Make Friends

Today, a cute cat slipped into the computer room. Everyone in the acm team likes this cat very much.
But the cat have x hostility towards us. We have to please the cats and reduce the hostility to 0.
There are n person in the computer room, numbered from 1 to n. Each person has one chance to feed the cat. Each time the cat fed, The hostility will decrease by 1.
But the cat can be a little naughty. There are m-1 naughty behaviors, numbered from 2 to m.
While person i is feeding the cat, if there exists a cat's behavior which id j is a factor of i, then the cat will make the confusion in computer room increase by 1.
If the confusion in computer room reaches y, then the cat will be found by the teacher and can no longer stay here.
Now we want to know if there exists a feeding order plan can make the cat become friends with person in computer room without being driven away?

The first line contains the number of test cases t(t<=1e5).
Each test case consists of 4 integers x, y, n, m(0

For each test case output a single line.
If there exists such plan print "(*^_^*)" (without quotes), otherwise print "(ToT)"(without quotes).
If the cat’s hostility is reduced to 0 while the confusion in computer room reaches y, the cat can become friends with us.

4
1999999999 1 29999999999999 9
998244353998244 1 12345678 9
3 1 3 4
5 1 6 7

(*^_^*)
(ToT)
(ToT)
(ToT)