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C. Different Differences

time limit per test

2 secondsmemory limit per test

512 megabytesinput

standard inputoutput

standard outputAn array $$$a$$$ consisting of $$$k$$$ integers is strictly increasing if $$$a_1 < a_2 < \dots < a_k$$$. For example, the arrays $$$[1, 3, 5]$$$, $$$[1, 2, 3, 4]$$$, $$$[3, 5, 6]$$$ are strictly increasing; the arrays $$$[2, 2]$$$, $$$[3, 7, 5]$$$, $$$[7, 4, 3]$$$, $$$[1, 2, 2, 3]$$$ are not.

For a strictly increasing array $$$a$$$ of $$$k$$$ elements, let's denote the characteristic as the number of different elements in the array $$$[a_2 - a_1, a_3 - a_2, \dots, a_k - a_{k-1}]$$$. For example, the characteristic of the array $$$[1, 3, 4, 7, 8]$$$ is $$$3$$$ since the array $$$[2, 1, 3, 1]$$$ contains $$$3$$$ different elements: $$$2$$$, $$$1$$$ and $$$3$$$.

You are given two integers $$$k$$$ and $$$n$$$ ($$$k \le n$$$). Construct an increasing array of $$$k$$$ integers from $$$1$$$ to $$$n$$$ with maximum possible characteristic.

Input

The first line contains one integer $$$t$$$ ($$$1 \le t \le 819$$$) — the number of test cases.

Each test case consists of one line containing two integers $$$k$$$ and $$$n$$$ ($$$2 \le k \le n \le 40$$$).

Output

For each test case, print $$$k$$$ integers — the elements of the strictly increasing array $$$a$$$ with the maximum possible characteristic. If there are multiple answers, print any of them.

Example

Input

75 94 123 33 44 44 68 11

Output

1 3 4 7 8 2 4 7 12 1 2 3 1 3 4 1 2 3 4 2 4 5 6 1 2 3 5 6 7 8 11

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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