Chef has a special affection for sets of binary strings of equal length which have same numbers of 1's. Given three integers n, k and m, your task is to find the the lexicographically m^th smallest string among strings which have length n and have k 1's. If no such string exists output -1.

Tips:
To see what lexicographic order means . See http://en.wikipedia.org/wiki/Lexicographical_order

Input
Input description.

The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows:
The first and only line of each test case contains three space separated integers N , K and M

Output
For each test case output the answer on a separate line .

Constraints

1 ≤ T ≤ 10
1 ≤ N ≤ 350
1 ≤ K ≤ N

Example
Input:
1
3 2 2

Output:
101

Explanation
Example case 1. The set of strings in lexicographic order is "011", "101", and "110"

Scoring
Subtask 1 (41 point):

1 ≤ N ≤ 20

Subtask 2 (59 points):

1 ≤ N ≤ 350

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