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?

The first line contains the number of test cases t (no more than 10000). In each of the following t lines there are numbers s₁ and s₂ (1 ≤ s₁, s₂ ≤ 10000) separated by a space. They are the sum of digits and the sum of squared digits of the number n.

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.