Migrated from Lutece 431 Sum of Digits

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Description

Petka thought of a positive integer n and reported to Chapaev the sum of its digits and the sum of its squared digits. Chapaev scratched his head and said: “Well, Petka, I won't find just your number, but I can find the smallest fitting number.” Can you do the same?

Input

The first line contains the number of test cases $t$ (no more than $10000$). In each of the following tlines there are numbers $s_1$ and $s_2$ ($1\leq s_1, s_2\leq 10000$) separated by a space. They are the sum of digits and the sum of squared digits of the number $n$.

Output

For each test case, output in a separate line the smallest fitting number n, or No solution if there is no such number or if it contains more than $100$ digits.

Samples

4
9 81
12 9
6 10
7 9

9
No solution
1122
111112

Resources

NEERC 2008, Eastern subregion quarterfin