AT_arc224_d [ARC224D] Angst for All Pairs

There are $ N $ cards, numbered $ 1 $ through $ N $ . Initially, nothing is written on any of the cards. You can write zero or more positive integers on each card. The cost of writing a positive integer $ k $ once is equal to the number of digits in the decimal representation of $ k $ . Determine whether it is possible to satisfy the following condition. If it is possible, output the minimum total cost required; if it is not possible, output $ -1 $ . - For every pair of positive integers $ (x,y) $ satisfying $ 1 \leq x < y \leq K $ , there exists a card containing exactly one of $ x $ and $ y $ . $ T $ test cases are given; solve each of them.

The input is given from Standard Input in the following format, where $ \mathrm{case}_i $ denotes the $ i $ -th test case: > $ T $ $ \mathrm{case}_1 $ $ \mathrm{case}_2 $ $ \vdots $ $ \mathrm{case}_T $ Each test case is given in the following format: > $ N $ $ K $

Output $ T $ lines. The $ i $ -th line should contain the answer for the $ i $ -th test case.

### Sample Explanation 1 This input contains four test cases. For the first test case, writing as follows satisfies the condition with a total cost of $ 5 $ . - Write $ 1, 5 $ on card $ 1 $ . - Write $ 2, 5 $ on card $ 2 $ . - Write $ 3 $ on card $ 3 $ . For the second test case, the minimum total cost required to satisfy the condition is $ 39 $ . For the third test case, it is impossible to satisfy the condition, so output $ -1 $ . For the fourth test case, the minimum total cost required to satisfy the condition is $ 17655598 $ . ### Constraints - $ 1 \leq T \leq 10^5 $ - $ 1 \leq N \leq 10^6 $ - $ 2 \leq K \leq 10^6 $ - The sum of $ N $ in each input is at most $ 10^6 $ . - The sum of $ K $ in each input is at most $ 10^6 $ . - All input values are integers.