password

题目描述

Frog Q has a secret integer $k$. Frog Q's friend F only knows that $k \in [1, n]$.

To reveal $k$ to F, Q may perform several hint operations. In each operation:

• Q chooses an integer $p$ satisfying $1 \le p \le k$;
• Q tells F: $k \bmod p = c$;
• The cost of this hint is $c$ (the value of $k \bmod p$).

After some number of hints, if F can uniquely determine the value of $k$, the communication succeeds.

Q wants to minimize the total cost. Compute this minimum total cost.

输入格式

The first line contains an integer $T\ (1 \le T \le 10^5)$, the number of test cases.

The next $T$ lines each contain two integers $n, k\ (1 \le k \le n \lt 2^{31})$, separated by a space.

输出格式

Output $T$ lines, each containing a single integer — the minimum total cost for the corresponding test case.

If F can never uniquely determine the value of $k$, output $-1$.

样例输入 #1

5
5 3
8 3
10 3
2147483647 10
144322 17

样例输出 #1

0
1
-1
-1
10