Valid Expression CodeChef Solution

Problem

The correct way of evaluating an expression with $\ast ,+,$ and $-$ is, first multiplication, then addition, and then subtraction. For example, the expression $2+3\ast 7-5=2+21-5=23-5=18$.

You are given integers $N$ and $X$. Your task is to generate a string $S$ of length $N$ consisting only of $\ast ,+,$ and $-$ such that when these $N$ operators are placed in order between $(N+1)$ ones, the result of the expression becomes $X$.
For example, if $S=$ ++-*-, the resulting expression is $1+1+1-1\ast 1-1$, which is then evaluated based on the rules above.

If multiple such strings exist, print any of them. If no such string exists, print $-1$ instead.

Input Format

• The first line of input will contain a single integer $T$, denoting the number of test cases.
• Each test case consists of two space-separated integers $N$ and $X$ — the number of characters in the string and the result of expression after appending $(N+1)$ ones between all operators.

Output Format

For each test case, output on a new line a string $S$ of length $N$ consisting only of $\ast ,+,$ and $-$ that satisfies the given condition.

If multiple such strings exist, print any of them. If no such string exists, print $-1$ instead.

Constraints

Sample 1:

3
3 4
2 -5
3 1

+++
-1
*+-

Explanation:

Test case $1$: A possible string satisfying the condition is +++. The corresponding expression is $1+1+1+1=4$ which is equal to $X$.

Test case $2$: It can be proven that no such string with length $N=2$ exists such that the corresponding expression evaluates to $-5$.

Test case $3$: A possible string satisfying the condition is *+-. The corresponding expression is $1\ast 1+1-1=1+1-1=2-1=1$ which is equal to $X$.
Note that there are other valid strings, such as +*- and -*+. Any valid string will be accepted as output.