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;
int check(int mid,int a,int b,int len)
{
	int g=mid/(len+1);
	b-=g;
	a-=mid-g;
	return a>=(b+len-1)/len-1;
}
int main()
{
	int q,a,b,c,d;
	scanf("%d",&q);
	while(q--)
	{
		scanf("%d%d%d%d",&a,&b,&c,&d);
		int x=max(a,b),y=min(a,b);
		int len=(x+(y+1)-1)/(y+1);
		int l=0,r=a+b;
		while(l<r)
		{
			int mid=(l+r+1)>>1;
			if(check(mid,a,b,len))
				l=mid;
			else
				r=mid-1;
		}
		if(c<=l&&d<=l)
		{
			for(int i=c;i<=d;i++)
				printf("%c",i%(len+1)?'A':'B');
		}
		else if(c>l&&d>l)
		{
			for(int i=c;i<=d;i++)
				printf("%c",(i-l)%(len+1)?'B':'A');
		}
		else
		{
			for(int i=c;i<=l;i++)
				printf("%c",i%(len+1)?'A':'B');
			for(int i=l+1;i<=d;i++)
				printf("%c",(i-l)%(len+1)?'B':'A');
		}
		puts("");
	}
	return 0;
}