#include using namespace std; //入力が必ず-mod //modが入力で与えられる場合. struct dynamic_modint{ //mod変更が可能 最初にsetmod必須 idxで複数個所持が可能. private: static int mod; public: long long v; static constexpr long long getmod(){return mod;} static void setmod(int m){ assert(m > 0); mod = m; } dynamic_modint():v(0){} template dynamic_modint(T a):v(a){if(v < 0) v += mod;} long long val()const{return v;} dynamic_modint &operator=(const dynamic_modint &b) = default; dynamic_modint &operator+()const{return (*this);} dynamic_modint operator-()const{return dynamic_modint(0)-(*this);} dynamic_modint operator+(const dynamic_modint b)const{return dynamic_modint(v)+=b;} dynamic_modint operator-(const dynamic_modint b)const{return dynamic_modint(v)-=b;} dynamic_modint operator*(const dynamic_modint b)const{return dynamic_modint(v)*=b;} dynamic_modint operator/(const dynamic_modint b)const{return dynamic_modint(v)/=b;} dynamic_modint &operator+=(const dynamic_modint b){ v += b.v; if(v >= mod) v -= mod; return *this; } dynamic_modint &operator-=(const dynamic_modint b){ v -= b.v; if(v < 0) v += mod; return *this; } dynamic_modint &operator*=(const dynamic_modint b){v = v*b.v%mod; return *this;} dynamic_modint &operator/=(dynamic_modint b){ //b!=0 mod素数が必須. assert(b.v != 0); (*this) *= b.pow(mod-2); return *this; } dynamic_modint pow(long long n)const{ dynamic_modint ret = 1,p = v; if(n < 0) p = p.inv(),n = -n; while(n){if(n&1) ret *= p; p *= p,n >>= 1;} return ret; } dynamic_modint inv()const{return pow(mod-2);} //素数mod必須. dynamic_modint &operator++(){*this += 1; return *this;} dynamic_modint &operator--(){*this -= 1; return *this;} dynamic_modint operator++(int){dynamic_modint ret = *this; *this += 1; return ret;} dynamic_modint operator--(int){dynamic_modint ret = *this; *this -= 1; return ret;} friend bool operator==(const dynamic_modint a,const dynamic_modint b){return a.v==b.v;} friend bool operator!=(const dynamic_modint a,const dynamic_modint b){return a.v!=b.v;} friend bool operator<(const dynamic_modint a,const dynamic_modint b){return a.v=(const dynamic_modint a,const dynamic_modint b){return a.v>=b.v;} friend bool operator>(const dynamic_modint a,const dynamic_modint b){return a.v>b.v;} friend ostream &operator<<(ostream &os,const dynamic_modint a){return os<>(istream &is,dynamic_modint &a){ //入力はmodをとってくれる. long long x; is >> x; x %= mod; a = dynamic_modint(x); return is; } }; template int dynamic_modint::mod=998244353; using mint = dynamic_modint<0>; template vector> multima(vector> &A,vector> &B){ assert(A.at(0).size() == B.size() && B.size()); int H = A.size(),W = B.at(0).size(); vector> ret(H,vector(W)); for(int i=0; i vector> Powmat(vector> A,vector> B,long long N){ //return A^N*B ABは行列; //n*n行列A n*1行列Bと想定 O(n^3*logN). assert(A.size() && A.size() == A.at(0).size() && N >= 0); while(N){ if(N&1) B = multima(A,B); A = multima(A,A); N >>= 1; } return B; } int main(){ ios_base::sync_with_stdio(false); cin.tie(nullptr); int T; cin >> T; while(T--){ long long N,M,L,mod; cin >> N >> M >> L >> mod; mint::setmod(mod); M %= mod,L %= mod; vector> A = { {0,M,L,0}, {1,0,0,L}, {1,0,0,M}, {0,1,1,0} },B = {{1},{0},{0},{0}}; B = Powmat(A,B,N); if(N%2) cout << B.at(2).at(0) << "\n"; else cout << B.at(0).at(0) << "\n"; } }