Obtain Desired Standard Deviation
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Given two integers N and σ, find any array a with length N such that the standard deviation of the elements of the array is equal to σ. The standard deviation is given by the following formula:
For each 1 ≤ i ≤ N, ai may be any real number with |ai| ≤ 108.
If there is more than one possible answer, you may output any one of them. If there is no such array, output -1 instead.
Please note that the denominator only contains N. (In the usual formula for standard deviation, N-1 is used. That's not the definition we're using here.)
The first line of the input contains an integer T denoting the number of test cases. The description of the test cases follows.
The first and only line of each test case contains two space separated integers N, σ.
For each test case, output a single line containing N space-separated real numbers denoting the elements of the array a.
If it is not possible to construct such an array, output -1 instead. If there is more than one possible solution, you may output any one.
Your answer will be considered correct if the standard deviation of the printed array doesn't differ from σ by more than 10-2 in absolute value.
- 1 ≤ T ≤ 105
- 1 ≤ N ≤ 105
- 0 ≤ σ ≤ 105
- Sum of N over all test cases won't exceed 106
Input 3 2 2 3 3 4 0 Output 2 6 3.5 2 8.979967 3 3 3 3
|Tags||acmind17, ad-hoc, admin2, simple|
|Time Limit:||1 sec|
|Source Limit:||50000 Bytes|
|Languages:||C, CPP14, JAVA, PYTH, PYTH 3.6, PYPY|
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