#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
ll read()
{
	ll x;scanf("%lld",&x);return x;
}
ll Aa,Ab;
// ll ask(ll beg,ll H)//询问天数
// {
// 	ll l=beg,r=1e9,mid;
// 	while(l+1<r)
// 	{
// 		mid=(l+r)/2;
// 		if( (beg+mid)*(mid-beg+1)/2>=H)
// 			r=mid;
// 		else
// 			l=mid;
// 	}
// 	if( (beg+l)*(l-beg+1)/2>=H)
// 		return l;
// 	return r;
// }

ll ask(ll beg,ll H)
{
	ll tH=2*H+beg*beg-beg-1;
	ll x=sqrt(tH);
	while((beg+x)*(x-beg+1)/2<H)
		x++;
	return x;
}
ll ask(ll beg,ll Ha,ll Hb)//受伤多少
{
	if(Ha<=0&&Hb<=0)
		return 0;
	if(Ha<=0)
	{
		ll t=ask(beg,Hb);
		return (t-beg+1)*Ab;
	}
	if(Hb<=0)
	{
		ll t=ask(beg,Ha);
		return (t-beg+1)*Aa;
	}
	ll ans=1e18;
	ll ta=ask(beg,Ha);
	ll tb;
	if(Hb>Ha-(ta-beg+1)*(beg+ta)/2)
		tb=ask(ta+1,Hb+Ha-(ta-beg+1)*(beg+ta)/2);
	else
		tb=ta;
	ans=(tb-beg+1)*Ab+(ta-beg+1)*Aa;

	tb=ask(beg,Hb);
	if(Ha>Hb-(tb-beg+1)*(beg+tb)/2)
		ta=ask(tb+1,Ha+Hb-(tb-beg+1)*(beg+tb)/2);
	else
		ta=tb;
	ans=min(ans,(ta-beg+1)*Aa+(tb-beg+1)*Ab);
	return ans;
	
}
void work()
{
	ll Ha=read(),Hb=read();
	Aa=read();Ab=read();
	ll ans=ask(1,Ha,Hb);
	cout<<ans<<' ';
	ll sum=0;
	for(int i=1;Ha>0||Hb>0;i++)
	{

		ll t;
		t=sum+(Ha>0)*Aa+(Hb>0)*Ab+ask(i+1,Ha-i,Hb);
		if(t==ans)
		{
			sum=sum+(Ha>0)*Aa+(Hb>0)*Ab;
			cout<<'A';
			Ha-=i;
		}
		else
		{
			sum=sum+(Ha>0)*Aa+(Hb>0)*Ab;
			cout<<'B';
			Hb-=i;
		}
	}
	cout<<'\n';
}
int main()
{
	// freopen("1.in","r",stdin);
	// freopen("1.out","w",stdout);
	for(int t=read();t;t--)
	 	work();
}