Problem Statement

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.

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.

Input

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

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