Time Limit: 10 Seconds
Memory Limit: 32768 KB
Nahid Khaleh decides to invite the kids of the "Shahr-e Ghashang"
to her wedding anniversary. She wants to prepare a square-shaped chocolate cake
with known size. She asks each invited person to determine the size of the piece
of cake that he/she wants (which should also be square-shaped). She knows that
Mr. Kavoosi would not bear any wasting of the cake. She wants to know whether
she can make a square cake with that size that serves everybody exactly with
the requested size, and without any waste.
The first line of the input file contains a single integer t (1 <= t <=
10), the number of test cases, followed by input data for each test case. Each
test case consist of a single line containing an integer s, the side of the
cake, followed by an integer n (1 <= n <= 16), the number of cake pieces,
followed by n integers (in the range 1...10) specifying the side of each piece.
There should be one output line per test case containing one of the words KHOOOOB!
or HUTUTU! depending on whether the cake can be cut into pieces of specified
size without any waste or not.
4 8 1 1 1 1 1 3 1 1
5 6 3 3 2 1 1 1
Source: Asia 2002, Tehran (Iran), Iran Domestic