Dark Light Solution | CodeChef Problem Solution 2022

Dark Light Solution | CodeChef Problem Solution 2022

Tonmoy has a special torch. The torch has 4$4$ levels numbered 1$1$ to 4$4$ and 2$2$ states (𝙾𝚗$\mathtt{\text{On}}$ and 𝙾𝚏𝚏$\mathtt{\text{Off}}$). Levels 1,2,$1,2,$ and 3$3$ correspond to the 𝙾𝚗$\mathtt{\text{On}}$ state while level 4$4$ corresponds to the 𝙾𝚏𝚏$\mathtt{\text{Off}}$ state.

The levels of the torch can be changed as:

• Level 1$1$ changes to level 2$2$.
• Level 2$2$ changes to level 3$3$.
• Level 3$3$ changes to level 4$4$.
• Level 4$4$ changes to level 1$1$.

Given the initial state as K$K$ and the number of changes made in the levels as N$N$, find the final state of the torch. If the final state cannot be determined, print 𝙰𝚖𝚋𝚒𝚐𝚞𝚘𝚞𝚜$\mathtt{\text{Ambiguous}}$ instead.

Input Format

• First line will contain T$T$, the number of test cases. Then the test cases follow.
• Each test case contains of a single line of input, two integers N,K$N,K$ - the number of changes made in the levels and initial state of the torch. Here, K=0$K=0$ denotes 𝙾𝚏𝚏$\mathtt{\text{Off}}$ state while K=1$K=1$ denotes 𝙾𝚗$\mathtt{\text{On}}$ state.

Output Format

For each test case, output in a single line, the final state of the torch, i.e. 𝙾𝚗$\mathtt{\text{On}}$ or 𝙾𝚏𝚏$\mathtt{\text{Off}}$. If the final state cannot be determined, print 𝙰𝚖𝚋𝚒𝚐𝚞𝚘𝚞𝚜$\mathtt{\text{Ambiguous}}$ instead.

You may print each character of the string in uppercase or lowercase (for example, the strings 𝙾𝚗$\mathtt{\text{On}}$, 𝙾𝙽$\mathtt{\text{ON}}$, 𝚘𝚗$\mathtt{\text{on}}$ and 𝚘𝙽$\mathtt{\text{oN}}$ will all be treated as identical).

Constraints

• 1≤T≤105$1\le T\le {10}^5$
• 0≤N≤109$0\le N\le {10}^9$
• 0≤K≤1$0\le K\le 1$

Sample Input 1 

3
4 0
0 1
3 1

Sample Output 1 

Off
On
Ambiguous

Explanation

Test Case 1$1$: Initially, the torch is in 𝙾𝚏𝚏$\mathtt{\text{Off}}$ state. Since only level 4$4$ corresponds to the 𝙾𝚏𝚏$\mathtt{\text{Off}}$ state, the torch is at level 4$4$ initially. After 4$4$ changes, the final level would be 4$4$. Level 4$4$ corresponds to the 𝙾𝚏𝚏$\mathtt{\text{Off}}$ state. Hence, finally the torch is 𝙾𝚏𝚏$\mathtt{\text{Off}}$.

Test Case 2$2$: Initially, the torch is in 𝙾𝚗$\mathtt{\text{On}}$ state. After 0$0$ changes, the torch remains in the 𝙾𝚗$\mathtt{\text{On}}$ state.

Test Case 3$3$: Initially, the torch is in 𝙾𝚗$\mathtt{\text{On}}$ state. This can correspond to any of the first 3$3$ levels. Thus, we cannot determine the final level after 3$3$ changes. Hence, the final state is 𝙰𝚖𝚋𝚒𝚐𝚞𝚘𝚞𝚜$\mathtt{\text{Ambiguous}}$.