GCD vs LCM solution codeforces
You are given a positive integer nn. You have to find 44 positive integers a,b,c,da,b,c,d such that
- a+b+c+d=na+b+c+d=n, and
- gcd(a,b)=lcm(c,d)gcd(a,b)=lcm(c,d).
Input
The input consists of multiple test cases. The first line contains a single integer tt (1≤t≤1041≤t≤104) — the number of test cases. Description of the test cases follows. Each test case contains a single line with integer nn (4≤n≤1094≤n≤109) — the sum of aa, bb, cc, and dd.Output
For each test case output 44 positive integers aa, bb, cc, dd such that a+b+c+d=na+b+c+d=n and gcd(a,b)=lcm(c,d)gcd(a,b)=lcm(c,d).Example
input
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5 4 7 8 9 10
output
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1 1 1 1 2 2 2 1 2 2 2 2 2 4 2 1 3 5 1 1
Note
In the first test case gcd(1,1)=lcm(1,1)=1gcd(1,1)=lcm(1,1)=1, 1+1+1+1=41+1+1+1=4. In the second test case gcd(2,2)=lcm(2,1)=2gcd(2,2)=lcm(2,1)=2, 2+2+2+1=72+2+2+1=7. In the third test case gcd(2,2)=lcm(2,2)=2gcd(2,2)=lcm(2,2)=2, 2+2+2+2=82+2+2+2=8. In the fourth test case gcd(2,4)=lcm(2,1)=2gcd(2,4)=lcm(2,1)=2, 2+4+2+1=92+4+2+1=9. In the fifth test case gcd(3,5)=lcm(1,1)=1gcd(3,5)=lcm(1,1)=1, 3+5+1+1=103+5+1+1=10.-
ANSWER
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