#include<bits/stdc++.h>
const int N=114514;
#define up(a,b,c)for(int a=b;a<=c;++a)
#define dn(a,b,c)for(int a=b;a>=c;--a)
using namespace std;
int T,S,m,n,hp[2],atk[2];
long long rs[2];
bool cc[2][N];
int mxc(int i,int n,int S,int u)
{
	if(u<=0)return 0;
	if(u<=i)return i;
	return u;
}
void clc(bool p)
{
	S=0;
	int V=hp[p];
	up(i,1,m)S+=i;
	fill(cc[p],cc[p]+m+1,p^1);
	int uu[2]={hp[0],hp[1]};
	dn(i,m,1)
	{
		if(S-i<V)
		{
			n=i;
			break;
		}
		S-=i,uu[p^1]-=i;
	}
	rs[p]=1ll*n*atk[p]+1ll*m*atk[p^1];
	up(i,1,n)
	{
		if(mxc(i+1,n,S-i,uu[0]-i)+mxc(i+1,n,S-i,uu[1])<=S-i)
			cc[p][i]=0,S-=i,uu[0]-=i;
		else cc[p][i]=1,S-=i,uu[1]-=i;
	}
}
bool cmp()
{
	if(rs[0]!=rs[1])return rs[1]<rs[0];
	up(i,1,m)
		if(cc[0][i]!=cc[1][i])return cc[1][i]<cc[0][i];
	return 0;
}
int main()
{
	cin>>T;
	while(T--)
	{
		cin>>hp[0]>>hp[1]>>atk[0]>>atk[1];
		S=0;
		for(m=1;;++m)
			if(S+m>=hp[0]+hp[1])break;
			else S+=m;
		clc(0),clc(1);
		bool p=cmp();
		cout<<rs[p]<<' ';
		up(i,1,m)
			cout<<(cc[p][i]?'B':'A');
		cout<<'\n';
	}
	return 0;
}