#include using namespace std; template inline void chmin(T1 &a,T2 b){if(a>b) a=b;} template inline void chmax(T1 &a,T2 b){if(a=n); return (s+s+n-1)*n/2; } // take n max elements from [s, t] Int calc_ub(Int s,Int t,Int n){ assert(num(s,t)>=n); return (t-(n-1)+t)*n/2; } // sum of [s, t] Int calc(Int s,Int t){ assert(s<=t+1); return (s+t)*(t-s+1)/2; } Int N,P,X,Y; // take X * F if S_contains_X // take C1 from [S1, T1] * F // take U from [S1, T1] at most F-1 // take C2 from [S2, T2] * F Int type01(Int F,Int C,Int S_contains_X, Int S1,Int T1,Int C1,Int U1, Int S2,Int T2,Int C2,Int U2){ assert(C1 + S_contains_X + C2 == C); assert(U1 > 0 and U2==0); Int D1=(U1-1)/(F-1); Int E1=U1-D1*(F-1); assert(0<=D1 and 0=C1+D1+1); assert(num(S2,T2)>=C2); Int act_X = X * S_contains_X; { Int lb=calc_lb(S1,T1-(D1+1),C1)+act_X+calc_lb(S2,T2,C2); Int ub=calc_ub(S1,T1-(D1+1),C1)+act_X+calc_ub(S2,T2,C2); if(lb<=Y*C and Y*C<=ub){ return +Y*C*F +(T1-D1)*E1 +calc(T1-D1+1,T1)*(F-1); } } { Int diff=(calc(T1-(C1+D1)+1,T1-D1)+act_X+calc(T2-C2+1,T2))-Y*C; if(0<=diff and diff<=C1) return +Y*C*F +(T1-(C1+D1)+diff)*E1 +calc(T2-C2+1,T2)*(F-1); } { Int lb=calc_lb(T1-(C1+D1)+1,T1,C1)+act_X+calc(T2-C2+1,T2); Int ub=calc_ub(T1-(C1+D1)+1,T1,C1)+act_X+calc(T2-C2+1,T2); if(lb<=Y*C and Y*C<=ub){ return +Y*C +(calc(T1-(C1+D1)+1,T1)+act_X)*(F-1) +(T1-(C1+D1))*E1 +calc(T2-C2+1,T2)*(F-1); } } abort(); } // take X * F if S_contains_X // take C1 from [S1, T1] * F // take U1 from [S1, T1] at most F-1 // take C2 from [S2, T2] * F // take U2 from [S2, T2] at most F-1 Int type02(Int F,Int C,Int S_contains_X, Int S1,Int T1,Int C1,Int U1, Int S2,Int T2,Int C2,Int U2){ assert(C1 + S_contains_X + C2 == C); assert(U1 > 0 and U2 > 0); Int D1=(U1-1)/(F-1); Int E1=U1-D1*(F-1); assert(0<=D1 and 0=C1+D1+1); assert(num(S2,T2)>=C2+D2+1); Int act_X = X * S_contains_X; { Int lb=calc_lb(S1,T1-(D1+1),C1)+act_X+calc_lb(S2,T2-(D2+1),C2); Int ub=calc_ub(S1,T1-(D1+1),C1)+act_X+calc_ub(S2,T2-(D2+1),C2); if(lb<=Y*C and Y*C<=ub){ return +Y*C*F +(T1-D1)*E1 +calc(T1-D1+1,T1)*(F-1) +(T2-D2)*E2 +calc(T2-D2+1,T2)*(F-1); } } { Int diff=(+calc(T1-(C1+D1)+1,T1-D1) +act_X +calc(T2-(C2+D2+1)+1,T2-(D2+1)))-Y*C; if(0<=diff and diff<=C1) return +Y*C*F +(T1-(C1+D1)+diff)*E1 +calc(T1-D1+1,T1)*(F-1) +(T2-C2)*E2 +calc(T2-D2+1,T2)*(F-1); } { Int diff=(calc(T1-(C1+D1)+1,T1-D1)+act_X+calc(T2-(C2+D2)+1,T2-D2))-Y*C; if(0<=diff and diff<=C2) return +Y*C*F +(T1-(C1+D1))*E1 +calc(T1-D1+1,T1)*(F-1) +(T2-(C2+D2)+diff)*E2 +calc(T2-D2+1,T2)*(F-1); } { Int lb=calc_lb(T1-(C1+D1)+1,T1,C1)+act_X+calc_lb(T2-(C2+D2)+1,T2,C2); Int ub=calc_ub(T1-(C1+D1)+1,T1,C1)+act_X+calc_ub(T2-(C2+D2)+1,T2,C2); if(lb<=Y*C and Y*C<=ub){ return +Y*C +(calc(T1-(C1+D1)+1,T1)+act_X+calc(T2-(C2+D2)+1,T2))*(F-1) +(T1-(C1+D1))*E1 +(T2-(C2+D2))*E2; } } abort(); } signed solve(){ cin>>N>>P>>X>>Y; if(N==1 or X==0 or X==P){ if(X==Y) cout< sum = Y * N // X \in S if(num(0,X-1)>=N/2 and num(X+1,P)>=N/2){ Int sum=Y*N; Int lb=calc_lb(0,X-1,N/2)+X+calc_lb(X+1,P,N/2); Int ub=calc_ub(0,X-1,N/2)+X+calc_ub(X+1,P,N/2); if(lb<=sum and sum<=ub) chmax(ans,sum); } // F > 1 for(Int F=2;F<=N;F++){ for(Int C=1;C*F<=N;C++){ // X \in S for(Int S_contains_X=0;S_contains_X<=1;S_contains_X++){ for(Int A=0;A+S_contains_X<=C;A++){ Int B=C-A-S_contains_X; if(!(num(0,X-1)>=A and num(X+1,P)>=B)) continue; Int act_X = X * S_contains_X; { Int lb=calc_lb(0,X-1,A)+act_X+calc_lb(X+1,P,B); Int ub=calc_ub(0,X-1,A)+act_X+calc_ub(X+1,P,B); if(!(lb<=Y*C and Y*C<=ub)) continue; } Int V=min((num(X+1,P)-B)*(F-1),N/2-B*F); Int W=S_contains_X?0:min(N-C*F-V,F-1); Int U=N-C*F-V-W; if(!(U>=0 and V>=0)) continue; if(!S_contains_X and !(W>0)) continue; if(!(num(0,X-1)>=A+(U+(F-2))/(F-1))) continue; if(!(num(X+1,P)>=B+(V+(F-2))/(F-1))) continue; if(!(A*F+U<=N/2 and B*F+V<=N/2)) continue; if(U==0 and V==0){ chmax(ans,Y*C*F+W*X); continue; } if(V==0){ chmax(ans, type01(F,C,S_contains_X, 0,X-1,A,U, X+1,P,B,V)+W*X); continue; } if(U==0){ chmax(ans, type01(F,C,S_contains_X, X+1,P,B,V, 0,X-1,A,U)+W*X); continue; } chmax(ans, type02(F,C,S_contains_X, 0,X-1,A,U, X+1,P,B,V)+W*X); chmax(ans, type02(F,C,S_contains_X, X+1,P,B,V, 0,X-1,A,U)+W*X); } } } } cout<