13:I[87,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"Header"] 14:I[1742,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"ProblemView"] 15:T5c0,

Given an integer $$$x$$$ and an integer $$$k$$$. In one operation, you can perform one of two actions:

choose an integer $$$1 \le a \le k$$$ and assign $$$x = x \cdot a$$$;
choose an integer $$$1 \le a \le k$$$ and assign $$$x = \frac{x}{a}$$$, where the value of $$$\frac{x}{a}$$$ must be an integer.

Find the minimum number of operations required to make the number $$$x$$$ equal to $$$y$$$, or determine that it is impossible.

Input

The first line of the input contains one integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.

The only line of each test case contains three integers $$$x$$$, $$$y$$$ and $$$k$$$ ($$$1 \le x, y, k \le 10^6$$$).

It is guaranteed that the sum of $$$x$$$ and the sum of $$$y$$$ across all test cases does not exceed $$$10^8$$$.

Output

For each test case, output $$$-1$$$ if it is impossible to achieve $$$x=y$$$ using the

Small Operations

Examples