Problem Description

For a positive integer $n$, let's denote function $f(n,m)$ as the $m$-th smallest integer $x$ that $x>n$ and $\gcd(x,n)=1$. For example, $f(5,1)=6$ and $f(5,5)=11$.

You are given the value of $m$ and $(f(n,m)-n)\oplus n$, where ``$\oplus$'' denotes the bitwise XOR operation. Please write a program to find the smallest positive integer $n$ that $(f(n,m)-n)\oplus n=k$, or determine it is impossible.

Input

The first line of the input contains an integer $T(1\leq T\leq 10)$, denoting the number of test cases.

In each test case, there are two integers $k,m(1\leq k\leq 10^{18},1\leq m\leq 100)$.

Output

For each test case, print a single line containing an integer, denoting the smallest $n$. If there is no solution, output ``$\texttt{-1}$'' instead.

2
3 5
6 100

5
-1