B. String Construction
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given two integers $$$n$$$ and $$$k$$$.

Construct a binary string$$$^{\text{∗}}$$$ $$$s$$$ of length $$$n$$$, such that both of the following conditions hold:

  • The absolute difference between the number of characters $$$\mathtt{0}$$$ and the number of characters $$$\mathtt{1}$$$ in $$$s$$$ is at most $$$1$$$.
  • There are exactly $$$k$$$ pairs of adjacent equal characters in $$$s$$$. Formally, there are exactly $$$k$$$ indices $$$i$$$ ($$$1 \le i \le n-1$$$) satisfying $$$s_i = s_{i + 1}$$$.

Or determine that no such string exists.

$$$^{\text{∗}}$$$A binary string is a string where each character is either $$$\mathtt{0}$$$ or $$$\mathtt{1}$$$.

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 1000$$$). The description of the test cases follows.

The only line of each test case contains two integers $$$n$$$ and $$$k$$$ ($$$2 \le n \le 2 \cdot 10^5$$$, $$$0 \le k \le n-1$$$).

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

Output

For each test case, output a binary string $$$s$$$ of length $$$n$$$ — the string you constructed. Print $$$-1$$$ if such a string does not exist.

If there are multiple answers, you may output any of them.

Example
Input
8
5 2
4 3
6 1
5 0
7 3
4 2
3 2
7 4
Output
01110
-1
101001
01010
0100011
0011
-1
0111000
Note

In the first test case, one possible answer is $$$s=\mathtt{01110}$$$. It contains three characters $$$\mathtt{1}$$$ and two characters $$$\mathtt{0}$$$, and there are exactly $$$2$$$ adjacent equal pairs in $$$s$$$: $$$(s_2, s_3)$$$ and $$$(s_3, s_4)$$$.

In the second test case, $$$k=n-1$$$. All characters in $$$s$$$ should be equal, so the numbers of characters $$$\mathtt{0}$$$ and $$$\mathtt{1}$$$ could not differ by at most $$$1$$$. Thus, the answer is $$$-1$$$.

In the third test case, note that $$$\mathtt{010110}$$$ is also a possible answer.