#include #pragma GCC optimize("Ofast") using namespace std; using std::cout; using std::cin; using std::endl; using ll=long long; using ld=long double; ll ILL=2167167167167167167; const int INF=2100000000; const int mod=998244353; #define rep(i,a,b) for (ll i=a;i using _pq = priority_queue, greater>; template ll LB(vector &v,T a){return lower_bound(v.begin(),v.end(),a)-v.begin();} template ll UB(vector &v,T a){return upper_bound(v.begin(),v.end(),a)-v.begin();} template bool chmin(T &a,const T &b){if(a>b){a=b;return 1;}else return 0;} template bool chmax(T &a,const T &b){if(a void So(vector &v) {sort(v.begin(),v.end());} template void Sore(vector &v) {sort(v.begin(),v.end(),[](T x,T y){return x>y;});} void yneos(bool a){if(a) cout<<"Yes\n"; else cout<<"No\n";} template void vec_out(vector &p){for(int i=0;i<(int)(p.size());i++){if(i) cout<<" ";cout< T min(vector &a){assert(!a.empty());T ans=a[0];for(auto &x:a) chmin(ans,x);return ans;} template T max(vector &a){assert(!a.empty());T ans=a[0];for(auto &x:a) chmax(ans,x);return ans;} template T sum(vector &a){assert(!a.empty());T ans=a[0]-a[0];for(auto &x:a) ans+=x;return ans;} ll jyo(ll x,ll y,ll z){ ll H=y; //ここから ll a=1,b=(x%z+z)%z,c=1; while(H>0){ a*=2; if(H%a!=0){ H-=a/2; c*=b; c%=z; } b*=b; b%=z; } //ここまで return c; } //最大公約数 long long Gcd(long long a,long long b){ if(b==0) return a; else return Gcd(b,a%b); } //最小公倍数 long long Lcm(long long a,long long b){ return (a/Gcd(a,b))*b; } //カーマイケル数の出力 long long carmichael(long long a){ long long ans=1,A=1; //2を素因数に持つときだけ場合わけ while(a%2==0) A*=2,a/=2; if(A==4) ans=2; else if(A>4) ans=A/4; A=a; for(long long k=3;k*k<=a;k++){ //for(auto k:div){ //配列divをsqrt(a)以下の素数を全列挙するやつにする if(A%k==0){ long long B=k-1; A/=k; while(A%k==0) A/=k,B*=k; ans=Lcm(ans,B); } } if(A!=1) ans=Lcm(ans,A-1); return ans; } namespace po167{ template struct Doubling_op { int _n; long long Log; std::vector> index_data; std::vector> value_data; Doubling_op(int n,long long limit,std::vector index,std::vector value):_n(n){ Log=2; while(limit){ limit/=2; Log++; } index_data.resize(Log); value_data.resize(Log); index_data[0]=index; value_data[0]=value; for(int i=1;i query(long long times,int start_index,T start_value){ for(int i=0;i>=1; } return std::make_pair(start_index,start_value); } }; struct Doubling { int _n; long long Log; std::vector> index_data; Doubling(int n,long long limit,std::vector index):_n(n){ Log=2; while(limit){ limit/=2; Log++; } index_data.resize(Log); index_data[0]=index; for(int i=1;i>=1; } return start_index; } }; } using po167::Doubling_op; using po167::Doubling; using doubleing_F=long long; doubleing_F d_op(doubleing_F l,doubleing_F r){ return l+r; } void solve(); // oddloop int main() { ios::sync_with_stdio(false); cin.tie(nullptr); int t=1; //cin>>t; rep(i,0,t) solve(); } void solve(){ ll M,D,N,B; cin>>M>>D>>N>>B; ll C=carmichael(B); ll X=8*11*7*9*5; auto f=[&](ll X)->void{ X%=B; if(X==10) cout<<"A\n"; else cout< to(X); rep(i,0,X) to[i]=jyo(i+D,X+i,X); Doubling p(X,N,to); ll ans=p.query(N,M%X)%B; if(ans==10) cout<<"A\n"; else cout<