【Gym

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

22 24 26

Output

119449

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 <map>#include <cmath>#include <queue>#include <stack>#include <vector>#include <cstdio>#include <string>#include <cstring>#include <iostream>#include <algorithm>#define LL long longusing namespace std;const int MX = 1e6 + 5;const int mod = 1e9 + 7;const int INF = 2e9 + 5;char s[MX];int main(){    int t;    scanf("%d", &t);    while(t--){        int n, ss;        scanf("%d%d", &n, &ss);        for(int i = 1; i <= n; i++){            s[i] = '9';        }        int sum = n * 9;        int mid = (1+n)/2;        if(sum < ss || (n % 2 == 0 && (ss & 1)) || (n & 1 && n != 1 && ss == 1)){            printf("-1\n");            continue;        }        if(n & 1){            while(sum > ss && s[mid] > '0'){                s[mid]--;                sum--;                if(s[mid] == '1' && (ss & 1)) break;            }            if(sum == ss){                for(int i = 1; i <= n; i++){                    printf("%c", s[i]);                }                printf("\n");                continue;            }            else mid--;            while(sum > ss){                s[mid]--;                s[n - mid + 1]--;                sum -= 2;                if(s[mid] == '0')   mid--;            }        }        else{            while(sum > ss){                s[mid]--;                s[n - mid + 1]--;                sum -= 2;                if(s[mid] == '0')   mid--;            }        }        for(int i = 1; i <= n; i++){            printf("%c", s[i]);        }        printf("\n");    }    return 0;}

 

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

22 24 26

Output

119449