Generate

#include <bits/stdc++.h>
using namespace std;
//MACROS
#define MX (1024)
int A[MX],N;
int nr(int p,int M){
    if(!M)return 0;
    return M-1==p;
}
bool wn(int p,int b,int r){
    if(r==1)F(N)if(!(b&1<<i))return nr(p,(A[i]+33333333)%3);
    int X(0);
    F(N)if(!(b&1<<i))FT(i+1,N)if(!(b&1<<k)){
        int a(abs(A[i]-A[k])),l(A[i]);
        A[i]=a;
        X|=!wn(p^1,b|1<<k,r-1);
        A[i]=-a;
        X|=!wn(p^1,b|1<<k,r-1);
        A[i]=l;
    }
    return X;
}
int main(void){
    FT(1,30){
        N=k;
        iota(A,A+k,1);
        printf("%d: %s\n",k,wn(0,0,k)?"A":"B");
    }
    return 0;
}