#include using namespace std; using ll = long long; using vec = vector; using mat = vector; using pll = pair; using dvec = vector; using dmat = vector; #define INF (1LL<<61) //#define MOD 1000000007LL #define MOD 998244353LL #define PR(x) cout << (x) << endl #define PS(x) cout << (x) << " " #define REP(i,m,n) for(ll (i)=(m),(i_len)=(n);(i)<(i_len);++(i)) #define FORE(i,v) for(auto (i):v) #define ALL(x) (x).begin(), (x).end() #define SZ(x) ((ll)(x).size()) #define REV(x) reverse(ALL((x))) #define ASC(x) sort(ALL((x))) #define DESC(x) {ASC((x)); REV((x));} #define BIT(s,i) (((s)>>(i))&1) #define pb push_back #define fi first #define se second class mint { public: ll x; mint(ll x=0) : x((x%MOD+MOD)%MOD) {} mint operator-() const {return mint(-x);} mint& operator+=(const mint& a) {if((x+=a.x)>=MOD) x-=MOD; return *this;} mint& operator-=(const mint& a) {if((x+=MOD-a.x)>=MOD) x-=MOD; return *this;} mint& operator*=(const mint& a) {(x*=a.x)%=MOD; return *this;} mint operator+(const mint& a) const {mint b(*this); return b+=a;} mint operator-(const mint& a) const {mint b(*this); return b-=a;} mint operator*(const mint& a) const {mint b(*this); return b*=a;} mint pow(ll t) const {if(!t) return 1; mint a=pow(t>>1); return (t&1?*this*a:a)*a;} mint inv() const {return pow(MOD-2);} mint& operator/=(const mint& a) {return *this*=a.inv();} mint operator/(const mint& a) const {mint b(*this); return b/=a;} }; istream &operator>>(istream& is, mint& a) {ll t; is>>t; a=t; return is;} ostream &operator<<(ostream& os, const mint& a) {return os<; using mmat = vector; template inline int chmin(T& a, T b) {if(a>b) {a=b; return 1;} return 0;} template inline int chmax(T& a, T b) {if(a> N >> K; vec dp(N+1); REP(i,1,N+1) dp[i] = (N/i)*(N/i); for(ll i=N; i>=1; --i) { for(ll j=i*2; j<=N; j+=i) dp[i] -= dp[j]; } if(dp[1] < K) { PR(-1); return; } bool f = false; if(K*2 > dp[1]) { K = dp[1]-K+1; f = true; } ll l = 0, r = N*N+1; while(r-l > 1) { ll x = (l+r)/2; for(ll i=N; i>=1; --i) { dp[i] = 0; for(ll j=1; j<=N/i; ++j) dp[i] += min(N/i, j*x/(N*N)); for(ll j=i*2; j<=N; j+=i) dp[i] -= dp[j]; } if(dp[1] < K) l = x; else r = x; } REP(i,1,N+1) { ll x = i*l/(N*N)+1, y = i*r/(N*N); if(x == y) { if(f) cout << i << "/" << x << endl; else cout << x << "/" << i << endl; return; } } } int main() { ll T; cin >> T; while(T--) solve(); return 0; } /* */