#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using ull = unsigned long long;
using uint = unsigned;
using pcc = pair<char, char>;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using pdd = pair<ld, ld>;
using tuplis = array<ll, 3>;
template<class T> using pq = priority_queue<T, vector<T>, greater<T>>;
const ll LINF=0x1fffffffffffffff;
const ll MINF=0x7fffffffffff;
const int INF=0x3fffffff;
const int MOD=1000000007;
const int MODD=998244353;
const ld DINF=numeric_limits<ld>::infinity();
const ld EPS=1e-9;
const ld PI=3.1415926535897932;
const ll dx[] = {0, 1, 0, -1, 1, -1, 1, -1};
const ll dy[] = {1, 0, -1, 0, 1, 1, -1, -1};
#define overload4(_1,_2,_3,_4,name,...) name
#define overload3(_1,_2,_3,name,...) name
#define rep1(n) for(ll i=0;i<n;++i)
#define rep2(i,n) for(ll i=0;i<n;++i)
#define rep3(i,a,b) for(ll i=a;i<b;++i)
#define rep4(i,a,b,c) for(ll i=a;i<b;i+=c)
#define rep(...) overload4(__VA_ARGS__,rep4,rep3,rep2,rep1)(__VA_ARGS__)
#define rrep1(n) for(ll i=n;i--;)
#define rrep2(i,n) for(ll i=n;i--;)
#define rrep3(i,a,b) for(ll i=b;i-->(a);)
#define rrep4(i,a,b,c) for(ll i=(a)+((b)-(a)-1)/(c)*(c);i>=(a);i-=c)
#define rrep(...) overload4(__VA_ARGS__,rrep4,rrep3,rrep2,rrep1)(__VA_ARGS__)
#define each1(i,a) for(auto&&i:a)
#define each2(x,y,a) for(auto&&[x,y]:a)
#define each3(x,y,z,a) for(auto&&[x,y,z]:a)
#define each(...) overload4(__VA_ARGS__,each3,each2,each1)(__VA_ARGS__)
#define all1(i) begin(i),end(i)
#define all2(i,a) begin(i),begin(i)+a
#define all3(i,a,b) begin(i)+a,begin(i)+b
#define all(...) overload3(__VA_ARGS__,all3,all2,all1)(__VA_ARGS__)
#define rall1(i) (i).rbegin(),(i).rend()
#define rall2(i,k) (i).rbegin(),(i).rbegin()+k
#define rall3(i,a,b) (i).rbegin()+a,(i).rbegin()+b
#define rall(...) overload3(__VA_ARGS__,rall3,rall2,rall1)(__VA_ARGS__)
#define sum(...) accumulate(all(__VA_ARGS__),0LL)
#define dsum(...) accumulate(all(__VA_ARGS__),0.0L)
#define Msum(...) accumulate(all(__VA_ARGS__),0_M)
#define elif else if
#define unless(a) if(!(a))
#define INT(...) int __VA_ARGS__;in(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__;in(__VA_ARGS__)
#define ULL(...) ull __VA_ARGS__;in(__VA_ARGS__)
#define STR(...) string __VA_ARGS__;in(__VA_ARGS__)
#define CHR(...) char __VA_ARGS__;in(__VA_ARGS__)
#define DBL(...) double __VA_ARGS__;in(__VA_ARGS__)
#define LD(...) ld __VA_ARGS__;in(__VA_ARGS__)
#define Sort(a) sort(all(a))
#define Rev(a) reverse(all(a))
#define Uniq(a) sort(all(a));a.erase(unique(all(a)),end(a))
#define vec(type,name,...) vector<type>name(__VA_ARGS__)
#define VEC(type,name,size) vector<type>name(size);in(name)
#define vv(type,name,h,...) vector<vector<type>>name(h,vector<type>(__VA_ARGS__))
#define VV(type,name,h,w) vector<vector<type>>name(h,vector<type>(w));in(name)
#define vvv(type,name,h,w,...) vector<vector<vector<type>>>name(h,vector<vector<type>>(w,vector<type>(__VA_ARGS__)))
template<class T> auto min(const T& a){ return *min_element(all(a)); }
template<class T> auto max(const T& a){ return *max_element(all(a)); }
inline ll popcnt(ull a){ return __builtin_popcountll(a); }
ll gcd(ll a, ll b){ while(b){ ll c = b; b = a % b; a = c; } return a; }
ll lcm(ll a, ll b){ if(!a || !b) return 0; return a * b / gcd(a, b); }
ll intpow(ll a, ll b){ ll ans = 1; while(b){ if(b & 1) ans *= a; a *= a; b /= 2; } return ans; }
ll modpow(ll a, ll b, ll p){ ll ans = 1; while(b){ if(b & 1) (ans *= a) %= p; (a *= a) %= p; b /= 2; } return ans; }
template<class T> bool chmin(T& a, const T& b){ if(a > b){ a = b; return 1; } return 0; }
template<class T> bool chmax(T& a, const T& b){ if(a < b){ a = b; return 1; } return 0; }
template<class T, class U> bool chmin(T& a, const U& b){ if(a > T(b)){ a = b; return 1; } return 0; }
template<class T, class U> bool chmax(T& a, const U& b){ if(a < T(b)){ a = b; return 1; } return 0; }
vector<ll> iota(ll n, ll begin = 0){ vector<ll> a(n); iota(a.begin(), a.end(), begin); return a; }
vector<pll> factor(ull x){ vector<pll> ans; for(ull i = 2; i * i <= x; i++) if(x % i == 0){ ans.push_back({i, 1}); while((x /= i) % i == 0) ans.back().second++; } if(x != 1) ans.push_back({x, 1}); return ans; }
map<ll,ll> factor_map(ull x){ map<ll,ll> ans; for(ull i = 2; i * i <= x; i++) if(x % i == 0){ ans[i] = 1; while((x /= i) % i == 0) ans[i]++; } if(x != 1) ans[x] = 1; return ans; }
vector<ll> divisor(ull x){ vector<ll> ans; for(ull i = 1; i * i <= x; i++) if(x % i == 0) ans.push_back(i); rrep(ans.size() - (ans.back() * ans.back() == x)) ans.push_back(x / ans[i]); return ans; }
template<class T> unordered_map<T, ll> press(vector<T> a){ Uniq(a); unordered_map<T, ll> ans; rep(a.size()) ans[a[i]] = i; return ans; }
template<class T> map<T, ll> press_map(vector<T> a){ Uniq(a); map<T, ll> ans; rep(a.size()) ans[a[i]] = i; return ans; }
int scan(){ return getchar(); }
void scan(int& a){ scanf("%d", &a); }
void scan(unsigned& a){ scanf("%u", &a); }
void scan(long& a){ scanf("%ld", &a); }
void scan(long long& a){ scanf("%lld", &a); }
void scan(unsigned long long& a){ scanf("%llu", &a); }
void scan(char& a){ do{ a = getchar(); }while(a == ' ' || a == '\n'); }
void scan(float& a){ scanf("%f", &a); }
void scan(double& a){ scanf("%lf", &a); }
void scan(long double& a){ scanf("%Lf", &a); }
void scan(vector<bool>& a){ for(unsigned i = 0; i < a.size(); i++){ int b; scan(b); a[i] = b; } }
void scan(char a[]){ scanf("%s", a); }
void scan(string& a){ cin >> a; }
template<class T> void scan(vector<T>&);
template<class T, size_t size> void scan(array<T, size>&);
template<class T, class L> void scan(pair<T, L>&);
template<class T, size_t size> void scan(T(&)[size]);
template<class T> void scan(vector<T>& a){ for(auto&& i : a) scan(i); }
template<class T> void scan(deque<T>& a){ for(auto&& i : a) scan(i); }
template<class T, size_t size> void scan(array<T, size>& a){ for(auto&& i : a) scan(i); }
template<class T, class L> void scan(pair<T, L>& p){ scan(p.first); scan(p.second); }
template<class T, size_t size> void scan(T (&a)[size]){ for(auto&& i : a) scan(i); }
template<class T> void scan(T& a){ cin >> a; }
void in(){}
template <class Head, class... Tail> void in(Head& head, Tail&... tail){ scan(head); in(tail...); }
void print(){ putchar(' '); }
void print(bool a){ printf("%d", a); }
void print(int a){ printf("%d", a); }
void print(unsigned a){ printf("%u", a); }
void print(long a){ printf("%ld", a); }
void print(long long a){ printf("%lld", a); }
void print(unsigned long long a){ printf("%llu", a); }
void print(char a){ printf("%c", a); }
void print(char a[]){ printf("%s", a); }
void print(const char a[]){ printf("%s", a); }
void print(float a){ printf("%.15f", a); }
void print(double a){ printf("%.15f", a); }
void print(long double a){ printf("%.15Lf", a); }
void print(const string& a){ for(auto&& i : a) print(i); }
template<class T> void print(const complex<T>& a){ if(a.real() >= 0) print('+'); print(a.real()); if(a.imag() >= 0) print('+'); print(a.imag()); print('i'); }
template<class T> void print(const vector<T>&);
template<class T, size_t size> void print(const array<T, size>&);
template<class T, class L> void print(const pair<T, L>& p);
template<class T, size_t size> void print(const T (&)[size]);
template<class T> void print(const vector<T>& a){ if(a.empty()) return; print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ putchar(' '); print(*i); } }
template<class T> void print(const deque<T>& a){ if(a.empty()) return; print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ putchar(' '); print(*i); } }
template<class T, size_t size> void print(const array<T, size>& a){ print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ putchar(' '); print(*i); } }
template<class T, class L> void print(const pair<T, L>& p){ print(p.first); putchar(' '); print(p.second); }
template<class T, size_t size> void print(const T (&a)[size]){ print(a[0]); for(auto i = a; ++i != end(a); ){ putchar(' '); print(*i); } }
template<class T> void print(const T& a){ cout << a; }
int out(){ putchar('\n'); return 0; }
template<class T> int out(const T& t){ print(t); putchar('\n'); return 0; }
template<class Head, class... Tail> int out(const Head& head, const Tail&... tail){ print(head); putchar(' '); out(tail...); return 0; }
#ifdef DEBUG
inline ll __lg(ull x){ return 63 - __builtin_clzll(x); }
#define debug(...) { print(#__VA_ARGS__); print(":"); out(__VA_ARGS__); }
#else
#define debug(...) void(0)
#endif
int first(bool i = true){ return out(i?"first":"second"); }
int First(bool i = true){ return out(i?"First":"Second"); }
int yes(bool i = true){ return out(i?"yes":"no"); }
int Yes(bool i = true){ return out(i?"Yes":"No"); }
int No(){ return out("No"); }
int YES(bool i = true){ return out(i?"YES":"NO"); }
int NO(){ return out("NO"); }
int Yay(bool i = true){ return out(i?"Yay!":":("); }
int possible(bool i = true){ return out(i?"possible":"impossible"); }
int Possible(bool i = true){ return out(i?"Possible":"Impossible"); }
int POSSIBLE(bool i = true){ return out(i?"POSSIBLE":"IMPOSSIBLE"); }
void Case(ll i){ printf("Case #%lld: ", i); }



namespace inner {

using i32 = int32_t;
using u32 = uint32_t;
using i64 = int64_t;
using u64 = uint64_t;

template <typename T>
T gcd(T a, T b) {
  while (b) swap(a %= b, b);
  return a;
}

template <typename T>
T inv(T a, T p) {
  T b = p, x = 1, y = 0;
  while (a) {
    T q = b / a;
    swap(a, b %= a);
    swap(x, y -= q * x);
  }
  assert(b == 1);
  return y < 0 ? y + p : y;
}

template <typename T, typename U>
T modpow(T a, U n, T p) {
  T ret = 1 % p;
  for (; n; n >>= 1, a = U(a) * a % p)
    if (n & 1) ret = U(ret) * a % p;
  return ret;
}

}  // namespace inner
using namespace std;

struct ArbitraryLazyMontgomeryModInt {
  using mint = ArbitraryLazyMontgomeryModInt;
  using i32 = int32_t;
  using u32 = uint32_t;
  using u64 = uint64_t;

  static u32 mod;
  static u32 r;
  static u32 n2;

  static u32 get_r() {
    u32 ret = mod;
    for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;
    return ret;
  }

  static void set_mod(u32 m) {
    assert(m < (1 << 30));
    assert((m & 1) == 1);
    mod = m;
    n2 = -u64(m) % m;
    r = get_r();
    assert(r * mod == 1);
  }

  u32 a;

  ArbitraryLazyMontgomeryModInt() : a(0) {}
  ArbitraryLazyMontgomeryModInt(const int64_t &b)
      : a(reduce(u64(b % mod + mod) * n2)){};

  static u32 reduce(const u64 &b) {
    return (b + u64(u32(b) * u32(-r)) * mod) >> 32;
  }

  mint &operator+=(const mint &b) {
    if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
    return *this;
  }

  mint &operator-=(const mint &b) {
    if (i32(a -= b.a) < 0) a += 2 * mod;
    return *this;
  }

  mint &operator*=(const mint &b) {
    a = reduce(u64(a) * b.a);
    return *this;
  }

  mint &operator/=(const mint &b) {
    *this *= b.inverse();
    return *this;
  }

  mint operator+(const mint &b) const { return mint(*this) += b; }
  mint operator-(const mint &b) const { return mint(*this) -= b; }
  mint operator*(const mint &b) const { return mint(*this) *= b; }
  mint operator/(const mint &b) const { return mint(*this) /= b; }
  bool operator==(const mint &b) const {
    return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
  }
  bool operator!=(const mint &b) const {
    return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
  }
  mint operator-() const { return mint() - mint(*this); }

  mint pow(u64 n) const {
    mint ret(1), mul(*this);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  friend ostream &operator<<(ostream &os, const mint &b) {
    return os << b.get();
  }

  friend istream &operator>>(istream &is, mint &b) {
    int64_t t;
    is >> t;
    b = ArbitraryLazyMontgomeryModInt(t);
    return (is);
  }

  mint inverse() const { return pow(mod - 2); }

  u32 get() const {
    u32 ret = reduce(a);
    return ret >= mod ? ret - mod : ret;
  }

  static u32 get_mod() { return mod; }
};
typename ArbitraryLazyMontgomeryModInt::u32 ArbitraryLazyMontgomeryModInt::mod;
typename ArbitraryLazyMontgomeryModInt::u32 ArbitraryLazyMontgomeryModInt::r;
typename ArbitraryLazyMontgomeryModInt::u32 ArbitraryLazyMontgomeryModInt::n2;
using namespace std;

struct montgomery64 {
  using mint = montgomery64;
  using i64 = int64_t;
  using u64 = uint64_t;
  using u128 = __uint128_t;

  static u64 mod;
  static u64 r;
  static u64 n2;

  static u64 get_r() {
    u64 ret = mod;
    for (i64 i = 0; i < 5; ++i) ret *= 2 - mod * ret;
    return ret;
  }

  static void set_mod(u64 m) {
    assert(m < (1LL << 62));
    assert((m & 1) == 1);
    mod = m;
    n2 = -u128(m) % m;
    r = get_r();
    assert(r * mod == 1);
  }

  u64 a;

  montgomery64() : a(0) {}
  montgomery64(const int64_t &b) : a(reduce((u128(b) + mod) * n2)){};

  static u64 reduce(const u128 &b) {
    return (b + u128(u64(b) * u64(-r)) * mod) >> 64;
  }

  mint &operator+=(const mint &b) {
    if (i64(a += b.a - 2 * mod) < 0) a += 2 * mod;
    return *this;
  }

  mint &operator-=(const mint &b) {
    if (i64(a -= b.a) < 0) a += 2 * mod;
    return *this;
  }

  mint &operator*=(const mint &b) {
    a = reduce(u128(a) * b.a);
    return *this;
  }

  mint &operator/=(const mint &b) {
    *this *= b.inverse();
    return *this;
  }

  mint operator+(const mint &b) const { return mint(*this) += b; }
  mint operator-(const mint &b) const { return mint(*this) -= b; }
  mint operator*(const mint &b) const { return mint(*this) *= b; }
  mint operator/(const mint &b) const { return mint(*this) /= b; }
  bool operator==(const mint &b) const {
    return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
  }
  bool operator!=(const mint &b) const {
    return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
  }
  mint operator-() const { return mint() - mint(*this); }

  mint pow(u128 n) const {
    mint ret(1), mul(*this);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  friend ostream &operator<<(ostream &os, const mint &b) {
    return os << b.get();
  }

  friend istream &operator>>(istream &is, mint &b) {
    int64_t t;
    is >> t;
    b = montgomery64(t);
    return (is);
  }

  mint inverse() const { return pow(mod - 2); }

  u64 get() const {
    u64 ret = reduce(a);
    return ret >= mod ? ret - mod : ret;
  }

  static u64 get_mod() { return mod; }
};
typename montgomery64::u64 montgomery64::mod, montgomery64::r, montgomery64::n2;
using namespace std;

using namespace std;

unsigned long long rng() {
  static unsigned long long x_ = 88172645463325252ULL;
  x_ = x_ ^ (x_ << 7);
  return x_ = x_ ^ (x_ >> 9);
}
namespace fast_factorize {
using u64 = uint64_t;

template <typename mint>
bool miller_rabin(u64 n, vector<u64> as) {
  if (mint::get_mod() != n) mint::set_mod(n);
  u64 d = n - 1;
  while (~d & 1) d >>= 1;
  mint e{1}, rev{int64_t(n - 1)};
  for (u64 a : as) {
    if (n <= a) break;
    u64 t = d;
    mint y = mint(a).pow(t);
    while (t != n - 1 && y != e && y != rev) {
      y *= y;
      t *= 2;
    }
    if (y != rev && t % 2 == 0) return false;
  }
  return true;
}

bool is_prime(u64 n) {
  if (~n & 1) return n == 2;
  if (n <= 1) return false;
  if (n < (1LL << 30))
    return miller_rabin<ArbitraryLazyMontgomeryModInt>(n, {2, 7, 61});
  else
    return miller_rabin<montgomery64>(
        n, {2, 325, 9375, 28178, 450775, 9780504, 1795265022});
}

template <typename mint, typename T>
T pollard_rho(T n) {
  if (~n & 1) return 2;
  if (is_prime(n)) return n;
  if (mint::get_mod() != n) mint::set_mod(n);
  mint R, one = 1;
  auto f = [&](mint x) { return x * x + R; };
  auto rnd = [&]() { return rng() % (n - 2) + 2; };
  while (1) {
    mint x, y, ys, q = one;
    R = rnd(), y = rnd();
    T g = 1;
    constexpr int m = 128;
    for (int r = 1; g == 1; r <<= 1) {
      x = y;
      for (int i = 0; i < r; ++i) y = f(y);
      for (int k = 0; g == 1 && k < r; k += m) {
        ys = y;
        for (int i = 0; i < m && i < r - k; ++i) q *= x - (y = f(y));
        g = inner::gcd<T>(q.get(), n);
      }
    }
    if (g == n) do
        g = inner::gcd<T>((x - (ys = f(ys))).get(), n);
      while (g == 1);
    if (g != n) return g;
  }
  exit(1);
}

vector<u64> inner_factorize(u64 n) {
  if (n <= 1) return {};
  u64 p;
  if (n <= (1LL << 30))
    p = pollard_rho<ArbitraryLazyMontgomeryModInt, uint32_t>(n);
  else
    p = pollard_rho<montgomery64, uint64_t>(n);
  if (p == n) return {p};
  auto l = inner_factorize(p);
  auto r = inner_factorize(n / p);
  copy(begin(r), end(r), back_inserter(l));
  return l;
}

vector<u64> factorize(u64 n) {
  auto ret = inner_factorize(n);
  sort(begin(ret), end(ret));
  return ret;
}

}  // namespace fast_factorize
using fast_factorize::factorize;
using fast_factorize::is_prime;

/**
 * @brief 高速素因数分解(Miller Rabin/Pollard's Rho)
 * @docs docs/prime/fast-factorize.md
 */

namespace kth_root_mod {

// fast BS-GS
template <typename T>
struct Memo {
  Memo(const T &g, int s, int period)
      : size(1 << __lg(min(s, period))),
        mask(size - 1),
        period(period),
        vs(size),
        os(size + 1) {
    T x(1);
    for (int i = 0; i < size; ++i, x *= g) os[x.get() & mask]++;
    for (int i = 1; i < size; ++i) os[i] += os[i - 1];
    x = 1;
    for (int i = 0; i < size; ++i, x *= g) vs[--os[x.get() & mask]] = {x, i};
    gpow = x;
    os[size] = size;
  }
  int find(T x) const {
    for (int t = 0; t < period; t += size, x *= gpow) {
      for (int m = (x.get() & mask), i = os[m]; i < os[m + 1]; ++i) {
        if (x == vs[i].first) {
          int ret = vs[i].second - t;
          return ret < 0 ? ret + period : ret;
        }
      }
    }
    assert(0);
  }
  T gpow;
  int size, mask, period;
  vector<pair<T, int> > vs;
  vector<int> os;
};

using inner::gcd;
using inner::inv;
using inner::modpow;
template <typename INT, typename LINT, typename mint>
mint pe_root(INT c, INT pi, INT ei, INT p) {
  if (mint::get_mod() != decltype(mint::a)(p)) mint::set_mod(p);
  INT s = p - 1, t = 0;
  while (s % pi == 0) s /= pi, ++t;
  INT pe = 1;
  for (INT _ = 0; _ < ei; ++_) pe *= pi;

  INT u = inv(pe - s % pe, pe);
  mint mc = c, one = 1;
  mint z = mc.pow((s * u + 1) / pe);
  mint zpe = mc.pow(s * u);
  if (zpe == one) return z;

  assert(t > ei);
  mint vs;
  {
    INT ptm1 = 1;
    for (INT _ = 0; _ < t - 1; ++_) ptm1 *= pi;
    for (mint v = 2;; v += one) {
      vs = v.pow(s);
      if (vs.pow(ptm1) != one) break;
    }
  }

  mint vspe = vs.pow(pe);
  INT vs_e = ei;
  mint base = vspe;
  for (INT _ = 0; _ < t - ei - 1; _++) base = base.pow(pi);
  Memo<mint> memo(base, (INT)(sqrt(t - ei) * sqrt(pi)) + 1, pi);

  while (zpe != one) {
    mint tmp = zpe;
    INT td = 0;
    while (tmp != 1) ++td, tmp = tmp.pow(pi);
    INT e = t - td;
    while (vs_e != e) {
      vs = vs.pow(pi);
      vspe = vspe.pow(pi);
      ++vs_e;
    }

    // BS-GS ... find (zpe * ( vspe ^ n ) ) ^( p_i ^ (td - 1) ) = 1
    mint base_zpe = zpe.inverse();
    for (INT _ = 0; _ < td - 1; _++) base_zpe = base_zpe.pow(pi);
    INT bsgs = memo.find(base_zpe);

    z *= vs.pow(bsgs);
    zpe *= vspe.pow(bsgs);
  }
  return z;
}

template <typename INT, typename LINT, typename mint>
INT inner_kth_root(INT a, INT k, INT p) {
  a %= p;
  if (k == 0) return a == 1 ? a : -1;
  if (a <= 1 || k <= 1) return a;

  assert(p > 2);
  if (mint::get_mod() != decltype(mint::a)(p)) mint::set_mod(p);
  INT g = gcd(p - 1, k);
  if (modpow<INT, LINT>(a, (p - 1) / g, p) != 1) return -1;
  a = mint(a).pow(inv(k / g, (p - 1) / g)).get();
  unordered_map<INT, int> fac;
  for (auto &f : factorize(g)) fac[f]++;
  if (mint::get_mod() != decltype(mint::a)(p)) mint::set_mod(p);
  for (auto pp : fac)
    a = pe_root<INT, LINT, mint>(a, pp.first, pp.second, p).get();
  return a;
}

int64_t kth_root(int64_t a, int64_t k, int64_t p) {
  if (max({a, k, p}) < (1LL << 30))
    return inner_kth_root<int32_t, int64_t, ArbitraryLazyMontgomeryModInt>(a, k,
                                                                           p);
  else
    return inner_kth_root<int64_t, __int128_t, montgomery64>(a, k, p);
}

}  // namespace kth_root_mod
using kth_root_mod::kth_root;

/**
 * @brief kth root(Tonelli-Shanks algorithm)
 * @docs docs/modulo/mod-kth-root.md
 */
int main(){
    LL(t);
    while(t--){
        LL(x,k);
        out(kth_root(x,k,MOD));
    }
}