#12041BFS (Binary Fibonacci String)

We are familiar with the Fibonacci sequence (1, 1, 2, 3, 5, 8, ...). What if we define a similar sequence for strings? Sounds interesting? Let’s see. We define the follwing sequence: BF S(0) = 0 BF S(1) = 1 (here “0” and “1” are strings, not simply the numerical digit, 0 or 1) for all (n > 1) BF S(n) = BF S(n − 2) + BF S(n − 1) (here, ‘+’ denotes the string concatenation operation). (i.e. the n-th string in this sequence is a concatenation of a previous two strings). So, the first few strings of this sequence are: 0, 1, 01, 101, 01101, and so on. Your task is to find the N -th string of the sequence and print all of its characters from the i-th to j-th position, inclusive. (All of N , i, j are 0-based indices)

Input

The first line of the input file contains an integer T (T ≤ 100) which denotes the total number of test cases. The description of each test case is given below: Three integers N , i, j (0 ≤ N, i, j ≤ 231 − 1) and (i ≤ j and j − i ≤ 10000). You can assume that, both i and j will be valid indices (i.e. 0 ≤ i, j < length of BF S(N )).

Output

For each test case, print the substring from the i-th to the j-th position of BF S(N ) in a single line.

3
3 1 2
1 0 0
9 5 12

01
1
10101101