Round Number

Time limit2sMemory limit256 MB

Summary

For each query, decide whether removing exactly k digits from x can leave a number with no leading zeros that is divisible by 100, and if so print one such result.

Level: Medium5 of 10
Topics: Greedy, Implementation, String, Math
Solved: No attempts yet

Problem

Everyone likes round numbers. There are many reasons for this, the main one being that a number divisible by, say, 100 is much easier to remember. Unfortunately, round numbers are far rarer in our lives than all the others. First-grader Petya is very upset about this. So he came up with his own definition of a round number.

By Petya's definition, a number is round only if exactly $k$ digits can be removed from it so that the resulting number has no leading zeros but is divisible by 100. For example, with $k = 2$ , the number 10304 is round, but the number 1000 is not.

Now Petya wants to know which numbers are round for which $k$ and which are not. Help him.

Input

The first line contains an integer $n$ , the number of pairs of numbers $k$ and $x$ that Petya wants to know about. The next $n$ lines each contain two positive integers $k$ and $x$ . Every $k$ is strictly less than the number of digits in the corresponding $x$ . Every $x$ has no leading zeros. The total number of digits across all $x$ does not exceed $10^5$ .

Output

For each pair $k$ and $x$ from the input, print -1 if the number $x$ is not round for the given $k$ . If the number $x$ is round for the given $k$ , print the number $x$ with exactly $k$ digits crossed out, after which it became divisible by 100. The number you print must not contain leading zeros, but it may be equal to zero.

Examples1

Example 1
Input
```
3
2 10304
2 1000
3 1023
```
Expected output
```
100
-1
0
```