/////////////////////////////////////////////////////////////////////////////// #include #include #include #include #include using namespace std; using namespace __gnu_pbds; /////////////////////////////////////////////////////////////////////////////// typedef long long ll; typedef unsigned long long ull; typedef __int128_t ll128; typedef tuple t2; typedef tuple t3; typedef tuple t4; typedef tuple t5; template using priority_queue_incr = priority_queue, greater>; template using binary_search_tree = tree, rb_tree_tag, tree_order_statistics_node_update>; #define pb push_back #define V vector #define S static #define SP << " " << #define rep(i,n) for(ll i=0LL; i=0LL; --i) #define rfrep(i,f,n) for(ll i=n-1LL; i>=f; --i) #define cfor(i,x) for(const auto & (i) : (x)) #define ALL(a) (a).begin(),(a).end() #define RALL(a) (a).rbegin(),(a).rend() #define CIN(x) do { \ assert(!cin.eof()); \ cin >> x; \ assert(!cin.fail()); \ } while(0); #define E18(x) ((x) * 1'000'000'000'000'000'000LL) #ifdef DEBUG #include "../../../template/debug.h" #else // DEBUG #define debug_print(...) #define debug_printf(...) #define debug_print_mod(...) #endif // DEBUG /////////////////////////////////////////////////////////////////////////////// ll llin() { ll a; CIN(a); return a; } V llina(ll count) { V v; for (ll i = 0LL; i < count; ++i) { ll a; CIN(a); v.push_back(a); } return v; } V> llinaa(ll h, ll w) { V> v(h, V(w)); rep (hh, h) rep (ww, w) { ll a; CIN(a); v[hh][ww] = a; } return v; } V llinl2(ll count) { V v; for (ll i = 0LL; i < count; ++i) { ll a, b; CIN(a >> b); v.push_back(t2(a, b)); } return v; } V llinl3(ll count) { V v; for (ll i = 0LL; i < count; ++i) { ll a, b, c; CIN(a >> b >> c); v.push_back(t3(a, b, c)); } return v; } V llinl4(ll count) { V v; for (ll i = 0LL; i < count; ++i) { ll a, b, c, d; CIN(a >> b >> c >> d); v.push_back(t4(a, b, c, d)); } return v; } string strin() { string s; CIN(s); return s; } V strina(ll count) { V slist(count); for (ll i = 0; i < count; ++i) CIN(slist[i]); return slist; } template void sort(V &v) { sort(v.begin(), v.end()); } template void sort_reverse(V &v) { sort(v.begin(), v.end(), greater()); } t2 _ext_gcd(ll a, ll b, ll g) { if (!b) return t2(1, 0); ll q = a / b; ll r = a % b; auto [sx, sy] = _ext_gcd(b, r, g); ll x = sy; ll y = sx - q * sy; return t2(x, y); } t2 ext_gcd(ll a, ll b) { return _ext_gcd(a, b, gcd(a, b)); } // x and mod must be coprime ll mod_inv(ll x, ll mod) { auto [ret, xxxx] = ext_gcd(x, mod); while (ret < 0) ret += mod; ret %= mod; return ret; } // O(log(exp)) ll mod_pow(ll base, ll exp, ll mod) { ll ret = 1LL; for ( ; exp; ) { if (exp & 1LL) { ret *= base; ret %= mod; } base = (base * base) % mod; exp >>= 1; } return ret; } ll mod_mlt(ll x, ll y, ll mod) { ll ret = 0LL; x %= mod; while (y) { if (y & 1LL) { ret += x; ret %= mod; } y >>= 1; x <<= 1; x %= mod; } return ret; } // returns t2(solution, mod) t2 chinese_remainder(ll a1, ll m1, ll a2, ll m2) { assert(a1 >= 0); assert(m1 > 0); assert(a2 >= 0); assert(m2 > 0); ll mgcd = gcd(m1, m2); if (a1 % mgcd != a2 % mgcd) return t2(0, 0); ll mlcm = m1 * m2 / mgcd; t2 z = ext_gcd(m1, m2); ll z1 = get<0>(z); ll z2 = get<1>(z); // ll x = a1 + ((a2 - a1) / mgcd) * m1 * z1; ll x = z1; while (x < 0) x += mlcm; x = mod_mlt(x, m1, mlcm); ll coef = (a2 - a1) / mgcd; while (coef < 0) coef += mlcm; x = mod_mlt(x, coef, mlcm); x += a1; x %= mlcm; return t2(x, mlcm); } void get_divisors(V &retlist, ll x) { for (ll i = 1LL; i < sqrt(x) + 3LL; ++i) { if (x % i == 0LL) { retlist.push_back(i); retlist.push_back(x / i); } } } // returns factors and 1 void get_factors(V &retlist, ll x) { retlist.pb(1LL); for (ll i = 2LL; i < (ll)(sqrt(x)) + 3LL; ++i) { while (x % i == 0LL) { retlist.pb(i); x /= i; } } retlist.pb(x); } bool is_prime(ll x) { V factors, factors2; get_factors(factors, x); for (auto factor : factors) { if (factor > 1) factors2.pb(factor); } return factors2.size() == 1 && x == factors2[0]; } V eratosthenes(ll n) { V primes; bool *is_not_prime = new bool[n+3LL]; memset(is_not_prime, 0, sizeof(bool) * (n+3LL)); srep (v, 2LL, (ll)sqrt(n)+10LL) { if (is_not_prime[v]) continue; for (ll vv = v * 2LL; vv <= n; vv += v) { is_not_prime[vv] = true; } } srep (v, 2LL, n+1LL) if (!is_not_prime[v]) primes.pb(v); delete [] is_not_prime; return primes; } // p must be prime ll mod_root(ll p) { if (p == 2) return 1; if (p == 3) return 2; V flist; get_factors(flist, p-1LL); set fs; for (auto f : flist) if (f > 1) fs.insert(f); srep (a, 2, p) { bool ok = true; for (auto f : fs) { if (mod_pow(a, (p-1LL) / f, p) == 1) { ok = false; break; } } if (ok) return a; } assert(false); } ull combination(ll x, ll y) { if (y > x / 2LL) y = x - y; ull ret = 1LL; for (ll i = 0LL; i < y; ++i) { ret *= x--; ret /= (i + 1LL); } return ret; } // count of integers coprime with x (1<=k<=x) ll euler_phi(ll x) { V flist; get_factors(flist, x); map fcnts; cfor (f, flist) { if (f == 1) continue; fcnts[f]++; } ll ret = 1; cfor (item, fcnts) { ll f = item.first; ll fc = item.second; ll a = 1; rep (xx, fc) a *= f; ll b = 1; rep (xx, fc-1) b *= f; ret *= a - b; } return ret; } #if 0 // (base[0] * x^0 + base[1] * x^1 + base[2] * x^2 + ... ) / (div[0] * x^0 + div[1] * x^1 + div[2] * x^2 + ... ) void polynomial_div(V &q, V &r, V base, V div) { ll blen = base.size(); ll dlen = div.size(); reverse(ALL(base)); reverse(ALL(div)); mint basemlt = div[0].inv(); rep (i, blen - dlen + 1) { mint mlt = basemlt * base[i]; rep (j, dlen) base[i+j] -= div[j] * mlt; q.pb(mlt); } reverse(ALL(q)); ll idx = blen; rep (xxx, dlen - 1) r.pb(base[--idx]); } #endif /////////////////////////////////////////////////////////////////////////////// void _main(); int main() { cout << fixed << setprecision(18); #ifndef DEBUG ios::sync_with_stdio(false); cin.tie(0); #endif // DEBUG _main(); return 0; } /////////////////////////////////////////////////////////////////////////////// void slv() { ll v = llin(); ll x = llin(); ll mod = v * x + 1LL; ll root = mod_root(mod); ll a = mod_pow(root, v, mod); V anslist; ll b = a; rep (i, x) { anslist.pb(b); b = (b * a) % mod; } sort(anslist); cfor (ans, anslist) cout << ans << " "; cout << "\n"; } void _main() { ll t = llin(); rep (i, t) slv(); } ///////////////////////////////////////////////////////////////////////////////