u64 = unsigned long long; using u128 = __uint128_t; u64 X = x; std::vector p; for(u64 i=2; i<100; i+=1+i%2) if(x%i==0){ p.push_back(i); while(x%i==0) x/=i; } u64 r=1; u128 n2=1; auto updX = [&](){ r = x; for(int t=0; t<6; t++) r*=2-r*x; n2 = -(u128)x % x; }; auto red = [&](u128 t) noexcept -> u64 { u64 s = ((u128)x*((u64)t*r)) >> 64; u64 t2 = t >> 64; return t2-s + (t2 < s ? x : 0); }; auto mult = [&](u64 a, u64 b) noexcept { return red((u128)red((u128)a*n2)*b); }; auto gcd = [](u64 a, u64 b) noexcept { if(!a || !b) return a|b; int q = LsbIndex(a|b); b >>= LsbIndex(b); a >>= LsbIndex(a); while(a!=b){ if(a>=LsbIndex(b); } else{ a-=b; a>>=LsbIndex(a); } } return a<>7; v^=v<<17; // Xorshift https://www.jstatsoft.org/article/download/v008i14/916 u64 c = red(v); if(c == 0) continue; auto f = [=](u64 a) noexcept -> u64 { return red((u128)a*a+c); }; u64 a=0, b=f(a); u64 buf = 1, sz = 1, nx = 10; while(true){ while(nx != sz && a != b){ buf = mult(buf, a<=b?b-a:a-b); sz++; a = f(a); b = f(f(b)); } u64 g = gcd(buf, x); if(g != 1){ while(p[pi] % g == 0) p[pi] /= g; p.push_back(g); break; } if(a == b) break; nx = sz * 3 / 2; } } } std::vector> res; for(u64 q : p) if(q != 1){ int e=0; while(X%q == 0){ e++; X/=q; } if(e) res.push_back({ q, e }); } return res; } unsigned long long Totient(unsigned long long x){ auto F = Factorize(x); for(auto f : F) x -= x / f.first; return x; } } // namespace nachia void testcase(){ int T; cin >> T; i64 M; cin >> M; auto pf = nachia::Factorize(M); int n = pf.size(); vector pes(n, 1); rep(i,n) rep(j,pf[i].second) pes[i] *= pf[i].first; rep(caseid, T){ int N; cin >> N; vector W(N); { int b,c,d; cin >> b >> c >> d; W[0] = b; rep(i,N-1) W[i+1] = W[i] * c + d; } vector A(N); rep(i,N) cin >> A[i]; rep(i,N) if(M % A[i] != 0){ A[i] = 1; W[i] = 0; } vector F(1<> T; for(int t=0; t