【Gym - 101498H Palindrome Number】 思维

H - Palindrome Number

A palindrome number is a number that can be read the same way from left to right and from right to left. For example: 961169, 111, 554455 are palindromes, while 856, 10180, 7226 are not.

Find the largest palindrome number that satisfies the following rules:

• The number of its digits is equal to n, and must not contain leading zeros.
• The sum of its digits is equal to s.

If there is no such number print  - 1.

Input

The first line of the input contains an integer T (1 ≤ T ≤ 500), where T is the number of the test cases.

Each test case has one line that contains two integers n (1 ≤ n ≤ 10⁶) number of digits, and s (1 ≤ s ≤ 9 × 10⁶) sum of digits.

Output

For each test case, print a single integer that represents the largest palindrome number that satisfies the mentioned rules, if there is no such number print  - 1.

Example

Input

2
2 2
4 26

Output

11
9449

题意：告诉你有一个n位数，这个数的各数位上的和为s，如果存在这样的回文数，则输出最大值，不存在输出-1。

分析：首先确定要把结果用字符串表示，然后判断不符合的条件，即（1）n为偶数s为奇数时 （2）9*n < s时 （3）n为奇数但不为1且s为1时。以上三种条件即输出-1。找到最大回文数的思路就是先把n位数全都赋值为9，然后从中间向两边递减，知道数位和等于s。然后对奇数要进行一次特殊处理，就是最中间的那一位，当s为奇数是，最中间那一位减到1就要停止，开始从两边减（因为之后的每次操作都是减2，只有现在的数位和为奇数才有可能使得总数位和符合条件）。

代码如下：

#include 

 

A palindrome number is a number that can be read the same way from left to right and from right to left. For example: 961169, 111, 554455 are palindromes, while 856, 10180, 7226 are not.

Find the largest palindrome number that satisfies the following rules:

• The number of its digits is equal to n, and must not contain leading zeros.
• The sum of its digits is equal to s.

If there is no such number print  - 1.

Input

The first line of the input contains an integer T (1 ≤ T ≤ 500), where T is the number of the test cases.

Each test case has one line that contains two integers n (1 ≤ n ≤ 10⁶) number of digits, and s (1 ≤ s ≤ 9 × 10⁶) sum of digits.

Output

For each test case, print a single integer that represents the largest palindrome number that satisfies the mentioned rules, if there is no such number print  - 1.

Example

Input

2
2 2
4 26

Output

11
9449