New Start day 3 :2/10/2020 codechef october long CVDRUN

 question (source:https://www.codechef.com/OCT20B/problems/CVDRUN)

Covid Run

Covid-19$19$ is spreading fast! There are N$N$ cities, numbered from 0$0$ to (N−1)$(N-1)$, arranged in a circular manner. City 0$0$ is connected to city 1$1$, 1$1$ to 2$2$, …$\dots$, city (N−2)$(N-2)$ to city (N−1)$(N-1)$, and city (N−1)$(N-1)$ to city 0$0$.

The virus is currently at city X$X$. Each day, it jumps from its current city, to the city K$K$ to its right, i.e., from city X$X$ to the city (X+K)%N$(X+K)\mathrm{\%}N$. As the virus jumps, the cities in between don't get infected. Cities once infected stay infected. You live in city Y$Y$. Find if it will reach your city eventually. If it will, print YES, else print NO.

Input:

• The first line of the input consists of an integer T, the number of test cases.
• The first and only line of each test case contains four space-separated integers - N, K, X and Y, denoting the number of cities, the size of jumps, Covid's current city, and the city that you live in, respectively.

Output:

For each test case, in a new line, print YES if Covid shall reach your city after a finite number of days, else print NO.

Constraints

• 1≤T≤100$1\le T\le 100$
• 1≤N≤1000$1\le N\le 1000$
• 0≤X,Y≤N−1$0\le X,Y\le N-1$
• 0≤K≤1000$0\le K\le 1000$

Subtasks

• Subtask 1 - 100% - Original constraints

Sample Input:

2
6 2 5 3
12 3 4 2

Sample Output:

YES
NO

Explanation:

• In the first sample, Covid starts at city 5, then goes to city 1, and then from city 1 to city 3. Thus, it reaches the city that you live in.

• In the second sample, Covid starts at city 4, goes to city 7, then 10$\mathrm{,}$ 1, then 4$\mathrm{,}$ 7, 10, …$\dots$, and so on. It never reaches city 2.

MY LOGIC:

I was trying to use conditional approach to get the answer but I don't know the reason why it always gave wrong answer. I assumed value of k into 4 categories as shown below with the conditions.

but it didn't work ..waiting for the editorial to get clearance on that.

approach that worked: I used brute force using while loop. I updated current infected city by formula cur=(cur+k)%N where initial value of cur was x.I ran the loop until cur was equal to x or y. if by any chance it's value again came to x then answer would be no.If it equals y then answer would be x.

my code: