1 #include<bits/stdc++.h> 2 using namespace std; 3 typedef long long int ll; 4 typedef unsigned long long int ull; 5 ull SEED=1; 6 ll n,mod; 7 ll w; 8 struct com 9 { 10 ll x,y; 11 com operator*(const com&A)const 12 { 13 com B; 14 B.x=(x*A.x+y*A.y%mod*w)%mod; 15 B.y=(x*A.y+y*A.x)%mod; 16 return B; 17 } 18 }; 19 inline ull R() 20 { 21 SEED^=SEED<<13; 22 SEED^=SEED>>5; 23 SEED^=SEED<<3; 24 return SEED; 25 } 26 inline ll qpow(ll x,ll y) 27 { 28 ll ans=1,base=x; 29 while(y) 30 { 31 if(y&1) 32 ans=ans*base%mod; 33 base=base*base%mod; 34 y>>=1; 35 } 36 return ans; 37 } 38 inline com qpow(com x,ll y) 39 { 40 com ans=x,base=x; 41 --y; 42 while(y) 43 { 44 if(y&1) 45 ans=ans*base; 46 base=base*base; 47 y>>=1; 48 } 49 return ans; 50 } 51 inline void solve() 52 { 53 cin>>n>>mod; 54 if(qpow(n,(mod-1)/2)==mod-1) 55 { 56 cout<<"Hola!"<<endl; 57 return; 58 } 59 ll a; 60 while(true) 61 { 62 a=R()%mod; 63 w=(a*a%mod-n+mod)%mod; 64 if(qpow(w,(mod-1)/2)==mod-1) 65 break; 66 } 67 com A; 68 A.x=a,A.y=1; 69 A=qpow(A,(mod+1)/2); 70 ll ans1=A.x; 71 ll ans2=(mod-ans1+mod)%mod; 72 if(ans1>ans2) 73 swap(ans1,ans2); 74 if(ans1==ans2) 75 cout<<ans1<<endl; 76 else 77 cout<<ans1<<" "<<ans2<<endl; 78 } 79 int main() 80 { 81 srand(time(0)); 82 ios::sync_with_stdio(false); 83 int T; 84 cin>>T; 85 while(T--) 86 solve(); 87 return 0; 88 }