Java Hyd Team
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Forwarded from Aman Raj
Alice is still not satisfied with Bob's math skills so she gave him a new challenge.

Given a positive integer NN, find any 33 distinct positive integers A, B, CA,B,C such that:

The product of any two of these 33 integers is a divisor of NN.
The product of all three integers is a multiple of NN.
If multiple solutions exist, you may print any of them.
Print -1−1 if no solution exists.

Input Format
The first line of input will contain a single integer TT, denoting the number of test cases.
The first and only line of each test case contains a single integer, NN.
Output Format
For each test case, output on a new line three space-separated integers satisfying the given condition.
Print -1−1 if the answer does not exist.

Constraints
1 \leq T \leq 1001≤T≤100
1 \leq N \leq 10^91≤N≤10
9
Forwarded from Aman Raj
Rushitote went to a programming contest to distribute apples and oranges to the contestants.
He has NN apples and MM oranges, which need to be divided equally amongst the contestants. Find the maximum possible number of contestants such that:

Every contestant gets an equal number of apples; and
Every contestant gets an equal number of oranges.
Note that every fruit with Rushitote must be distributed, there cannot be any left over.

For example, 22 apples and 44 oranges can be distributed equally to two contestants, where each one receives 11 apple and 22 oranges.
However, 22 apples and 55 oranges can only be distributed equally to one contestant.

Input Format
The first line of input will contain a single integer TT, denoting the number of test cases.
The first and only line of each test case contains two space-separated integers NN and MM — the number of apples and oranges, respectively.
Output Format
For each test case, output on a new line the answer: the maximum number of contestants such that everyone receives an equal number of apples and an equal number of oranges.

Constraints
1 \leq T \leq 10001≤T≤1000
1 \leq N , M \leq 10^91≤N,M≤10
9
Forwarded from Aman Raj
Alice gave Bob 33 integers N, K,N,K, and SS. Help Bob find an SS-good sequence.

A sequence BB of length NN is called SS-good if the following conditions are met:

B_i \in \{-1, 0, 1\}B
i
​
∈{−1,0,1} for each 1 \leq i \leq N1≤i≤N
\sum_{i=1}^N B_i\cdot K^{i-1} = S∑
i=1
N
​
B
i
​
â‹…K
i−1
=S
If there are multiple SS-good sequences, print any of them.
If no SS-good sequence exists, print -2−2.

Input Format
The first line of input will contain a single integer TT, denoting the number of test cases.
Each test case consists of a single line of input containing three space-separated integers — N, K,N,K, and SS.
Output Format
For each test case:

If no SS-good sequence exists, print -2−2.
Otherwise, output NN space-separated integers denoting the SS-good sequence.
If multiple SS-good sequences exist, you may print any of them.

Constraints
1 \leq T \leq 10^41≤T≤10
4

1 \leq N \leq 1001≤N≤100
2 \leq K \leq 1002≤K≤100
1 \leq S \leq 10^{18}1≤S≤10
18
Forwarded from Aman Raj
Test case 11: We have B = [1,1,1,1]B=[1,1,1,1] and S = 15S=15
\sum_{i=1}^N B_i\cdot K^{i-1} = 1\cdot 1 + 2\cdot 1 + 4\cdot 1 + 8\cdot 1 = 15∑
i=1
N
​
B
i
​
â‹…K
i−1
=1â‹…1+2â‹…1+4â‹…1+8â‹…1=15, hence BB is an SS-good sequence.

Test case 22: We have B = [0, 0, 1]B=[0,0,1] and S = 36S=36. 6^2 = 366
2
=36 so clearly BB is SS-good.

Test case 33: No SS-good sequence of length 55 exists.
Forwarded from Aman Raj
Bob received an assignment from his school: he has two numbers AA and BB, and he has to find the sum of these two numbers.
Alice, being a good friend of Bob, told him that the answer to this question is CC.
Bob doesn't completely trust Alice and asked you to tell him if the answer given by Alice is correct or not.
If the answer is correct print "YES", otherwise print "NO" (without quotes).

Input Format
The first line of input will contain a single integer TT, denoting the number of test cases.
The first and only line of each test case consists of three space-separated integers A, B,A,B, and CC.
Output Format
For each test case, output on a new line the answer: YES if Alice gave the right answer, and NO otherwise.

Each character of the output may be printed in either uppercase or lowercase, i.e, the outputs Yes, YES, yEs and yes will be treated as equivalent.

Constraints
1 \leq T \leq 1001≤T≤100
0 \leq A , B , C \leq 1000≤A,B,C≤100
Forwarded from Aman Raj
Alice thinks Bob has very weak math skills.
Alice gave Bob three numbers A, B,A,B, and CC and challenged him to find any positive integer KK strictly less than 100100 such that none of the three numbers are divisible by KK.

Help Bob find one such integer KK.

Under the given constraints, a valid KK will always exist.

Input Format
The first line of input will contain a single integer TT, denoting the number of test cases.
The first and only line of each test case contains three space-separated integers A, B,A,B, and CC.
Output Format
For each test case, output on a new line any positive integer KK less than 100100 that does not divide any of A, B,A,B, or CC.

Constraints
1 \leq T \leq 10001≤T≤1000
2 \leq A , B , C \leq 1002≤A,B,C≤100