# PROBLEM LINK:

Contest Division 1

Contest Division 2

Contest Division 3

Contest Division 4

Setter: Kanhaiya Mohan

Tester: Felipe Mota, Aryan

Editorialist: Pratiyush Mishra

# DIFFICULTY:

591

# PREREQUISITES:

None

# PROBLEM:

In Chefland, each chicken has X legs and each duck has Y legs. Chef’s farm can have **exactly one type** of bird.

Given that the birds on the farm have a total of Z legs:

- Print
`CHICKEN`

, if the farm can have only chickens but not ducks. - Print
`DUCK`

, if the farm can have only ducks but not chickens. - Print
`ANY`

, if the farm can have either chickens or ducks. - Print
`NONE`

, if the farm can have neither chickens nor ducks.

# EXPLANATION:

Given that each chicken has X legs and each duck has Y legs, we are given the total number of legs as Z. Now there can be four cases here:

- For the farm to only have Chickens.

Z \;mod \; X = 0 \; and \; Z \;mod\; Y \neq 0

- For the farm to only have Ducks.

Z \;mod \; X \neq 0 \; and \; Z \;mod\; Y = 0

- For the farm to have Any.

Z \;mod \; X = 0 \; and \; Z \;mod\; Y = 0

- For the farm to have None.

Z \;mod \; X \neq 0 \; and \; Z \;mod\; Y \neq 0

# TIME COMPLEXITY:

O(1) for each test case.

# SOLUTION:

Editorialist’s Solution

Setter’s Solution

Tester-1’s Solution

Tester-2’s Solution