Problem:
Score : 1100 points

Problem Statement

Let f(A, B), where A and B are positive integers, be the string satisfying the following conditions:

f(A, B) has length A + B;

f(A, B) contains exactly A letters A and exactly B letters B;

The length of the longest substring of f(A, B) consisting of equal letters (ex., AAAAA or BBBB) is as small as possible under the conditions above;

f(A, B) is the lexicographically smallest string satisfying the conditions above.

For example, f(2, 3) = BABAB, and f(6, 4) = AABAABAABB.

Answer Q queries: find the substring of f(A_i, B_i) from position C_i to position D_i (1-based).

Constraints

1 \leq Q \leq 10^3

1 \leq A_i, B_i \leq 5 \times 10^8

1 \leq C_i \leq D_i \leq A_i + B_i

D_i - C_i + 1 \leq 100

All input values are integers.

Partial Score

500 points will be awarded for passing the testset satisfying 1 \leq A_i, B_i \leq 10^3.

Input

Input is given from Standard Input in the following format:

Q
A_1 B_1 C_1 D_1
A_2 B_2 C_2 D_2
:
A_Q B_Q C_Q D_Q

Output

For each query i in order of input, print a line containing the substring of f(A_i, B_i) from position C_i to position D_i (1-based).

Sample Input 1

5
2 3 1 5
6 4 1 10
2 3 4 4
6 4 3 7
8 10 5 8

Sample Output 1

BABAB
AABAABAABB
A
BAABA
ABAB

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>

using namespace std;
inline int read()
{
	int x=0,f=1; char ch=getchar();
	while(ch<'0'||ch>'9'){if(ch=='-')f=-1; ch=getchar();}
	while(ch>='0'&&ch<='9'){x=x*10+ch-'0'; ch=getchar();}
	return x*f;
}
int q,a,b,c,d;
string x,s;
int main()
{
	q=read(); while(q--)
	{
		a=read(); b=read(); c=read(); d=read();
		x="";s="";
		if(a>b)
		{
			int d=a/(b+1)+(a%(b+1)!=0);
			while(a>=d)
			{
				for(int i=1;i<=d;i++) x+='A';
				x+='B'; a-=d; b--;
			}
			for(int i=1;i<=a;i++) x+='A';
			for(int i=1;i<=b;i++) x+='B';
		}
		else 
		{
			int d=b/(a+1)+(b%(a+1)!=0);
			while(a&&b>=d)
			{
				s+='A'; a--; b-=d;
				for(int i=1;i<=d;i++) s+='B';
			}
			for(int i=1;i<=a;i++) x+="A";
			for(int i=1;i<=b;i++) x+='B';
			x=x+s;
		}
		for(int i=c-1;i<=d-1;i++) printf("%c",x[i]); puts("");
	}
	return 0;
}