#pragma region kyopro_template #define Nyaan_template #include #include #define pb push_back #define eb emplace_back #define fi first #define se second #define each(x, v) for (auto &x : v) #define all(v) (v).begin(), (v).end() #define sz(v) ((int)(v).size()) #define mem(a, val) memset(a, val, sizeof(a)) #define ini(...) \ int __VA_ARGS__; \ in(__VA_ARGS__) #define inl(...) \ long long __VA_ARGS__; \ in(__VA_ARGS__) #define ins(...) \ string __VA_ARGS__; \ in(__VA_ARGS__) #define inc(...) \ char __VA_ARGS__; \ in(__VA_ARGS__) #define in2(s, t) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i]); \ } #define in3(s, t, u) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i]); \ } #define in4(s, t, u, v) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i], v[i]); \ } #define rep(i, N) for (long long i = 0; i < (long long)(N); i++) #define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--) #define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++) #define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--) #define reg(i, a, b) for (long long i = (a); i < (b); i++) #define die(...) \ do { \ out(__VA_ARGS__); \ return; \ } while (0) using namespace std; using ll = long long; template using V = vector; using vi = vector; using vl = vector; using vvi = vector>; using vd = V; using vs = V; using vvl = vector>; using P = pair; using vp = vector

; using pii = pair; using vpi = vector>; constexpr int inf = 1001001001; constexpr long long infLL = (1LL << 61) - 1; template inline bool amin(T &x, U y) { return (y < x) ? (x = y, true) : false; } template inline bool amax(T &x, U y) { return (x < y) ? (x = y, true) : false; } template ostream &operator<<(ostream &os, const pair &p) { os << p.first << " " << p.second; return os; } template istream &operator>>(istream &is, pair &p) { is >> p.first >> p.second; return is; } template ostream &operator<<(ostream &os, const vector &v) { int s = (int)v.size(); for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i]; return os; } template istream &operator>>(istream &is, vector &v) { for (auto &x : v) is >> x; return is; } void in() {} template void in(T &t, U &... u) { cin >> t; in(u...); } void out() { cout << "\n"; } template void out(const T &t, const U &... u) { cout << t; if (sizeof...(u)) cout << " "; out(u...); } #ifdef NyaanDebug #define trc(...) \ do { \ cerr << #__VA_ARGS__ << " = "; \ dbg_out(__VA_ARGS__); \ } while (0) #define trca(v, N) \ do { \ cerr << #v << " = "; \ array_out(v, N); \ } while (0) #define trcc(v) \ do { \ cerr << #v << " = {"; \ each(x, v) { cerr << " " << x << ","; } \ cerr << "}" << endl; \ } while (0) template void _cout(const T &c) { cerr << c; } void _cout(const int &c) { if (c == 1001001001) cerr << "inf"; else if (c == -1001001001) cerr << "-inf"; else cerr << c; } void _cout(const unsigned int &c) { if (c == 1001001001) cerr << "inf"; else cerr << c; } void _cout(const long long &c) { if (c == 1001001001 || c == (1LL << 61) - 1) cerr << "inf"; else if (c == -1001001001 || c == -((1LL << 61) - 1)) cerr << "-inf"; else cerr << c; } void _cout(const unsigned long long &c) { if (c == 1001001001 || c == (1LL << 61) - 1) cerr << "inf"; else cerr << c; } template void _cout(const pair &p) { cerr << "{ "; _cout(p.fi); cerr << ", "; _cout(p.se); cerr << " } "; } template void _cout(const vector &v) { int s = v.size(); cerr << "{ "; for (int i = 0; i < s; i++) { cerr << (i ? ", " : ""); _cout(v[i]); } cerr << " } "; } template void _cout(const vector> &v) { cerr << "[ "; for (const auto &x : v) { cerr << endl; _cout(x); cerr << ", "; } cerr << endl << " ] "; } void dbg_out() { cerr << endl; } template void dbg_out(const T &t, const U &... u) { _cout(t); if (sizeof...(u)) cerr << ", "; dbg_out(u...); } template void array_out(const T &v, int s) { cerr << "{ "; for (int i = 0; i < s; i++) { cerr << (i ? ", " : ""); _cout(v[i]); } cerr << " } " << endl; } template void array_out(const T &v, int H, int W) { cerr << "[ "; for (int i = 0; i < H; i++) { cerr << (i ? ", " : ""); array_out(v[i], W); } cerr << " ] " << endl; } #else #define trc(...) #define trca(...) #define trcc(...) #endif inline int popcnt(unsigned long long a) { return __builtin_popcountll(a); } inline int lsb(unsigned long long a) { return __builtin_ctzll(a); } inline int msb(unsigned long long a) { return 63 - __builtin_clzll(a); } template inline int getbit(T a, int i) { return (a >> i) & 1; } template inline void setbit(T &a, int i) { a |= (1LL << i); } template inline void delbit(T &a, int i) { a &= ~(1LL << i); } template int lb(const vector &v, const T &a) { return lower_bound(begin(v), end(v), a) - begin(v); } template int ub(const vector &v, const T &a) { return upper_bound(begin(v), end(v), a) - begin(v); } template int btw(T a, T x, T b) { return a <= x && x < b; } template T ceil(T a, U b) { return (a + b - 1) / b; } constexpr long long TEN(int n) { long long ret = 1, x = 10; while (n) { if (n & 1) ret *= x; x *= x; n >>= 1; } return ret; } template vector mkrui(const vector &v) { vector ret(v.size() + 1); for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i]; return ret; }; template vector mkuni(const vector &v) { vector ret(v); sort(ret.begin(), ret.end()); ret.erase(unique(ret.begin(), ret.end()), ret.end()); return ret; } template vector mkord(int N, F f) { vector ord(N); iota(begin(ord), end(ord), 0); sort(begin(ord), end(ord), f); return ord; } template vector mkiota(int N) { vector ret(N); iota(begin(ret), end(ret), 0); return ret; } template vector mkinv(vector &v) { vector inv(v.size()); for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i; return inv; } struct IoSetupNya { IoSetupNya() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); cerr << fixed << setprecision(7); } } iosetupnya; void solve(); int main() { solve(); } #pragma endregionusing namespace std; struct ArbitraryModInt { int x; ArbitraryModInt() : x(0) {} ArbitraryModInt(int64_t y) : x(y >= 0 ? y % get_mod() : (get_mod() - (-y) % get_mod()) % get_mod()) { } ArbitraryModInt &operator+=(const ArbitraryModInt &p) { if ((x += p.x) >= get_mod()) x -= get_mod(); return *this; } ArbitraryModInt &operator-=(const ArbitraryModInt &p) { if ((x += get_mod() - p.x) >= get_mod()) x -= get_mod(); return *this; } ArbitraryModInt &operator*=(const ArbitraryModInt &p) { unsigned long long a = (unsigned long long)x * p.x; unsigned xh = (unsigned)(a >> 32), xl = (unsigned)a, d, m; asm("divl %4; \n\t" : "=a"(d), "=d"(m) : "d"(xh), "a"(xl), "r"(get_mod())); x = m; return *this; } ArbitraryModInt &operator/=(const ArbitraryModInt &p) { *this *= p.inverse(); return *this; } ArbitraryModInt operator-() const { return ArbitraryModInt(-x); } ArbitraryModInt operator+(const ArbitraryModInt &p) const { return ArbitraryModInt(*this) += p; } ArbitraryModInt operator-(const ArbitraryModInt &p) const { return ArbitraryModInt(*this) -= p; } ArbitraryModInt operator*(const ArbitraryModInt &p) const { return ArbitraryModInt(*this) *= p; } ArbitraryModInt operator/(const ArbitraryModInt &p) const { return ArbitraryModInt(*this) /= p; } bool operator==(const ArbitraryModInt &p) const { return x == p.x; } bool operator!=(const ArbitraryModInt &p) const { return x != p.x; } ArbitraryModInt inverse() const { int a = x, b = get_mod(), u = 1, v = 0, t; while (b > 0) { t = a / b; swap(a -= t * b, b); swap(u -= t * v, v); } return ArbitraryModInt(u); } ArbitraryModInt pow(int64_t n) const { ArbitraryModInt ret(1), mul(x); while (n > 0) { if (n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } friend ostream &operator<<(ostream &os, const ArbitraryModInt &p) { return os << p.x; } friend istream &operator>>(istream &is, ArbitraryModInt &a) { int64_t t; is >> t; a = ArbitraryModInt(t); return (is); } int get() const { return x; } static int &get_mod() { static int mod = 0; return mod; } static void set_mod(int md) { get_mod() = md; } };using namespace std; long long my_gcd(long long x, long long y) { long long z; if (x > y) swap(x, y); while (x) { x = y % (z = x); y = z; } return y; } long long my_lcm(long long x, long long y) { return 1LL * x / my_gcd(x, y) * y; } #define gcd my_gcd #define lcm my_lcm // Prime -> 1 {0, 0, 1, 1, 0, 1, 0, 1, ...} vector Primes(int N) { vector A(N + 1, 1); A[0] = A[1] = 0; for (int i = 2; i * i <= N; i++) if (A[i] == 1) for (int j = i << 1; j <= N; j += i) A[j] = 0; return A; } // Prime Sieve {2, 3, 5, 7, 11, 13, 17, ...} vector PrimeSieve(int N) { vector prime = Primes(N); vector ret; for (int i = 0; i < (int)prime.size(); i++) if (prime[i] == 1) ret.push_back(i); return ret; } // Factors (using for fast factorization) // {0, 0, 1, 1, 2, 1, 2, 1, 2, 3, ...} vector Factors(int N) { vector A(N + 1, 1); A[0] = A[1] = 0; for (int i = 2; i * i <= N; i++) if (A[i] == 1) for (int j = i << 1; j <= N; j += i) A[j] = i; return A; } // totient function φ(N)=(1 ~ N , gcd(i,N) = 1) // {0, 1, 1, 2, 4, 2, 6, 4, ... } vector EulersTotientFunction(int N) { vector ret(N + 1, 0); for (int i = 0; i <= N; i++) ret[i] = i; for (int i = 2; i <= N; i++) { if (ret[i] == i) for (int j = i; j <= N; j += i) ret[j] = ret[j] / i * (i - 1); } return ret; } // Divisor ex) 12 -> {1, 2, 3, 4, 6, 12} vector Divisor(long long N) { vector v; for (long long i = 1; i * i <= N; i++) { if (N % i == 0) { v.push_back(i); if (i * i != N) v.push_back(N / i); } } return v; } // Factorization // ex) 18 -> { (2,1) , (3,2) } vector > PrimeFactors(long long N) { vector > ret; for (long long p = 2; p * p <= N; p++) if (N % p == 0) { ret.emplace_back(p, 0); while (N % p == 0) N /= p, ret.back().second++; } if (N >= 2) ret.emplace_back(N, 1); return ret; } // Factorization with Prime Sieve // ex) 18 -> { (2,1) , (3,2) } vector > PrimeFactors(long long N, const vector &prime) { vector > ret; for (auto &p : prime) { if (p * p > N) break; if (N % p == 0) { ret.emplace_back(p, 0); while (N % p == 0) N /= p, ret.back().second++; } } if (N >= 2) ret.emplace_back(N, 1); return ret; } // modpow for mod < 2 ^ 31 long long modpow(long long a, long long n, long long mod) { a %= mod; long long ret = 1; while (n > 0) { if (n & 1) ret = ret * a % mod; a = a * a % mod; n >>= 1; } return ret % mod; }; // Check if r is Primitive Root bool isPrimitiveRoot(long long r, long long mod) { r %= mod; if (r == 0) return false; auto pf = PrimeFactors(mod - 1); for (auto &x : pf) { if (modpow(r, (mod - 1) / x.first, mod) == 1) return false; } return true; } // Get Primitive Root long long PrimitiveRoot(long long mod) { long long ret = 1; while (isPrimitiveRoot(ret, mod) == false) ret++; return ret; } // Euler's phi function long long phi(long long n) { auto pf = PrimeFactors(n); long long ret = n; for (auto p : pf) { ret /= p.first; ret *= (p.first - 1); } return ret; } // Extended Euclidean algorithm // solve : ax + by = gcd(a, b) // return : pair(x, y) pair extgcd(long long a, long long b) { if (b == 0) return make_pair(1, 0); long long x, y; tie(y, x) = extgcd(b, a % b); y -= a / b * x; return make_pair(x, y); } // Check if n is Square Number bool isSquare(long long n) { if (n == 0 || n == 1) return true; long long d = (long long)sqrt(n) - 1; while (d * d < n) ++d; return d * d == n; } // return a number of n's digit // zero ... return value if n = 0 (default -> 1) int isDigit(long long n, int zero = 1) { if (n == 0) return zero; int ret = 0; while (n) { n /= 10; ret++; } return ret; }//Binomial C(2002002); void solve() { auto sieve = Primes(5050505); using mint = ArbitraryModInt; ini(T); rep(_,T){ ini(a,p); if(!sieve[p])out(-1); else{ mint::set_mod(p); out(mint(a).pow(p - 1)); } } }