[Solution] Beautiful Array Codeforces Solution

B. Beautiful Array

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

Stanley defines the beauty of an array a$a$ of length n$n$, which contains non-negative integers, as follows:

∑i=1n⌊aik⌋,$$\sum _{i=1}^n\lfloor \frac{a_i}{k}\rfloor ,$$

which means that we divide each element by k$k$, round it down, and sum up the resulting values.

Stanley told Sam the integer k$k$ and asked him to find an array a$a$ of n$n$ non-negative integers, such that the beauty is equal to b$b$ and the sum of elements is equal to s$s$. Help Sam — find any of the arrays satisfying the conditions above.

Input

Each test contains multiple test cases. The first line contains the number of test cases t$t$ (1≤t≤1000$1\le t\le 1000$). Description of the test cases follows.

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The first line of each test case contains integers n$n$, k$k$, b$b$, s$s$ (1≤n≤105$1\le n\le {10}^5$, 1≤k≤109$1\le k\le {10}^9$, 0≤b≤109$0\le b\le {10}^9$, 0≤s≤1018$0\le s\le {10}^{18}$).

It is guaranteed that the sum of n$n$ over all test cases does not exceed 105${10}^5$.

Output

For each test case print −1$-1$ if such array a$a$ does not exist. Otherwise print n$n$ non-negative integers a1,a2,…,an$a_1,a_2,\dots ,a_n$ (0≤ai≤1018$0\le a_i\le {10}^{18}$) — the answer.